{
 "metadata": {
  "name": "MorePyMC"
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     "cell_type": "markdown",
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     "source": [
      "Chapter 2\n",
      "======\n",
      "______\n",
      "\n",
      "This chapter introduces more PyMC syntax and design patterns, and ways to think about how to model a system from a Bayesian perspective. It also contains tips and data visualization techniques for assessing goodness-of-fit for your Bayesian model."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## A little more on PyMC\n",
      "\n",
      "### Parent and Child relationships\n",
      "\n",
      "To assist with describing Bayesian relationships, and to be consistent with PyMC's documentation, we introduce *parent and child* variables. \n",
      "\n",
      "*  *parent variables* are variables that influence another variable. \n",
      "\n",
      "*  *child variable* are variables that are affected by other variables, i.e. are the subject of parent variables. \n",
      "\n",
      "A variable can be both a parent and child. For example, consider the PyMC code below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as mc\n",
      "\n",
      "parameter = mc.Exponential( \"poisson_param\", 1 )\n",
      "\n",
      "data_generator = mc.Poisson(\"data_generator\", parameter )\n",
      "\n",
      "data_plus_one = data_generator + 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "`parameter` controls the parameter of `data_generator`, hence influences its values. The former is a parent of the latter. By symmetry, `data_generator` is a child of `parameter`.\n",
      "\n",
      "Likewise, `data_generator` is a parent to the variable `data_plus_one` (hence making `data_generator` both a parent and child variable). Although it does not look like one, `data_plus_one` should be treated as a PyMC variable as it is a *function* of another PyMC variable, hence is a child variable to `data_generator`.\n",
      "\n",
      "This nomenclature is introduced to help us describe relationships in PyMC modeling. You can access a variables children and parent variables using the `children` and `parents` attributes attached to variables."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Children of `parameter`: \"\n",
      "print parameter.children\n",
      "print \"\\nParents of `data_generator`: \"\n",
      "print data_generator.parents\n",
      "print \"\\nChildren of `data_generator`: \"\n",
      "print  data_generator.children"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Children of `parameter`: \n",
        "set([<pymc.distributions.Poisson 'data_generator' at 0x0000000008DF5198>])"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "Parents of `data_generator`: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "{'mu': <pymc.distributions.Exponential 'poisson_param' at 0x0000000008DF57B8>}"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "Children of `data_generator`: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "set([<pymc.PyMCObjects.Deterministic '(data_generator_add_1)' at 0x0000000008DE3CC0>])"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Of course a child can  have more than one parent, and a parent can have many children."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### PyMC Variables\n",
      "\n",
      "All PyMC variables also expose a `value` attribute. This method produces the *current* (possibly random) internal value of the variable. If the variable is a child variable, its value changes given the variable's parents' values. Using the same variables from before:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"parameter.value =\",parameter.value\n",
      "print \"data_generator.value =\",data_generator.value\n",
      "print \"data_plus_one.value =\", data_plus_one.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "parameter.value = 2.13659208293\n",
        "data_generator.value ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 3\n",
        "data_plus_one.value ="
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 4\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "PyMC is concerned with two types of programming variables: `stochastic` and `deterministic`.\n",
      "\n",
      "*  *stochastic variables* are variables that are not deterministic, i.e., even if you knew all the values of the variables' parents (if it even has any parents), it would still be random. Included in this category are instances of classes `Poisson`, `DiscreteUniform`, and `Exponential`.\n",
      "\n",
      "*  *deterministic variables* are variables that are not random if the variables' parents were known. This might be confusing at first: a quick mental check is *if I knew all of variable `foo`'s parent variables, I could determine what `foo`'s value is.* \n",
      "\n",
      "We will detail each below.\n",
      "\n",
      "#### Initializing Stochastic variables\n",
      "\n",
      "Initializing a stochastic variable requires a `name` argument, plus additional parameters that are class specific. For example:\n",
      "\n",
      "`some_variable = mc.DiscreteUniform( \"discrete_uni_var\", 0, 4 )`\n",
      "\n",
      "where 0,4 are the `DiscreteUniform`-specific upper and lower bound on the random variable. The [PyMC docs](http://pymc-devs.github.com/pymc/distributions.html) contain the specific parameters for stochastic variables. (Or use `??` if you are using IPython!)\n",
      "\n",
      "The `name` attribute is used to retrieve the posterior distribution later in the analysis, so it is best to use a descriptive name. Typically, I use the Python variable's name as the name.\n",
      "\n",
      "For multivariable problems, rather than creating a Python array of stochastic variables, addressing the `size` keyword in the call to a `Stochastic` variable creates multivariate array of (independent) stochastic variables. The array behaves like a Numpy array when used like one, and references to its `value` attribute return Numpy arrays.  \n",
      "\n",
      "The `size` argument also solves the annoying case where you may have many variables $\\beta_i, \\; i = 1,...,N$ you wish to model. Instead of creating arbitrary names and variables for each one, like:\n",
      "\n",
      "    beta_1 = mc.Uniform( \"beta_1\", 0, 1)\n",
      "    beta_2 = mc.Uniform( \"beta_2\", 0, 1)\n",
      "    ...\n",
      "\n",
      "we can instead wrap them into a single variable:\n",
      "\n",
      "    betas = mc.Uniform( \"betas\", 0, 1, size = N )\n",
      "\n",
      "#### Calling `random()`\n",
      "We can also call on a stochastic variable's `random()` method, which (given the parent values) will generate a new, random value. Below we demonstrate this using the texting example from the previous chapter."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lambda_1 = mc.Exponential( \"lambda_1\",  1 ) #prior on first behaviour\n",
      "lambda_2 = mc.Exponential( \"lambda_2\", 1 ) #prior on second behaviour\n",
      "tau = mc.DiscreteUniform( \"tau\", lower = 0, upper = 10 ) #prior on behaviour change\n",
      "\n",
      "print \"lambda_1.value = %.3f\"%lambda_1.value\n",
      "print \"lambda_2.value = %.3f\"%lambda_2.value\n",
      "print \"tau.value = %.3f\"%tau.value\n",
      "print\n",
      "\n",
      "lambda_1.random(), lambda_2.random(), tau.random()\n",
      "\n",
      "print \"After calling random() on the variables...\"\n",
      "print \"lambda_1.value = %.3f\"%lambda_1.value\n",
      "print \"lambda_2.value = %.3f\"%lambda_2.value\n",
      "print \"tau.value = %.3f\"%tau.value\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "lambda_1.value = 0.450\n",
        "lambda_2.value = 0.807"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "tau.value = 6.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "After calling random() on the variables...\n",
        "lambda_1.value = 0.847"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "lambda_2.value = 3.247"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "tau.value = 3.000"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The call to `random` stores a new value into the variable's `value` attribute. In fact, this new value is stored in the computer's cache for faster recall and efficiency."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### **Warning**: *Don't update stochastic variables' values in-place.*\n",
      "\n",
      "\n",
      "Straight from the PyMC docs, we quote [4]:\n",
      "\n",
      "> `Stochastic` objects' values should not be updated in-place. This confuses PyMC's caching scheme... The only way a stochastic variable's value should be updated is using statements of the following form:\n",
      "\n",
      "        A.value = new_value\n",
      "\n",
      "> The following are in-place updates and should **never** be used:\n",
      "\n",
      "    \n",
      "        A.value += 3\n",
      "        A.value[2,1] = 5\n",
      "        A.value.attribute = new_attribute_value\n",
      "    "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### Deterministic variables\n",
      "\n",
      "Since most variables you will be modeling are stochastic, we distinguish deterministic variables with a `pymc.deterministic` wrapper. (If you are unfamiliar with Python wrappers (also called decorators), that's no problem. Just prepend the `pymc.deterministic` decorator before the variable declaration and you're good to go. No need to know more. ) The declaration of a deterministic variable uses a Python function:\n",
      "\n",
      "    @mc.deterministic\n",
      "    def some_deterministic_var(v1=v1,):\n",
      "         #jelly goes here.\n",
      "\n",
      "For all purposes, we can treat the object `some_deterministic_var` as a variable and not a Python function. \n",
      "\n",
      "Prepending with the wrapper is the easiest way, but not the only way, to create deterministic variables. This is not completely true: elementary operations, like addition, exponentials etc. implicitly create deterministic variables. For example, the following returns a deterministic variable:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "type( lambda_1 + lambda_2 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "pymc.PyMCObjects.Deterministic"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The use of the `deterministic` wrapper was seen in the previous chapter's text-message example.  Recall the model for $\\lambda$ looked like: \n",
      "\n",
      "$$\n",
      "\\lambda = \n",
      "\\cases{\n",
      "\\lambda_1  & \\text{if } t \\lt \\tau \\cr\n",
      "\\lambda_2 & \\text{if } t \\ge \\tau\n",
      "}\n",
      "$$\n",
      "\n",
      "And in PyMC code:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n_data_points = 5 # in CH1 we had ~70 data points\n",
      "\n",
      "@mc.deterministic\n",
      "def lambda_( tau = tau, lambda_1 = lambda_1, lambda_2 = lambda_2 ):\n",
      "    out = np.zeros(n_data_points)  \n",
      "    out[:tau] = lambda_1 #lambda before tau is lambda1\n",
      "    out[tau:] = lambda_2 #lambda after tau is lambda1\n",
      "    return out"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Clearly, if $\\tau, \\lambda_1$ and $\\lambda_2$ are known, then $\\lambda$ is known completely, hence it is a deterministic variable. \n",
      "\n",
      "Inside the deterministic decorator, the `Stochastic` variables passed in behave like scalars or Numpy arrays ( if multivariable), and *not* like `Stochastic` variables. For example, running the following:\n",
      "\n",
      "    @mc.deterministic\n",
      "    def some_deterministic( stoch = some_stochastic_var ):\n",
      "        return stoch.value**2\n",
      "\n",
      "\n",
      "will return an `AttributeError` detailing that `stoch` does not have a `value` attribute. It simply needs to be `stoch**2`. During the learning phase, it the variables `value` that is repeatedly passed in, not the actual variable.  \n",
      "\n",
      "Notice in the creation of the deterministic function we added defaults to each variable used in the function. This is a necessary step, and all variables *must* have default values. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Including observations in the Model\n",
      "\n",
      "At this point, it may not look like it, but we have fully specified our priors. For example, we can ask and answer questions like \"What does my prior distribution of $\\lambda_1$ look like?\" "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%pylab inline\n",
      "figsize(12.5, 4)\n",
      "\n",
      "samples = [ lambda_1.random() for i in range( 20000) ]\n",
      "hist( samples, bins = 70, normed=True )\n",
      "plt.title( \"Prior distribution for $\\lambda_1$\")\n",
      "plt.xlim( 0, 8);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "(0, 8)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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3h1rw4osvyuv1atGiRZKkJUuWqKSkRPPnzz9m7dq1azV9+nRt2LBBJ598ctB7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\nAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To frame this in the notation of the first chapter, though this is a slight abuse of notation, we have specified $P(A)$. Our next goal is to include data/evidence/observations $X$ into our model. \n",
      "\n",
      "PyMC stochastic variables have a keyword argument `observed` which accepts a boolean (`False` by default). The keyword `observed` has a very simple role: fix the variable's current value, i.e. make `value` immutable. We have to specify an initial `value` in the variable's creation, equal to the observations we wish to include, typically an array (and it should be an Numpy array for speed). For example:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = np.array( [10, 5] )\n",
      "fixed_variable = mc.Poisson( \"fxd\", 1, value = data, observed = True )\n",
      "print \"value: \",fixed_variable.value\n",
      "print \"calling .random()\"\n",
      "fixed_variable.random()\n",
      "print \"value: \",fixed_variable.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "value:  [10  5]\n",
        "calling .random()"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "value: "
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " [10  5]\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is how we include data into our models: initializing a stochastic variable to have a *fixed value*. \n",
      "\n",
      "To complete our text message example, we fix the PyMC variable `observations` to the observed dataset. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#we're using some fake data here\n",
      "data = np.array( [ 10, 25, 15, 20, 35] )\n",
      "obs = mc.Poisson( \"obs\", lambda_, value = data, observed = True )\n",
      "print obs.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[10 25 15 20 35]\n"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Finally...\n",
      "\n",
      "We wrap all the created variables into a `mc.Model` class. With this `Model` class, we can analyze the variables as a single unit."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = mc.Model( [obs, lambda_, lambda_1, lambda_2, tau] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Modeling approaches\n",
      "\n",
      "A good starting thought to Bayesian modeling is to think about *how your data might have been generated*. Position yourself in an omniscient position, and try to imagine how *you* would recreate the dataset. \n",
      "\n",
      "In the last chapter we investigated text message data. We begin by asking how our observations may have been generated:\n",
      "\n",
      "1.  We started by thinking \"what is the best random variable to describe this count data?\" A Poisson random variable is a good candidate because it can represent count data. So we model the number of sms's received as sampled from a Poisson distribution.\n",
      "\n",
      "2.  Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameters $\\lambda$. \n",
      "\n",
      "3.  Do we know $\\lambda$? No. In fact, we have a suspicion that there are *two* $\\lambda$ values, one for the earlier behaviour and one for the latter behaviour. We don't know when the behaviour switches though, but call the switchpoint $\\tau$.\n",
      "\n",
      "4. What is a good distribution for the two $\\lambda$s? The exponential is good, as it assigns probabilities to positive real numbers. Well the exponential distribution has a parameter too, call it $\\alpha$.\n",
      "\n",
      "5.  Do we know what the parameter $\\alpha$ might be? No. At this point, we could continue and assign a distribution to $\\alpha$, but it's better to stop once we reach a set level of ignorance: whereas we have a prior belief about $\\lambda$, (\"it probably changes over time\", \"it's likely between 10 and 30\", etc.), we don't really have any strong beliefs about $\\alpha$. So it's best to stop here. \n",
      "\n",
      "    What is a good value for $\\alpha$ then? We think that the $\\lambda$s are between 10-30, so if we set $\\alpha$ really low (which corresponds to larger probability on high values) we are not reflecting our prior well. Similar, a too-high alpha misses our prior belief as well. A good idea for $\\alpha$ as to reflect our belief is to set the value so that the mean of $\\lambda$, given $\\alpha$, is equal to our observed mean. This was shown in the last chapter.\n",
      "\n",
      "6. We have no expert opinion of when $\\tau$ might have occurred. So we will suppose $\\tau$ is from a discrete uniform distribution over the entire timespan.\n",
      "\n",
      "\n",
      "Below we give a graphical visualization of this, where arrows denote `parent-child` relationships. (provided by the [Daft Python library](http://daft-pgm.org/) )\n",
      "\n",
      "<img src=\"http://i.imgur.com/7J30oCG.png\" width = 700/>\n",
      "\n",
      "\n",
      "PyMC, and other probabilistic programming languages, have been designed to tell these data-generation *stories*. More generally, B. Cronin writes [5]:\n",
      "\n",
      "> Probabilistic programming will unlock narrative explanations of data, one of the holy grails of business analytics and the unsung hero of scientific persuasion. People think in terms of stories - thus the unreasonable power of the anecdote to drive decision-making, well-founded or not. But existing analytics largely fails to provide this kind of story; instead, numbers seemingly appear out of thin air, with little of the causal context that humans prefer when weighing their options."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Same story; different ending.\n",
      "\n",
      "Interestingly, we can create *new datasets* by retelling the story.\n",
      "For example, if we reverse the above steps, we can simulate a possible realization of the dataset.\n",
      "\n",
      "1\\. Specify when the user's behaviour switches by sampling from $\\text{DiscreteUniform}(0, 80)$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tau = mc.rdiscrete_uniform(0, 80)\n",
      "print tau"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "63\n"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2\\. Draw $\\lambda_1$ and $\\lambda_2$ from an $\\text{Exp}(\\alpha)$ distribution:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha = 1./20.\n",
      "lambda_1, lambda_2 = mc.rexponential( alpha, 2 )\n",
      "print lambda_1, lambda_2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "16.7630558157 33.1568046968\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3\\.  For days before $\\tau$, represent the user's received SMS count by sampling from $\\text{Poi}(\\lambda_1)$, and sample from  $\\text{Poi}(\\lambda_2)$ for days after $\\tau$. For example:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = np.r_[ mc.rpoisson( lambda_1, tau ), mc.rpoisson( lambda_2,80 - tau) ]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "4\\. Plot the artificial dataset:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.bar( np.arange( 80 ), data, color =\"#348ABD\"  )\n",
      "plt.bar( tau-1, data[tau-1], color = \"r\", label = \"user behaviour changed\" )\n",
      "plt.xlabel( \"Time (days)\")\n",
      "plt.ylabel(\"count of text-msgs received\")\n",
      "plt.title(\"Artifical dataset\")\n",
      "plt.xlim( 0, 80 );\n",
      "plt.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "<matplotlib.legend.Legend at 0x12f67710>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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WiI2Nxbhx49C0aVNs3boVK1euxLp16+Dl5YWlS5fCwsIiz7oTJkxAvXr1AADm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\n"
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It is okay that our fictional dataset does not look like our observed dataset: the probability is incredibly small it indeed would. PyMC's engine is designed to find good parameters, $\\lambda_i, \\tau$, that maximize this probability.  \n",
      "\n",
      "\n",
      "The ability to generate artifical dataset is an interesting side effect of our modeling, and we will see that this ability is a very important method of Bayesian inference. We produce a few more datasets below:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_artificial_sms_dataset():\n",
      "    tau = mc.rdiscrete_uniform(0, 80)\n",
      "    alpha = 1./20.\n",
      "    lambda_1, lambda_2 = mc.rexponential( alpha, 2 )\n",
      "    data = np.r_[ mc.rpoisson( lambda_1, tau ), mc.rpoisson( lambda_2,80- tau) ]\n",
      "    plt.bar( np.arange( 80 ), data, color =\"#348ABD\"  )\n",
      "    plt.bar( tau-1, data[tau-1], color = \"r\", label = \"user behaviour changed\" )\n",
      "    plt.xlim( 0, 80 );\n",
      "\n",
      "figsize( 12.5,5)\n",
      "plt.title(\"More example of artificial datasets\" )\n",
      "for i in range(4):\n",
      "    plt.subplot(4,1,i)\n",
      "    plot_artificial_sms_dataset()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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n4v1eOhrkGV49kIfZysPx9/Kw3crFfNVx5YIDs9UX1R3xzZs3IzY2FlarFQBn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\nwZtvvomqqircuHEDx48fR2Njo8xNEBEREREFBKkD8fr6eqx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      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Later we will see how we use this to make predictions and test the appropriateness of our models."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## An algorithm for human deceit\n",
      "\n",
      "Likely the most common statistical task is estimating the frequency of events. However, there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is 0.166. Knowing the frequency of events like baseball home runs, frequency of social attributes, fraction of internet users with cats etc. are common requests we ask of Nature. Unfortunately, in general Nature hides the true frequency from us and we must *infer* it from observed data.\n",
      "\n",
      "The *observed frequency* is then the frequency we observe: say rolling the die 100 times you may observe 20 rolls of 1. The observed frequency, 0.2, differs from the true frequency, 0.166. We can use Bayesian statistics to infer probable values of the true frequency using an appropriate prior and observed data.\n",
      "\n",
      "Social data is really interesting as people are not always honest with responses, which adds a further complication into inference. For example, simply asking individuals \"Have you ever cheated on a test?\" will surely contain some rate of dishonesty. What you can say for certain is that the true rate is less than your observed rate (assuming individuals lie *only* about *not cheating*; I cannot imagine one who would admit \"Yes\" to cheating when in fact they hadn't cheated). \n",
      "\n",
      "To present an elegant solution to circumventing this dishonesty problem, and to demonstrate Bayesian modeling, we first need to introduce the binomial distribution.\n",
      "\n",
      "### The Binomial Distribution\n",
      "\n",
      "The binomial distribution is one of the most popular distributions, mostly because of its simplicity and usefulness. Unlike the other distributions we have encountered thus far in the book, the binomial distribution has 2 parameters: $N$, a positive integer representing $N$ trials or number of instances of potential events, and $p$, the probability of an event occurring in a single trial. Like the Poisson distribution, it is a discrete distribution, but unlike the Poisson distribution, it only weighs integers from $0$ to $N$. The mass distribution looks like:\n",
      "\n",
      "$$P( X = k ) =  {{N}\\choose{k}}  p^k(1-p)^{N-k}$$\n",
      "\n",
      "If $X$ is a binomial random variable with parameters $p$ and $N$, denoted $X \\sim \\text{Bin}(N,p)$, then $X$ is the number of events that occured in the $N$ trials (obviously $0 \\le X \\le N$). The larger $p$ is (while still remaining between 0 and 1), the more events are likely to occur. The expected value of a binomial is equal to $Np$. Below we plot the mass probability distribution for varying parameters. \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12.5, 4) \n",
      "\n",
      "import scipy.stats as stats\n",
      "binomial = stats.binom\n",
      "\n",
      "parameters = [ (10, .4) , (10, .9) ]  \n",
      "colors = [\"#348ABD\", \"#A60628\"]\n",
      "\n",
      "for i in range(2):\n",
      "    N, p = parameters[i]\n",
      "    _x = np.arange( N+1 )\n",
      "    plt.bar( _x - 0.5,  binomial.pmf( _x, N, p ), color = colors[i], \n",
      "             edgecolor=colors[i],\n",
      "             alpha = 0.6, \n",
      "             label = \"$N$: %d, $p$: %.1f\"%(N,p), \n",
      "             linewidth=3)\n",
      "    \n",
      "plt.legend(loc=\"upper left\")\n",
      "plt.xlim(0, 10.5)\n",
      "plt.xlabel(\"$k$\")\n",
      "plt.ylabel(\"$P(X = k)$\")\n",
      "plt.title(\"Probability mass distributions of binomial random variables\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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phJeXl3pZjx49/vLI/Zw5c+qsU0OPWVxcjCVLluCdd975S3XSJPc8OTI+xgRJ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\n"
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The special case when $N = 1$ corresponds to the Bernoulli distribution. If  $ X\\ \\sim \\text{Ber}(p)$, then $X$ is 1 with probability $p$ and 0 with probability $1-p$.\n",
      "The Bernoulli distribution is useful for indicators, e.g. $Y = X\\alpha + (1-X)\\beta$ is $\\alpha$ with probability $p$ and $\\beta$ with probability $1-p$. \n",
      "\n",
      "There is another connection between Bernoulli and Binomial random variables. If we have $X_1, X_2, ... , X_N$ Bernoulli random variables with the same $p$, then $Z = X_1 + X_2 + ... + X_N \\sim \\text{Binomial}(N, p )$.\n",
      "\n",
      "The expected value of a Bernoulli random variable is $p$. This can be seen by noting the more general Binomial random variable has expected value $Np$ and setting $N=1$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Example: Cheating among students\n",
      "\n",
      "We will use the binomial distribution to determine the frequency of students cheating during an exam. If we let $N$ be the total number of students who took the exam, and assuming each student is interviewed post-exam (answering without consequence), we will receive integer $X$ \"Yes I did cheat\" answers. We then find the posterior distribution of $p$, given $N$, some specified prior on $p$, and observed data $X$. \n",
      "\n",
      "This is a completely absurd model. No student, even with a free-pass against punishment, would admit to cheating. What we need is a better *algorithm* to ask students if they had cheated. Ideally the algorithm should encourage individuals to be honest while preserving privacy. The following proposed algorithm is a solution I greatly admire for its ingenuity and effectiveness:\n",
      "\n",
      "> In the interview process for each student, the student flips a coin, hidden from the interviewer. The student agrees to answer honestly if the coin comes up heads. Otherwise, if the coin comes up tails, the student (secretly) flips the coin again, and answers \"Yes, I did cheat\" if the coin flip lands heads, and \"No, I did not cheat\", if the coin flip lands tails. This way, the interviewer does not know if a \"Yes\" was the result of a guilty plea, or a Heads on a second coin toss. Thus privacy is preserved and the researchers receive honest answers. \n",
      "\n",
      "I call this the Privacy Algorithm. One could of course argue that the interviewers are still receiving false data since some \"Yes\"'s are not confessions but instead randomness, but an alternative perspective is that the researchers are discarding approximately half of their original dataset since half of the responses will be noise. But they have gained a systematic data generation process that can be modeled. Furthermore, they do not have to incorporate (perhaps somewhat naively) the possibility of deceitful answers. We can use PyMC to dig through this noisy model, and find a posterior distribution for the true frequency of liars. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Suppose 100 students are being surveyed for cheating, and we wish to find $p$, the proportion of cheaters. There a few ways we can model this in PyMC. I'll demonstrate the most explicit way, and later show a simplified version. Both versions arrive at the same inference. In our data-generation model, we sample $p$, the true proportion of cheaters, from a prior. Since we are quite ignorant about $p$, we will assign it a $\\text{Uniform}(0,1)$ prior."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as mc\n",
      "\n",
      "N = 100\n",
      "\n",
      "p = mc.Uniform( \"freq_cheating\", 0, 1) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, thinking of our data-generation model, we assign Bernoulli random variables to the 100 students: 1 implies they cheated and 0 implies they did not. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "true_answers = mc.Bernoulli( \"truths\", p, size = N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "If we carry out the algorithm, the next step that occurs is the first coin-flip each student makes. This can be modeled again by sampling 100 Bernoulli random variables with $p=1/2$: denote a 1 as a *Heads* and 0 a *Tails*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "first_coin_flips = mc.Bernoulli( \"first_flips\", 0.5, size = N)\n",
      "print first_coin_flips.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[False  True  True False  True  True False  True  True  True  True  True\n",
        " False  True  True  True False  True False  True  True False False  True\n",
        "  True False  True False  True False False False False False  True False\n",
        "  True False  True False False  True  True False  True False False False\n",
        " False False  True False False  True  True  True  True  True False False\n",
        " False  True  True False  True False  True False  True  True  True  True\n",
        " False  True False  True False  True  True False  True  True  True False\n",
        " False  True  True False False  True  True  True False False False  True\n",
        "  True  True False False]\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Although *not everyone* flips a second time, we can still model the possible realization of second coin-flips:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "second_coin_flips = mc.Bernoulli(\"second_flips\", 0.5, size = N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using these variables, we can return a possible realization of the *observed proportion* of \"Yes\" responses. We do this using a PyMC `deterministic` variable:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@mc.deterministic\n",
      "def observed_proportion( t_a = true_answers, \n",
      "                         fc = first_coin_flips,\n",
      "                         sc = second_coin_flips ):\n",
      "    \n",
      "    observed = fc*t_a + (1-fc)*sc \n",
      "    return observed.sum()/float(N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The line `fc*t_a + (1-fc)*sc` contains the heart of the Privacy algorithm. Elements in this array are 1 *if and only if* i) the first toss is heads and the student cheated or ii) the first toss is tails, and the second is heads, and are 0 else. Summing this vector and dividing by `float(N)` produces a proportion. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "observed_proportion.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "0.32000000000000001"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we need a dataset. After performing our coin-flipped interviews the researchers received 35 \"Yes\" responses. To put this into a relative perspective, if there truly were no cheaters, we should expect to see on average 1/4 of all responses being a \"Yes\" (half chance of having first coin land Tails, and another half chance of having second coin land Heads), so about 25 responses in a cheat-free world. On the other hand, if *all students cheated*, we should expected to see on approximately 3/4 of all response be \"Yes\". \n",
      "\n",
      "The researchers observe a Binomial random variable, with `N = 100` and `p = observed_proportion` with `value = 35`:  "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "X = 35\n",
      "\n",
      "observations = mc.Binomial(\"obs\", N, observed_proportion, observed = True, value = X)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = mc.Model( [p, true_answers, first_coin_flips, \n",
      "                   second_coin_flips, observed_proportion, observations] )\n",
      "\n",
      "### To be explained in Chapter 3!\n",
      "mcmc = mc.MCMC( model )\n",
      "mcmc.sample( 150000, 120000,4 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  150000 of 150000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 3 )\n",
      "from scipy.stats.mstats import mquantiles\n",
      "\n",
      "p_trace = mcmc.trace(\"freq_cheating\")[:]\n",
      "quantiles =mquantiles( p_trace, prob=[0.05, 0.95] )\n",
      "\n",
      "plt.title(\"Posterior distribution of frequency of cheaters\")\n",
      "plt.hist( p_trace, histtype=\"stepfilled\" , normed = True, \n",
      "    alpha = 0.85, bins = 30, label = \"posterior distribution\",\n",
      "    color = \"#348ABD\")\n",
      "plt.vlines( quantiles, [0,0], [5,5], linestyles = \"--\" )\n",
      "plt.xlim(0,1)\n",
      "plt.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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iolBSUmKaX7s658Xej0Wv8BhiqXvcgsTERERFRdkrHpsMGzYMycnJSEhIMEsW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\nm4iIiIjIjv4ff4RvwocEZQ4AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "With regards to the above plot, we are still pretty uncertain about what the true frequency of cheaters might be, but we have narrowed the true frequency down to a range between 0.05 to 0.45 (marked by the dashed lines). This is pretty good, as *a priori* we had no idea how many students might have cheated (hence the uniform distribution for our prior). On the other hand, it is also pretty bad since there is a .4 length window the true value most likely lives in. Have we even gained anything, or are we still too uncertain about the true frequency? \n",
      "\n",
      "I would argue, yes, we have discovered something. It is implausible, according to our posterior, that there are *no cheaters*, i.e. the posterior assigns low probability to $p=0$. Since we started with an uniform prior, treating all values of $p$ as equally plausible, but the data ruled out $p=0$ as a possibility, we can be confident that there were cheaters. \n",
      "\n",
      "This kind of algorithm can be used to gather private information from users and be *reasonably* confident that the data, though noisy, is truthful. \n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Alternative PyMC Model\n",
      "\n",
      "Given a value for $p$ (which from our god-like position we know), we can find the probability the student will answer yes: \n",
      "\n",
      "\\begin{align}\n",
      "P(\\text{\"Yes\"}) = & P( \\text{Heads on first coin} )P( \\text{cheater} ) + P( \\text{Tails on first coin} )P( \\text{Heads on second coin} ) \\\\\\\\\n",
      "& = \\frac{1}{2}p + \\frac{1}{2}\\frac{1}{2}\\\\\\\\\n",
      "& = \\frac{p}{2} + \\frac{1}{4}\n",
      "\\end{align}\n",
      "\n",
      "Thus, knowing $p$ we know the probability a student will respond \"Yes\". In PyMC, we can create a deterministic function to evaluate the probability of responding \"Yes\", given $p$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p = mc.Uniform( \"freq_cheating\", 0, 1) \n",
      "\n",
      "@mc.deterministic\n",
      "def p_skewed( p =  p ):\n",
      "    return 0.5*p + 0.25"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I could have typed `p_skewed  = 0.5*p + 0.25` instead for a one-liner, as the elementary operations of addition and scalar multiplication will implicitly create a `deterministic` variable, but I wanted to make the deterministic boilerplate explicit for clarity's sake. \n",
      "\n",
      "If we know the probability of respondents saying \"Yes\", which is `p_skewed`, and we have $N=100$ students, the number of \"Yes\" responses is a binomial random variable with parameters `N` and `p_skewed`.\n",
      "\n",
      "This is were we include our observed 35 \"Yes\" responses. In the declaration of the `mc.Binomial`, we include `value = 35` and `observed = True`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "yes_responses = mc.Binomial( \"number_cheaters\", 100, p_skewed, \n",
      "                                value = 35, observed = True )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = mc.Model( [yes_responses, p_skewed, p ] )\n",
      "\n",
      "### To Be Explained in Chapter 3!\n",
      "mcmc = mc.MCMC(model)\n",
      "mcmc.sample( 12500, 2500 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  12500 of 12500 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 3 )\n",
      "p_trace = mcmc.trace(\"freq_cheating\")[:]\n",
      "quantiles =mquantiles( p_trace, prob=[0.05, 0.95] )\n",
      "\n",
      "plt.title(\"Posterior distribution of frequency of cheaters\")\n",
      "plt.hist( p_trace, histtype=\"stepfilled\" , normed = True, \n",
      "    alpha = 0.85, bins = 30, label = \"posterior distribution\",\n",
      "    color = \"#348ABD\")\n",
      "plt.vlines( quantiles, [0,0], [5,5], linestyles = \"--\" )\n",
      "plt.xlim(0,1)\n",
      "plt.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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8+PGYOHEiwsLCMGDAAKxbtw4bN27EwoULERkZidLSUkREROCVV16xiKO62AAg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\n2EREREREdvT/AP1/1OX6owobAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### More PyMC Tricks\n",
      "\n",
      "#### Protip: *Lighter* deterministic variables with `Lambda` class\n",
      "\n",
      "Sometimes writing a deterministic function using the `@mc.deterministic` decorator can seem like a chore, especially for a small function. I have already mentioned that elementary math operations *can* produce deterministic variables implicitly, but what about operations like indexing or slicing? Built-in `Lambda` functions can handle this with the elegance and simplicity required. For example,  \n",
      "\n",
      "    beta = mc.Normal( \"coefficients\", 0, size=(N,1) )\n",
      "    x = np.random.randn( (N,1) )\n",
      "    linear_combination = mc.Lambda( lambda x=x, beta = beta: np.dot( x.T, beta ) )\n",
      "\n",
      "\n",
      "#### Protip: Arrays of PyMC variables\n",
      "There is no reason why we cannot store multiple heterogeneous PyMC variables in a Numpy array. Just remember to set the `dtype` of the array to `object` upon initialization. For example:\n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "N = 10\n",
      "x = np.empty( N , dtype=object )\n",
      "for i in range(0, N):\n",
      "        x[i] = mc.Exponential('x_%i' % i, (i+1)**2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The remainder of this chapter examines some practical examples of PyMC and PyMC modeling:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "#####Example: Challenger Space Shuttle Disaster <span id=\"challenger\"/>\n",
      "\n",
      "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1]):\n",
      "\n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12.5, 3.5 )\n",
      "np.set_printoptions(precision=3, suppress= True)\n",
      "challenger_data = np.genfromtxt(\"data/challenger_data.csv\", skip_header = 1, \\\n",
      "                               usecols=[1,2], missing_values=\"NA\", delimiter=\",\")\n",
      "#drop the NA values\n",
      "challenger_data = challenger_data[ ~np.isnan(challenger_data[:,1]) ]\n",
      "\n",
      "#plot it, as a function of tempature (the first column)\n",
      "print \"Temp (F), O-Ring failure?\"\n",
      "print challenger_data\n",
      "\n",
      "plt.scatter( challenger_data[:,0], challenger_data[:,1], s = 75, color=\"k\", \n",
      " alpha = 0.5) \n",
      "plt.yticks([0,1])\n",
      "plt.ylabel(\"Damage Incident?\")\n",
      "plt.xlabel(\"Outside temperature (Fahrenheit)\" )\n",
      "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\");\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Temp (F), O-Ring failure?\n",
        "[[ 66.   0.]\n",
        " [ 70.   1.]\n",
        " [ 69.   0.]\n",
        " [ 68.   0.]\n",
        " [ 67.   0.]\n",
        " [ 72.   0.]\n",
        " [ 73.   0.]\n",
        " [ 70.   0.]\n",
        " [ 57.   1.]\n",
        " [ 63.   1.]\n",
        " [ 70.   1.]\n",
        " [ 78.   0.]\n",
        " [ 67.   0.]\n",
        " [ 53.   1.]\n",
        " [ 67.   0.]\n",
        " [ 75.   0.]\n",
        " [ 70.   0.]\n",
        " [ 81.   0.]\n",
        " [ 76.   0.]\n",
        " [ 79.   0.]\n",
        " [ 75.   1.]\n",
        " [ 76.   0.]\n",
        " [ 58.   1.]]"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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XxfrX5dseHh6QJKnS/JaUlMgmXt427+2yk4fLinIXFxed21ZWVrhx44Zs4q3L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\nCCGE+JG/AUV2/ATzTJjPAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "It looks clear that *the probability* of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature $t$, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n",
      "\n",
      "We need a function of temperature, call it $p(t)$, that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function.*\n",
      "\n",
      "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t } } $$\n",
      "\n",
      "In this model, $\\beta$ is the variable we are uncertain about. Below is the function plotted for $\\beta = 1, 3, -5$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12,3)\n",
      "\n",
      "def logistic( x, beta):\n",
      "    return 1.0/( 1.0 + np.exp( beta*x) )\n",
      "\n",
      "x = np.linspace( -4, 4, 100 )\n",
      "plt.plot(x, logistic( x, 1), label = r\"$\\beta = 1$\")\n",
      "plt.plot(x, logistic( x, 3), label = r\"$\\beta = 3$\")\n",
      "plt.plot(x, logistic( x, -5), label = r\"$\\beta = -5$\")\n",
      "plt.legend();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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GxvjTZrGxptDId3l1bC9rYlVBA6sKGgjw0DIpMZApycEMCTp+Udgf8mkIDWLM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\nSBEshBBCCCEuOVIECyGEEEKIS87/Bw+kv7B3kPZFAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "But something is missing. In the plot of the logistic function, the probability changes only near zero, but in our data above the probability changes around 65 to 70. We need to add a *bias* term to our logistic function:\n",
      "\n",
      "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n",
      "\n",
      "Some plots are below, with differing $\\alpha$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def logistic( x, beta, alpha=0):\n",
      "    return 1.0/( 1.0 + np.exp( np.dot(beta, x) + alpha) )\n",
      "\n",
      "x = np.linspace( -4, 4, 100 )\n",
      "\n",
      "plt.plot(x, logistic( x, 1), label = r\"$\\beta = 1$\", ls= \"--\", lw =1 )\n",
      "plt.plot(x, logistic( x, 3), label = r\"$\\beta = 3$\", ls= \"--\", lw =1)\n",
      "plt.plot(x, logistic( x, -5), label = r\"$\\beta = -5$\", ls= \"--\", lw =1)\n",
      "\n",
      "\n",
      "plt.plot(x, logistic( x, 1,1), label = r\"$\\beta = 1, \\alpha = 1$\", \n",
      "    color = \"#348ABD\")\n",
      "plt.plot(x, logistic( x, 3, -2), label = r\"$\\beta = 3, \\alpha = -2$\", \n",
      "    color=\"#A60628\")\n",
      "plt.plot(x, logistic( x, -5, 7), label = r\"$\\beta = -5, \\alpha = 7$\",\n",
      "    color = \"#7A68A6\")\n",
      "\n",
      "plt.legend(loc = \"lower left\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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IrTaxraierUUNFNW1tD2mUsgYH+PP9IRAJg8SiVx31Bqt7DzeepHiqemcH5sR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      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Adding a constant term $\\alpha$ amounts to shifting the curve left or right (hence why it is called a *bias*. )\n",
      "\n",
      "Let's start modeling this in PyMC. The $\\beta, \\alpha$ paramters have no reason to be positive, bounded or relatively large, so they are best modeled by a *Normal random variable*, introduced next."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Normal distributions\n",
      "\n",
      "A Normal random variable, denoted $X \\sim N(\\mu, 1/\\tau)$, has a distribution with two parameters: the mean, $\\mu$, and the *precision*, $\\tau$. Those familar with the Normal distribution already have probably seen $\\sigma^2$ instead of $\\tau$. They are in fact reciprocals of each other. The change was motivated by simpler mathematical analysis and is an artifact of older Bayesian methods. Just remember: The smaller $\\tau$, the larger the spread of the distribution (i.e. we are more uncertain); the larger $\\tau$, the tighter the distribution (i.e. we are more certain). Regardless, $\\tau$ is always positive. \n",
      "\n",
      "The probability density function of a $N( \\mu, 1/\\tau)$ random variable is:\n",
      "\n",
      "$$ f(x | \\mu, \\tau) = \\sqrt{\\frac{\\tau}{2\\pi}} \\exp\\left( -\\frac{\\tau}{2} (x-\\mu)^2 \\right) $$\n",
      "\n",
      "We plot some different density functions below. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.stats as stats\n",
      "\n",
      "nor = stats.norm\n",
      "x = np.linspace( -8, 7, 150 )\n",
      "mu = (-2, 0, 3)\n",
      "tau = (.7, 1, 2.8 )\n",
      "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n",
      "parameters = zip( mu, tau, colors )\n",
      "\n",
      "for _mu, _tau, _color in parameters:\n",
      "    plt.plot( x, nor.pdf( x, _mu , scale = 1./_tau ), \\\n",
      "        label =\"$\\mu = %d,\\;\\\\tau = %.1f$\"%(_mu, _tau), color = _color )\n",
      "    plt.fill_between( x, nor.pdf( x, _mu, scale =1./_tau ), color = _color, \\\n",
      "         alpha = .33)\n",
      "\n",
      "plt.legend(loc = \"upper right\")\n",
      "plt.xlabel(\"$x$\")\n",
      "plt.ylabel(\"density function at $x$\")\n",
      "plt.title(\"Probability distribution of three different Normal random variables\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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KiYnB9u3bAQAtW7aEi4sL7t69q7F4rl+/jo4dO/LLXbp0wdWrV6ttp6enh7Fj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\nJAWJTK4lSZIkSZIkKUj+P8qJ0t2XezF5AAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A Normal random variable can be take on any real number, but the variable is very likely to be relatively close to $\\mu$. In fact, the expected value of a Normal is equal to its $\\mu$ parameter:\n",
      "\n",
      "$$ E[ X | \\mu, \\tau] = \\mu$$\n",
      "\n",
      "and its variance is equal to the inverse of $\\tau$:\n",
      "\n",
      "$$Var( X | \\mu, \\tau ) = \\frac{1}{\\tau}$$\n",
      "\n",
      "\n",
      "\n",
      "Below we continue our modeling of the Challenger space craft:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as mc\n",
      "\n",
      "temperature = challenger_data[:,0]\n",
      "D = challenger_data[:,1] #defect or not?\n",
      "\n",
      "#notice the`value` here. We explain why below. \n",
      "beta = mc.Normal( \"beta\", 0, 0.001, value = 0 ) \n",
      "alpha = mc.Normal( \"alpha\", 0, 0.001, value = 0 )\n",
      "\n",
      "@mc.deterministic\n",
      "def p( t = temperature, alpha = alpha, beta = beta):\n",
      "    return 1.0/( 1. + np.exp( beta*t + alpha) ) \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have our probabilities, but how do we connect them to our observed data? A *Bernoulli* random variable with parameter $p$, denoted $\\text{Ber}(p)$, is a random variable that takes value 1 with probability $p$, and 0 else. Thus, our model can look like:\n",
      "\n",
      "$$ \\text{Defect Incident, $D_i$} \\sim \\text{Ber}( \\;p(t_i)\\; ), \\;\\; i=1..N$$\n",
      "\n",
      "where $p(t)$ is our logistic function and $t_i$ are the temperatures we have observations about. Notice in the above code we had to set the values of `beta` and `alpha` to 0. The reason for this is that if `beta` and `alpha` are very large, they make `p` equal to 1 or 0. Unfortunately, `mc.Bernoulli` does not like probabilities of exactly 0 or 1, though they are mathematically well-defined probabilities. So by setting the coefficient values to `0`, we set the variable `p` to be a reasonable starting value. This has no effect on our results, nor does it mean we are including any additional information in our prior. It is simply a computational caveat in PyMC. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 30,
       "text": [
        "array([ 0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,\n",
        "        0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,\n",
        "        0.5])"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# connect the probabilities in `p` with our observations through a \n",
      "# Bernoulli random variable.\n",
      "observed = mc.Bernoulli( \"bernoulli_obs\", p, value = D, observed=True)\n",
      "\n",
      "model = mc.Model( [observed, beta, alpha] )\n",
      "\n",
      "#mysterious code to be explained in Chapter 3\n",
      "map_ = mc.MAP(model)\n",
      "map_.fit()\n",
      "mcmc = mc.MCMC( model )\n",
      "mcmc.sample( 120000, 100000, 2 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  120000 of 120000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have trained our model on the observed data, now we can sample values from the posterior. Let's look at the posterior distributions for $\\alpha$ and $\\beta$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha_samples = mcmc.trace( 'alpha' )[:, None] #best to make them 1d\n",
      "beta_samples = mcmc.trace( 'beta' )[:, None]\n",
      "\n",
      "figsize(12.5, 6)\n",
      "\n",
      "#histogram of the samples:\n",
      "plt.subplot(211)\n",
      "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n",
      "plt.hist( beta_samples, histtype='stepfilled', bins = 35, alpha = 0.85, \\\n",
      "        label = r\"posterior of $\\beta$\", color = \"#7A68A6\",normed = True )\n",
      "plt.legend()\n",
      "\n",
      "plt.subplot(212)\n",
      "plt.hist( alpha_samples, histtype='stepfilled', bins = 35, alpha = 0.85, \\\n",
      "        label = r\"posterior of $\\alpha$\", color = \"#A60628\",normed = True )\n",
      "plt.legend();\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ERGQTVE/Wp0+fjqKiIjg4OODDDz+Ei4uL2kOSArm5uZaeAjXAeIiDsRAL4yEWxkMcjIXt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\ninUAAAAgRP0fIA26JISGiXEAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice that neither distribution has postive probability at 0. What would it mean if a variable assigned positive probability at 0? If the coefficient *was* zero, then it would not influence the probability of defect. The larger the probability at 0, the larger the probability the variable has no effect on the outcome. In this example though, both variables are significant to the outcome.\n",
      "\n",
      "Regarding the spread of the data, we are very uncertain about what the true parameters might be (though considering the low sample size and the large overlap of defects-to-nondefects this behaviour is perhaps expected).  \n",
      "\n",
      "Next, let's look at the *expected probability* for a specific value of the temperature. That is, we average over all samples from the posterior to get a likely value for $p(t_i)$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t = np.linspace( temperature.min() - 5, temperature.max()+5, 50 )[:,None]\n",
      "p_t= logistic( t.T, beta_samples, alpha_samples )\n",
      "\n",
      "mean_prob_t = p_t.mean(axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12.5, 4)\n",
      "\n",
      "plt.plot( t, mean_prob_t, lw = 3, label = \"average posterior \\nprobability \\\n",
      "of defect\")\n",
      "plt.plot( t, p_t[0, :], ls=\"--\",label=\"realization from posterior\" )\n",
      "plt.plot( t, p_t[-2, :], ls=\"--\", label=\"realization from posterior\"  )\n",
      "plt.scatter( temperature, D, color = \"k\", s = 50, alpha = 0.5 )\n",
      "plt.title(\"Posterior expected value of probability of defect; plus realizations\")\n",
      "plt.legend(loc= \"lower left\")\n",
      "plt.ylim( -0.1, 1.1 )\n",
      "plt.xlim( t.min(), t.max() )\n",
      "plt.ylabel(\"probability\")\n",
      "plt.xlabel(\"temperature\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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QQgghhHRQ1GFvA52tVsxsNuPs2bPYunUrfvnlF9TU1Lg6JKv2lOvS0lLs2LED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ZAsFrY3Kbtcc2gE9joRtH5rPlabE6vdic3mYEBMMDqVg+OJA8qUz23YClPd+igH9im+\nmNgh43A4ubdxHVR6iaDBY8uUv9zubvLqN8cSH4/slJFlGZwy9cP9kc1KRj7/mKusLEmkde1PXuO2\nSHB1XI8MMmiVEnq7hQmv/KMkusiSxKU7+kIvz73r4KOEPS0trUzPRWxsLPv3779umdTUVI8J+/Tp\n011jq4OCgmjduvV1xyAufXabx+lPv+J+pFpR+YrKemPTpk2sX78eg8FARkYGDz74IO+88w49e/bk\nu+++Y/z48Rw4cICwsDAiIiJYt24d9erV48cff2TEiBEkJCTQpk0bt3pL974kJSW5/n7ppZc4cOAA\n0dHR5OfnM3bsWD744APsdjuPP/44s2fP5qOPPmLu3LkcOHCAESNGMHbsWLf6AWbPnk1hYSE///wz\n2dnZDB06lMjISFf5w4cPM3r0aM6ePcsHH3zAjBkz+O2339zq2bJlCwMGDHBb1saNG9mwYQMdO3ak\noKCAe+65h3HjxrF582b27t3L2LFj2bFjB40bN3bVs3HjRpo1a8bIkSPp3bs3zz33HK+88goLFy5k\n7ty5bNmypcLP4quvvuLbb7+lsLCQwYMHu07Rf/zxx6xbt44vvvgCg8HAtGnTmD17NqtWrWLdunUU\nFBTw66+/otVqOXbsGDqdzmP8jEYjQ4YM4bnnnuPf//43v/32G0OGDKF58+Y0a9bMbZ0tFgsbNmxw\nfZY//PADL730Eps2baJZs2a88MILTJo0iS+//NK1Dlu3bmXHjh3XTcJ2794N/DE2urKvS6b92fnF\na9/E22q1olKpSE5OBnDtH5OTkzGbzVitVnQ63XXr++677zCbza6k1mwuftqjTqdDpVJx+vRpr9tn\nt9tJSUlxaw9A06ZNvV6/kydPunpiy69fSkoKP/zwAw888IBX9eXk5KDRaMoMESpJmPPz833+ee/Z\ns4e0tDRXwl56/RwOB7t37yYiIsLreKempnqMd8l3qy/Xz2KxkJqair+/f5lroZKTkwkNDXVdk+BN\nfXZ78S0O8/KKe0hLPr/8/HzS0v5IOn21fs2bN0eWZY//bxaLBaPR6HH+PXv2uNV33JhNZECka35X\nfWoVh6P9iOnc3G35ntZXFeiPYvHjAHTr2pXu1ysfoEe14hmcdjt3tG6LbHPw4yRKdtAAABbcSURB\nVOGfMFksODNS3NojKxXsSIgiOjKSYd17Izsc/HTqOJJS4bF+SaUiu/8dyE6ZhMg4ZKeDwynny1zA\nWyY+SgUXExshO2XahEaC08mRzHQUGg0KpQKFUsH+A6W2d6uFCw0MyE4nrf2Lf58vyEThyKBZ6+gy\n9TetXx97gZEtoWqQoZU2GNnp5MqV4ygLzzFt3LPl2tMIW34hK9U2kGVaKIuHKmX98j+UZ3bx9Jk9\n5cq3w5bfmBVvvAZAC4UeSZbJ/+5TVAc28/iZH3E6ZXbv3o0sy/z97tuRi4pY8UIuF2QzJoo7Wi99\n/y6JsytO2H0yhn3jxo1s27aN1atXA7B27Vr279/PihUrXGX69+/PP/7xD1cvc69evVi8eLHbePU/\nO4a9JhP2du3aMWvWLEaPHg0Un947efIkq1atcpUZNmwYw4YNY9SoUW7zjxs3jq5duzJlyhS3Mezt\n2rVj+fLl3H333a7ymzdvZv78+ezcuZOwMPer548dO8bAgQM5d+4cAAMGDGD48OFlxmCX9LDHxcUR\nExPDDz/84PqS/fDDD9m4cSOff/45n3zyCa+99hoHDx4EwGQyERcXx8mTJz1e7FR+WY899hiyLLNy\nZfGR+N69e5kwYQInTpxwzTN58mQaN27M7NmzmT59OhqNhtdffx2A1atXs2bNGvbu3QvA8ePHuf/+\n+zl//rzHz8JgMLBhwwZ69OgBwJo1a/jiiy/YvHkzgwYNYuDAgTz88MMAnDlzhi5dupCens66dev4\n6KOPeO2112jRosU112nz5s289957/Pe//3WVefLJJ4mOjmbWrFmuU/gl61wSh5iYGObMmcOMGTMw\nGAyu3j6j0UjDhg05dOgQsbGxGAwGtmzZcs0eSjGG/dZy6dIl3nzzTbdeaCgeGjFz5kyvhlY4HA46\ndeqEzWZze89sNrNs2TJXcnw9X3/9Nfv373fr9S05QzVy5Eiv6snPz2fZsmUeL1SUZZlnnnnGder+\nesaMGUN+vvtt9IxGI7NmzXKdyfMVk8nEkiVLPB5422w2Zs2a5fWFtatXryYrK8vtczYajQwcOJAO\nHTpUSZu9ZbPZWLRokcczGmazmaefftrjGRhPpk2bxoULF9yG0JjNZgYMGMDjjz9eJW32ltPpZPHi\nxR7/p4xGI0899RQhISFe1bVhwwZOnz7tNoTGarXSoUMH+vXrVyVt9pYsy7z22muug6TSjEYjjz76\nqPhu8UCW5eIx6/LVnncZ12tPzwmQZRmHqehqmT/mP3b29wrHsPtksHBMTIyrpwWKe0XKj4MsXyY1\nNZWYmJgqa8PTr/Tx+FOZ8jei9LqkpKSwZcsWGjRo4Po5cOAAly9fBmD79u307t2bRo0a0aBBA/73\nv/+Rk5Pj1XJ++eUXZs+ezdq1a13Juslk4sknn6Rt27bUq1ePBx54gPz8fEofq1X0ZZ6VlYXNZnM7\n+3Hx4kXX69KnbEu+VEt6GDwpv6zSF1ZlZGS4fe5xcXFkZGS45i19IKDT6dxeX2vZUPaziI2NddVd\nMr6y9Ht2u50rV64wcuRIevTowcSJE2nZsiXz5s0rs0MrvU4pKSkcOnSozOe7ceNGrly54ip7rW07\nIyOjTDv8/f0JCwsrE/Oq/N+4lvI9NEL1+rPxjoyMpGnTpq4e8RJGo5Hu3bt7PQ5aqVQyZswYt3qs\nVisxMTFeJ+sAd999NxqNpsxQHVmWsdvt3HfffV7XExQURKtWrdzaZDKZ6Nq1q9fJOsCECRMwmUyu\nfV9eXh5Wq5Xo6Gh69+7tdT1VRa/Xk5iYSFFR2QvxTCYTnTp1qtRdcPr27YvZbC6zX7fZbBgMBtq1\nq/z9uG+UWq3mzjvvxGQyuaYlJydTVFREQkKC18k6wBNPPIHVai2zbna7HT8/P1cHiy8pFAruvvvu\nMusGxXf7admypdfJOkDv3r1xOp2u4ayAawz8Pffc86fb+Gf3JZIk0aNHDwoLC8tMN5vNNGrUSCTr\nFdizZw+SQoGkVKJQqVCoVSg06gof6iVJEip/PaoAf1SB/qiDAjzearQ0nyTsiYmJ/P777yQlJWG1\nWvnss88YMKDsWKIBAwa4rpTft28fISEhtWL8eonSX5ixsbGMGDGC8+fPu36Sk5OZMWMGFouF8ePH\n8/jjj3P69GnOnz/PvffeizcnQq5cucK4ceNYsmQJrVq1ck1fuXIlZ8+eZfv27Vy4cIEvv/wSueQo\nkGtfNGkwGFCr1a5TY1B8MFWZuxdcT+nlR0VFkZaWVmZ9U1JSqnQnUXLauOTvkrqjoqLc1lOlUhER\nEYFKpWLWrFns3buXbdu28fXXX7Nu3Tq39kPx59ulSxe3z3fJkiVeta98O4xGI9nZ2WViUNsfQiFU\n3ujRo+nUqRMKhQKr1Yper2f48OGV7ll98sknmTlzJnq9HrvdjiRJdOjQocwZI2/4+fkxbdo04uPj\ncTqd2O12IiMjmTZtWqUSGig+A9m1a1dUKpVreM+AAQMqfYFuz549mTt3LiEhIdhsNmRZpkOHDqxe\nvbrGLnbv168fPXv2RK1WY7Va0Wg09O3bl169elWqntjYWCZOnEhYWJhr3Zo1a8aUKVMqdVBTlXr2\n7Enfvn3RarWuYVs9evSgf//+laqnWbNmLF26lIiICGw2Gw6HgyZNmvD//t//83hWyRc6d+7MwIED\n0el0WK1WlEolXbp0Yfjw4ZWqJzg4mGnTphEdHY3dbsfhcBAfH8/06dP/1O0vq0JCQgKjRo3C398f\nm82GQqGgY8eOFQ6bFXzDJ2PYVSoVb775Jvfddx8Oh4OJEyfSvHlz3nnnHQCmTJlCv379+Oqrr2jc\nuDH+/v68//77vmhajRg+fDi9evVi586ddOvWDZvNxsGDB2nYsCGBgYFYrVYMBgMKhYLt27fz7bff\nug3DKM9ut/PQQw8xYsQIBg4cWOY9o9GITqcjKCiInJwcFi9eXOb98PDwMuPfS1MqlQwaNIiXX36Z\nt956i5ycHFatWsVjjz3msbw3Sifj5Q9EEhMT8fPzY/ny5UybNo39+/fzzTffuG4DWhUjuFauXEli\nYiKFhYW8++67riEqQ4YMYfny5fTq1YuwsDAWLFjAkCFDUCgU7N69m7CwMJo1a0ZAQABqtdr1JVg+\nfr1792b+/PmsX7+ewYMHA8XDkAICAmjatKnHdSh9ADV06FAmT57MsGHDaNKkCQsWLCAxMdHru3NU\nJXGHGN+6kXgrlUr69OlTJcM6HnnkER555JEbricoKKhKvuQlSaJnz54VniqujO7du9O9e/cbrqeq\nSJLEXXfdxV133XXDdcXFxVXJ51aV7rjjDu64444brqdt27asWbOmClpUddq3b+9xiG5lGQwGHnro\noRtvUCk3uu9u2bIlLVu2rKLW1H6++K70WZdC3759OXXqFGfOnGHOnDlAcaI+ZcoUV5k333yTM2fO\ncPTo0Sr5J7hZxcTEsHbtWl5//XWaNm1KmzZtWLlyJbIsExgYyKuvvsqECRNo2LAhGzdupG/fvmXm\n99S7mp6ezr59+3j77beJj48nPj6eevXqkZaWxtSpUzGbzTRp0oQ+ffrQq1evMnVMmTKFzz//nIYN\nG7ruUlLaokWL0Ov1tG/fnn79+jFs2DDGjBnjakv59lyv97f0++XnV6vVfPLJJ2zfvp0mTZowa9Ys\nVq1a5brg1JvlXW/5ffv2pXv37nTr1o3evXu71mXs2LGMGDGC+++/n/bt2+Pn58eiRYsAuHz5Mg8/\n/DD169fnzjvvpGvXrq4xuOXjFxAQwMaNG9m0aRMtW7akefPmvPTSS65xwRWtQ8m0bt268eyzzzJ+\n/HhatGjBhQsXeO+997xeP0EQBEEQahefPTipqtzqD04Sbkzp21XWZlX1/yDuw+5bIt6+JeLtWyLe\nviNi7VtVFe/Dhw/X7EWngiAIgiAIgiD8OSJhF24pYjhJ5YgeGt8S8fYtEW/fEvH2HRFr3/JFvH1y\n0akg3CwyMzNrugmCIAiCIAiVUmt62P9iQ/EFoVpV1f+DuA+7b4l4+5aIt2+JePuOiLVv+SLetSZh\nB5G0CwKI/wNBEARBqG1qzV1iCgsLsVgsGAyGGmiVINw8srKy0Gq1NfZAEUEQBEEQKu9ad4mpNWPY\nAwICsFgspKeniwsLhVuWLMsiWRcEQRCEWqbWJOxAjfWui/ud+o6ItW+JePuWiLdviXj7loi374hY\n+5Yv4l2rxrDXlGPHjtV0E24ZIta+JeLtWyLeviXi7Vsi3r4jYu1bvoi3SNirQH5+fk034ZYhYu1b\nIt6+JeLtWyLeviXi7Tsi1r7li3iLhF0QBEEQBEEQbmIiYa8CycnJNd2EW4aItW+JePuWiLdviXj7\nloi374hY+5Yv4v2XvK2jIAiCIAiCINQ2Fd3W8S+XsAuCIAiCIAjCrUQMiREEQRAEQRCEm5hI2AVB\nEARBEAThJiYS9kqqX78+bdq0ISEhgdtvvx2A7Oxs7r33Xpo2bUrv3r3Jzc2t4VbWHp7iPW/ePGJj\nY0lISCAhIYFt27bVcCtrj9zcXIYNG0bz5s1p0aIF+/fvF9t3NSkf63379oltu5qcOnXKFdOEhASC\ng4NZvny52Lariad4//Of/xTbdzVauHAhLVu2pHXr1owePRqLxSK272riKda+2LbFGPZKatCgAYcO\nHSIsLMw1bdasWdSpU4dZs2axaNEicnJyePXVV2uwlbWHp3jPnz+fwMBAnnrqqRpsWe00fvx4unXr\nxoQJE7Db7RiNRl5++WWxfVcDT7F+4403xLZdzZxOJzExMRw4cIAVK1aIbbualY73mjVrxPZdDZKS\nkujRowcnTpxAq9UycuRI+vXrx2+//Sa27ypWUayTkpKqfdsWPex/QvljnM8//5zx48cDxV/C//nP\nf2qiWbWWp2NKcZxZ9fLy8ti1axcTJkwAQKVSERwcLLbvalBRrEFs29Vt+/btNG7cmLi4OLFt+0Dp\neMuyLLbvahAUFIRarcZkMmG32zGZTNStW1ds39XAU6xjYmKA6t93i4S9kiRJolevXiQmJrJ69WoA\nLl26RGRkJACRkZFcunSpJptYq3iKN8CKFSto27YtEydOFKf5qsj58+cJDw/n4Ycfpn379kyePBmj\n0Si272rgKdYmkwkQ23Z1W7duHQ8++CAg9t2+UDrekiSJ7bsahIWFMXPmTOLj46lbty4hISHce++9\nYvuuBp5i3atXL6D6990iYa+kPXv28PPPP7N161ZWrlzJrl27yrwvSRKSJNVQ62ofT/F+9NFHOX/+\nPEeOHCE6OpqZM2fWdDNrBbvdzuHDh5k2bRqHDx/G39/f7fSp2L6rRkWxnjZtmti2q5HVauWLL75g\n+PDhbu+JbbvqlY+32HdXj7Nnz/LGG2+QlJREeno6hYWFrF27tkwZsX1XDU+x/vjjj32ybYuEvZKi\no6MBCA8PZ/DgwRw4cIDIyEgyMjIAuHjxIhERETXZxFrFU7wjIiJcO59JkyZx4MCBGm5l7RAbG0ts\nbCwdO3YEYNiwYRw+fJioqCixfVeximIdHh4utu1qtHXrVjp06EB4eDiA2HdXs/LxFvvu6nHw4EE6\nd+6MwWBApVIxZMgQ9u7dK/bd1cBTrH/88UefbNsiYa8Ek8lEQUEBAEajkW+++YbWrVszYMAAPvzw\nQwA+/PBDBg0aVJPNrDUqinfJDghg8+bNtG7duqaaWKtERUURFxfH6dOngeKxpy1btqR///5i+65i\nFcVabNvV69NPP3UNzwDEvrualY/3xYsXXX+L7bvq3Hbbbezbt4+ioiJkWWb79u20aNFC7LurQUWx\n9sW+W9wlphLOnz/P4MGDgeJT2mPGjGHOnDlkZ2czYsQIkpOTqV+/PuvXryckJKSGW/vXV1G8//a3\nv3HkyBEkSaJBgwa88847rnF6wo05evQokyZNwmq10qhRI95//30cDofYvqtB+VivWbOGGTNmiG27\nmhiNRurVq8f58+cJDAwEEPvuauQp3mLfXX0WL17Mhx9+iEKhoH379rz33nsUFBSI7bsalI/16tWr\nmTRpUrVv2yJhFwRBEARBEISbmBgSIwiCIAiCIAg3MZGwC4IgCIIgCMJNTCTsgiAIgiAIgnATEwm7\nIAiCIAiCINzERMIuCIJwk6hfvz47d+6s6WbcsHnz5jFu3LiaboYgCEKtIRJ2QRCEm4QkSdzsN+6y\n2+21YhmCIAh/JSJhFwRBuAmMGzeO5ORk+vfvT2BgIEuXLmXfvn107tyZ0NBQ2rVrx/fff+8qf889\n9/D888/TpUsXAgMDGTBgAJmZmYwZM4bg4GBuv/12Lly44CqvUChYsWIFjRo1Ijw8nFmzZpU5OFiz\nZg0tWrQgLCyMPn36kJycXGbet956iyZNmtCsWTMAnnjiCeLj4wkODiYxMZHdu3cDsG3bNhYuXMhn\nn31GYGAgCQkJQPHZgx07drjqLN0Ln5SUhEKhYM2aNdSrV49evXpdt02CIAi3EpGwC4Ig3AQ++ugj\n4uPj+fLLLykoKODBBx/kgQce4IUXXiAnJ4elS5cydOhQsrKyXPN89tlnrF27lrS0NM6ePcudd97J\nxIkTyc7Opnnz5syfP7/MMv7zn/9w6NAhDh8+zJYtW1izZg0AW7ZsYeHChWzevJnMzEzuuuuuMk+o\nLCnz008/cfz4cQBuv/12jh49Sk5ODqNHj2b48OFYrVb69OnDs88+y6hRoygoKODnn38GcD22u0Tp\nv0v88MMPnDx5km3btnnVJkEQhFuFSNgFQRBuQmvXrqVfv3706dMHgF69epGYmMh///tfoDjhffjh\nh2nQoAFBQUH07duXpk2b0qNHD5RKJcOHD3clyyVmz55NSEgIcXFx/P3vf+fTTz8F4O2332bOnDk0\na9YMhULBnDlzOHLkCCkpKa5558yZQ0hICFqtFoAxY8YQGhqKQqHgqaeewmKxcOrUKQBkWb7u0B5P\n78+bNw8/Pz90Op1XbRIEQbhViIRdEAThJnThwgU2bNhAaGio62fPnj1kZGS4ypR+9LVOpyMiIqLM\n68LCwjJ1xsXFuf6Oj48nPT3dtawnnnjCtRyDwQBAWlqax3kBli5dSosWLQgJCSE0NJS8vDwyMzNv\naJ1LL8ObNgmCINwqVDXdAEEQBKFY6WEi8fHxjBs3jnfffbfS81YkOTmZ5s2bu/6OiYlxLev555+/\n5pCT0vXv2rWLJUuWsHPnTlq2bAlAWFiYq9fcU1v8/f0xGo2u16UPPDwtw5s2CYIg3CpED7sgCMJN\nIjIykrNnzwLFQ06++OILvvnmGxwOB2azme+++65MD3PpYSXe3F1m6dKl5ObmkpKSwvLlyxk5ciQA\nU6dO5ZVXXnGNT8/Ly2PDhg0V1lNQUIBKpaJOnTpYrVZefPFF8vPzXe9HRUWRlJRUpk3t2rVj3bp1\n2O12Dh48yMaNG695kFHZNgmCINRmImEXBEG4ScyZM4cFCxYQGhrKhg0b2LJlC6+88goRERHEx8ez\nbNmyMklw+Ys4yyfA5V8PHDiQDh06kJCQwAMPPMCECRMAGDRoELNnz2bUqFEEBwfTunVrvv766wrr\n6dOnD3369KFp06bUr18fPz8/4uPjXe8PHz4cAIPBQGJiIgAvvfQSZ8+eJTQ0lHnz5jFmzJhrtvV6\nbRIEQbiVSPLNftNfQRAE4YYpFArOnDlDw4YNa7opgiAIQiWJHnZBEARBEARBuImJhF0QBOEW4M1F\nqYIgCMLNSQyJEQRBEARBEISbmOhhFwRBEARBEISbmEjYBUEQBEEQBOEmJhJ2QRAEQRAEQbiJiYRd\nEARBEARBEG5iImEXBEEQBEEQhJuYSNgFQRAEQRAE4Sb2/wEjy0CjkxwUYwAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Above we also plotted two possible realizations of what the actual underlying system might be. Both are equally likely as any other draw. The blue line is what occurs when we average all the 20000 possible dotted lines together.\n",
      "\n",
      "\n",
      "An interesting question to ask is for what temperatures are we most uncertain about the defect-probability? Below we plot the expected value line **and** the associated 95% intervals for each temperature. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats.mstats import mquantiles\n",
      "\n",
      "# vectorized bottom and top 5% quantiles for \"confidence interval\"\n",
      "qs = mquantiles(p_t,[0.05,0.95],axis=0)\n",
      "plt.fill_between(t[:,0],*qs,alpha = 0.7,\n",
      "                color = \"#7A68A6\")\n",
      "\n",
      "plt.plot(t[:,0], qs[0], label=\"95% CI\", color = \"#7A68A6\", alpha =0.7)\n",
      "\n",
      "plt.plot( t, mean_prob_t, lw = 1, ls= \"--\", color = \"k\",\n",
      "        label = \"average posterior \\nprobability of defect\")\n",
      "\n",
      "plt.xlim( t.min(), t.max() )\n",
      "plt.ylim( -0.02, 1.02 )\n",
      "plt.legend(loc=\"lower left\")\n",
      "plt.scatter( temperature, D, color = \"k\", s = 50, alpha = 0.5 )\n",
      "plt.xlabel(\"temp, $t$\")\n",
      "\n",
      "plt.ylabel(\"probability estimate\" )\n",
      "plt.title( \"Posterior probability estimates given temp. $t$\" );"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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NBkwmAyazQQoUHZhMZrIH55M9OL/N26trynnqj/ehGgzkZo8iN3sUQ7NHMWjA\nUBmN7yGGI+1kTXYPjQ029u2uIibWyoAhCQwfky5tM0IIIUQP6ZMj7F0V8De31jQX8i7q6xzU2hzU\n1zpxO714vX78vu/645uLeCMmc3MBX7x/C/l544Mak2jbsT3smqZRVX2Y4n3b2bNvK8X7tpOclM5d\ntzwe4ij7js6cM9A844xKQnIUeaPTyBwYL7PNdJP0nepL8q0vybd+JNf6Cla++90Ie1epBpXY+Ahi\n4yNgyHfrfV4/DXUu6moc1NqaqK6yU1PVhMvRXMS7XV78fo2ayiZsMY2YLEeK+CNtNTIS37MURSE1\nOZPU5EymntY8D3wg4G9z2337d1JVfZj8vPHExiToGWafZzCqaEB1lZ3KTxuIjLaQMTCOEeMypN9d\nCCGECAIZYe8in9dPfa2T2moHddVN2Crs1NocuJxefL7mkXi/XwO05lF4i6GliJd540Nnx+5v+PyL\nd9hVvJmk+FTyh01gxLAJDB86Fqs1MtTh9TkBfwBFUYhLjCB7WApDcpNlmkghhBCiAzLCHkRGk4Gk\n1GiSUr+b7cTr8VNf46C2uvlPdWVjSxHvdftxNnkJBJoLGLPFgOmYdhpDD0wzKU404kiB7vf7KTmw\nm527v+HT1f/C7/MxcZz8bBhsR6dPra918vV/Sti2sYzk9BhGjs0gPjkqxNEJIYQQvYsU7EGwbv2X\nTJ8+neT0mJZ1HrePuurmVpqa6iaqDttpqHPidnmbT2xtdBMINM8Xf3wRL1NMtu9U52E3GAwMHTKC\noUNGcME5P2h3u/XfrCY1OZOsAUNRVUO3H6+3O9V8H50m0ucLcPhAHYf21xETZ2FIXjK5I9PkC+tx\npO9UX5JvfUm+9SO51pfMw96LmS1GUjNjSc2MbVnndHiaC3ibg9qqJqrKG7E3uvG4fTibPNgbAmgB\nDaNJxWw1YbYYMFuMUtSEwP4DRby//BUaG+sYPeI0xo2awugRp3U4j7zomKIoKIbmWWY2rz/I7q0V\nDBySwKiJA2SGGSGEEKID0sMeQlpAw97optbWRG21g5pKO1UVjTjsHrwePz6fn4Bfw2BUsViNmCxG\nzJbmNhrphddHTV0VW7avY9PWtRw8tJenHn21X4+4B5vfH8BoNJCWGcOY0wYRE2sNdUhCCCFESHTU\nwy4Fe5jx+wPUVTuwVdqxlTdSXtaAvd6Fx+PD5w00t9GoCharEfPRAl5OZtWF3+/HYDixWPf6PKiK\noc3bROfVvRVbAAAgAElEQVQEAhoKkJASxegJA0jJiJHXtBBCiH6lo4Jdei2CoLCwMGj7MhhUklKj\nGT46nWlz8rjs2olc8sMJnH1+PuOnDGLA4Hiios3Nc8c3uKgqt1NR1kCtrYmmRjc+r59e9h2sS3bt\n2RSyx26vIN+yfT33P3IFS1/5Neu+XkmTo1HnyHqOXvlWVQVFVai1NbFm+S5WvLONvbuqmi9g1o8E\n87NEnJzkW1+Sb/1IrvWlR76lcTTMqapCfFIk8UmR5I5MQwtoNDa4sFXYsVXYqSirp67Ggdvlo6nR\nTUOdC4NBwRphwmw1YrEY5SI2PWzi2OlkZ+Wzefs61m9cxav//CNZA3O56NxrGDFsQqjD61UURcFg\nVGiyu/m6sITt3x5i8NAk8sdlYDLJLxhCCCH6J2mJ6eU0TaOp0Y2twk7l4QYO7a9rvkKr29cy2m6x\nGrFYTVisRmmf0YHH42ZH0TckJqQyKDMn1OH0en5fALPFSMbAOMacNpCISHOoQxJCCCGCTuZh78MU\nRSE61kp0rJUhecloAY3aagcVZfUcPlBHeVkDToenefS91onBqLaMvpstRplCsgeYzRbGjZrS7u2b\nt61j6JARREXFtruN+I7BqOL3ByjdV0PZ/loGDElg/BlZMrOMEEKIfkN62IMgnHrFFFUhMSWKEeMz\nmXXRSL53wyTmXjKKiWcOZsCQBCIizXg8fuqOFPU1Vfbm3ndfINShd0ooe9iDIRAI8OWGz3jwl9fy\nx6U/579ffYrD2RTqsNoVTvlWVQUNKC2u5uM3N/PtulJ8Xn+owwqqcPos6Q8k3/qSfOtHcq0v6WEX\np8xiNZE1NImsoUmtR98P1lNeVo+z6bvRd5PZgDXShDXChFH6hXuEqqosuP7nuFwONm1by1ffrOb1\nfy1h8vgCrp//41CH1yuoBhV/QKNoWwUH9tYwdEQq+WPSW66uKoQQQvQ10sPej7ldXioPNXLoQB0H\n99VQX+vE4/Hj9/oxmlSskeYjxbv0vfckh9PO4YoDDB0yItSh9Ep+X4DIKDP5YzPIGZ4iJ1kLIYTo\nlWQednFSfl+g+aTV0jpKi6upq3Hicfvw+QLNs84cGXk3mQ1SvOuopHQ30dGxJCemhzqUsBfwBYiK\ntTJm0gAGDEmQ16kQQoheReZh72F9oVfMYFTJGBTPpGlDuOSHE7jgyrGcXpDDoOwErJEmPC4f1ZVN\nVB5qpKHWidvlC8l87+HUU62HPfu28qun7+T3zyxk3dcr8Xo9uj5+b8q3alRxNLlZu3ovn763ncrD\nDaEOqcv6wmdJbyL51pfkWz+Sa33pkW/dCvbly5eTn59PXl4eixcvPuF2m83GvHnzGD9+PKNHj+al\nl17SKzRxHNWgkpoZy4QpWVw0fzwXzh/PlLOHMjg3ichoMx63n1pbExVlDdTXOHG7vH36Yk2hNKfg\ncn676HWmTz2P/6xfwU8XXc1rb/0Jl9sZ6tDCkqIoqAaFxnonXyzfxcoPdlBX4wh1WEIIIcQp0aUl\nxu/3M3z4cD777DMGDBjAaaedxuuvv86IEd/17C5atAi3282TTz6JzWZj+PDhVFRUYDS2Pi9WWmJC\nR9M06qodlJXWcWBvDbbyRlxOL94jM3VYI0xYI5vne5d2hJ5RXVPBhm+/YO7M76Gq8gPZyWiaBhqk\nZsZy2lnZWCNMoQ5JCCGEaFPI52Ffv349ubm5DBkyBID58+fz3nvvtSrYMzIy2Lx5MwANDQ0kJSWd\nUKyL0FIUhYTkKBKSoxg1IZOGOheHSms5uK+GirIGnE4vddUONE07png3yVzvQZSUmMa5s65o8zaf\nz4vBIF+WjqUoCihQcaiBT/61hbzR6YwYmyEnpgohhOhVdBmiKysrY9CgQS3LAwcOpKysrNU2t956\nK9u2bSMzM5Nx48bxxz/+UY/QgqI/9oopikJcQgQjxmUy99LRXHLNRGbMG87wMenEJUQSCGg01Dip\nKKun1taEs8lDIHDqP+b0pp5qvRWuXc6jT93C6v98gDtILTN9Jd+qquAPaGzfWMYn72zFVtEY6pDa\n1B8/S0JJ8q0vybd+JNf66jPzsHdmxO/Xv/4148ePZ/Xq1RQXFzN37lw2bdpETEzMCdveeeedZGVl\nARAbG8uYMWOYPn068F3S9FzesmVLSB8/XJaHx6VTVbeHdIuXwQNHUravljVr1uAq95GVOYJAjYOD\nFbswWwyMGTkR1aC2FITDc8cBnHS5tKy4S9v3p+WCaRfi9XlYu+Fz3v3oRaadfi6DB+URF5vY7f33\ntXwXlWxB0zSaGt1kZsXjVsswGg1h8f4B2LJlS0gfv78tS74l37Isy6GuHxsamidIKC0t5eabb6Y9\nuvSwr127lkWLFrF8+XIAnnzySVRVZeHChS3bnH/++fz85z9n2rRpAMyePZvFixczefLkVvuSHvbe\nxenwcLi0joMltZTtr6XJ7sHr8RPwB7BEGJvnerca5aI3QVZVfZhVhe/zn3Wf8PMfLyE1OTPUIYWd\ngD+A2WJkxPhMckekSiuREEKIkAp5D/vkyZMpKiqipKSEzMxM3njjDV5//fVW2+Tn5/PZZ58xbdo0\nKioq2LVrFzk5OXqEJ3pQRKSZnPxUcvJTcbu8HD5Qz8GSWg6W1GBvcNNY56I+EMBiNRERacISIT3v\nwZCSlMGVlyzg0vNuwGy2hDqcsKQaVHy+AN+uO0DJbhunF2QTlxAZ6rCEEEKIE+gyrGk0GlmyZAnn\nnnsuI0eO5KqrrmLEiBE899xzPPfccwA89NBDbNiwgXHjxjFnzhx+85vfkJiYqEd4p0x6xTrHYjUx\nJC+Z6XPzuPy6Scy5eCSjJw4gMTkKgIY6JxUHG5p73h1t97z3lZ5qvbRXrNfVV1NTV3XS+/eHfBsM\nCg31Tj5ftoMNhfvwHZn1KBTks0Rfkm99Sb71I7nWlx751mWEHeC8887jvPPOa7VuwYIFLf+fnJzM\nsmXL9ApHhJjZYmRIXjJD8pJxOb0cKq3j4L4aDpbU4rC7aah1ogWcR9pmZLaZYNtbsoOX3vg9o4ZN\nZHbBZeRmjwp1SCF1tB2mZLeN8oP1jJk8iMG5SSGOSgghhGjWqR72QCDAX//6V/7xj39QVVXFli1b\n+OKLLygvL+fKK6/UI84W0sPetzkdHg4dmef9UGlzz7vP4yegaVgjTUREmmWe9yBxupr4z/oVfL7m\nHeLjkrhg7g8YlT9ZcgsE/BqJKVGcXpBNdIw11OEIIYToBzrqYe9Uwf7II4+wYsUK7rvvPm6//Xbq\n6+spLi7miiuuYOPGjUEPuCNSsPcfjiYPh/bXcmBfDYdK63A0NZ+wqigQGW0hIsqM0Sgnq54qv9/P\nhm/XsHzlP7n7lsdJTEgNdUhhQdM0VEUhf2wG+eMy5IuMEEKIHtVRwd6paufFF1/kgw8+4Oqrr265\numJ2djZ79+4NXpS9mPSK9YzIKDO5I9M4+4IRXHbtRArOG45bKSMy2oLL4aXqUAPVlXZcDi86THbU\nZxkMBs6YNItHf/KXE4r1/tDD3h5FUdCAbd+UserDnbic3h5/TPks0ZfkW1+Sb/1IrvUVNj3sgUCA\n6OjoVuuampranCNdiJ4QGW1h2Kh0KmqGMGL4OEp2V7Fvl436Oid1NQ4Ujo66mzCaDKEOt1dqbwS5\nvrGWyIgoTEazzhGFB9WgUmNr4pO3tzJhShZZQ6W3XQghhL461RJz8803Yzab+cMf/kBGRgbV1dX8\n+Mc/xuPx8Mwzz+gRZwtpiRFHedw+DuyrYe+uKg6X1uF0ePH5/JgtRiKjzVgjTNLGEAQffvp3Vhcu\n45yzv8+MqedjsUSEOqSQCQQ0MrPiOf2sbPliKIQQIqhOuYe9vr6eG264gY8//hiv14vFYuGcc87h\nlVdeITY2NugBd0QKdnE8TdOorXZQstvG3l2V1Nc48bh9aEBktJmIKDMmKa5OSenBPXz46esUFW9m\n1oxLmXXWJURGRJ/8jn2Q3x8gItLMlJk5JKfJr4xCCCGC45R72OPi4njnnXfYv38/X375JcXFxbz7\n7ru6F+vhSnrF9NNWrhVFITE5iolnDuaSH05k1kUjyBudTkysFbfTh63cTnWFHafDI73uXXS0hz1r\nYC533PgIP73raSqqynjst7fj8/tCHF1oGAwqbpeXNR/v4pu1+9u8XkB3yWeJviTf+pJ860dyra+w\n6WGfMGEC33zzDWlpaaSlpbWsnzx5Mhs2bOix4IToKpPZQPawFLKHpVBX7WBfkY29u6qoq26ivsZJ\ng+IiKqZ51N1gkBlmuiojPYubf/gznK4mjAbdLuMQdhRFAQX27Kik8lAj02bnEh0n0z8KIYToGZ1q\niYmJiaGxsbHVOk3TSEpKoqampseCa4u0xIiu8nn9HNhXQ9H2Cg6X1uN0ePD7NSIiTUTFmDGZ+2/h\nKU6dpmmoqsLoiQPIHZkm500IIYTolo5aYjqsVK699loA3G431113Xat2gpKSEkaN6t9XRxS9g9HU\nPOo+JC8ZW7mdPTsq2Lfbhr3Bja2iCbPZQGSMnKR6qjRN4/lXn2R0/mSmTJ6NqvaP8wYURUHTYNP6\nA5Ttr+PM2bmYLfIlUAghRPB02BMwdOhQhg4diqIoLf8/dOhQcnNzueaaa3jvvff0ijOsSa+Yfk4l\n14qikJIRw9RZuVzywwmcOXsomYPiUFWF+honlYcasTe48PsDQYy4d+vKPOyKonD29Iv599qPWfSb\nBWzcXNivzhlQDSq2SjvL/7WFsv213dqHfJboS/KtL8m3fiTX+gp5D/uiRYsAmDJlCvPmzevxYITQ\nS1SMhdGTBpI/NqNVu4zD7qGx3n2kXcaCydw/RomDJS9nND+7+/ds2bGedz58kY8/e4MrLrmVYUPH\nhjo0Xaiqgs8X4MuVxWQNTWTStCFyroQQQohT1qkedgCPx8OuXbuw2WytRs1mzZrVY8G1RXrYRU/Q\nNO24dhkXXq8fs9ko7TLdFAgE+Oqb1QS0AFMnzwl1OLrz+zWiYyycOSeXuPj+O3e9EEKIzul2D/tR\nhYWFXHHFFbjdburr64mLi6OhoYGsrCz27t0b1GCFCIWj7TIpGTGMPW0Q+3ZXUbStgpqqI7PLqC6i\nYixERplRVSncO0NVVc6YpO8X+nBiMCg4mtysfH8HoydlygmpQgghuq1Tv9Xed999/PSnP6WmpobY\n2Fhqamp49NFHueOOO3o6vl5BesX0o0euj7bLXHT1eM6+cARD81OIiDDhaHBTWdZAQ60Tn9ff43GE\ng670sHdFIOCn0V7XI/sOJ4qioKHx7foD/HtFEV5Px68b+SzRl+RbX5Jv/Uiu9aVHvjtVsBcVFXHf\nffcBtLTDPPjgg/zhD3/ouciECDGjyUDO8BTOuXQ0874/htGTBhCbEIHb5aOqvJGaqibcLl+/OrEy\nWEoO7OaRJ29hxaq38Pm8oQ6nxxkMKpWH6vnk7S1Uljee/A5CCCHEMTrVw56VlcWmTZtISEhg5MiR\nvPnmmyQnJzNs2DDq6+v1iLOF9LCLUGqoc1K8o5Ki7ZXU1zrwuv0YTCpRMRYiIqXPvSsOV5Tyz/ee\no7LqEFddejtjRp7e5/OnaRpokDsylbGTB6FIe5UQQogjOuphNyw6OhVMB0pKSnA4HIwdOxan08mC\nBQt4/vnnufjii7nkkkuCHW+H9u3bR0ZGhq6PKcRRFquJjEHx5I5MIy4+Ap8vgMvpxWF309TgRtPA\naFKlz70TYqLjmDJpNinJGfzzvefYvH0dY0ecjtlsCXVoPUZRFBRFobq8icMH6snIisNkkpmIhBBC\nwOHDh8nJyWnztk7PEnOsf//73zQ2NjJv3jxUVd8py8JxhL2wsJDp06eHOox+IdxyHfAHKNtfx+6t\n5ZTtr8XR5MHvDxARae4T00Lu2rOJ4bnjevxxfH4f677+nKmT5/SbCy5pAQ2jycCEKVlkDU0Cwu/1\n3ddJvvUl+daP5Fpfwcr3Kc8Sc7yzzjrrlAISoq9QDSqDchIZmJ1AdVUTxdsr2LurisZ6F7YKOxar\nkehYi1z58iSMBiPTTj831GHoSlEV/P4AX32xj0MH6jjtrOxQhySEECJMdWqEff/+/Tz22GN88803\n2O327+6sKOzevbtHAzxeOI6wC3GspkY3xTsr2bWlnLpqBx6PH7PF0FK49/U+7WCrb6ghLjYx1GH0\nqOY5282cOTuPuASZs10IIfqjUx5hv+KKKxgxYgS//OUvsVqtQQ1OiL4mKsbC2NMGMXxMBsU7Ktm5\n+TA1VXZqqhyYTCrRsVYsEVK4d4amafzpr48SH5fElRffRmrKgFCH1COa52z3sHLZdkZNHMCw0emh\nDkkIIUQY6VQD+q5du3jhhRe48MILmTNnTqs/QuY71VNvyrXFamTkhEwuuno8M+YNZ+CQBAwGlboa\nB7ZyO84mT9hPCdlT87B3lqIoLLz79+QMHsGv/+ce/rXsr7jdzpDG1FMURWHnnk1s/uog//l8D35f\nINQh9Xm96fOkL5B860dyra+wmYf9wgsvZM2aNT0dixB9kslsYNjodC68ahwzL8gna2gSJrOB+lon\nVYcbcdjDv3APJZPJzPlz5rPoZ0upqavi0cW3hvyLRE9SDQqH99ey4t2t2OtdoQ5HCCFEGOhUD7vN\nZmPq1KkMGzaM1NTU7+6sKLzwwgs9GuDxpIdd9HYBf4AD+2rYsekwhw/U43J6AIiOtRIRZZYpIU9i\n266viYmKI2tgbqhD6VGapmFQVSZMzWJwbnKowxFCCNHDTrmH/aabbsJsNjNixAisVmvz5bY1TXpw\nhegG1aAyODeZrJwkykrr2LnpEAf312JvcNNY7yI61kJktEUK93aMGj4p1CHoQlEUAprGV4UlVJU3\nMvHMIfKaEEKIfqpTBfuqVasoKysjNja2p+PplWS+U/30pVwrqsLAIQkMGBxPRVkDOzcdpnRvNY5G\nD00NbqLjrERGmUN6NUy95mEPhr4wiNBWvlVVoWS3jVqbg7POHYY1whSi6PqevvR50htIvvUjudaX\nHvnuVME+duxYqqurpWAXogcoikL6wDjSBsRiq7CzbWMZ+/dUY29wY29wExNnISLK3OuL0Z72z/ee\nw+fzctkFNxEZERXqcIJKNarU1zn55J2tnFGQQ/qAuFCHJIQQQked6mF/5JFHeOONN7jxxhtJS0sD\nvhvNuummm3o8yGNJD7vo6zRNo+JQA1u/LuPgvhqcTR5QFWLirEREmqRwb0dTUwP/+uAFNm9fy5WX\n3s5p4wv6XK40TQMNho1OZ/SkAX3u+QkhRH/WUQ97pwr2mTNnNm/cxj8Oq1atOrXoukgKdtFfaJrG\nodI6tm0so2x/HU6HB4NBITrOijVCCvf27Nm3jb/984/ExSbyw+/f3Sfnbg/4AiSnxzBtTi4ms1xF\nVwgh+oKOCvZOTeu4evVqVq9ezapVq074I2S+Uz31p1wrisKAwQnMvWQUsy8aQXZeMiazkfoaJ7YK\nOy6nt8eng+yN0yfmZo/i4Z88w4jhE1nz5UehDqdLOptv1ahiq2jkk7e3UWNr6uGo+q7+9HkSDiTf\n+pFc60uPfLc7NHPsCVyBQPsX8FDVTtX8QohuUlSFrKFJDBySwP7iarZtPETFoXpqbQ7MZgPRcVYs\nVhllPZbRYGTerCtDHUaPUg0qbreX1R/tZMykAeSNkqujCiFEX9VuS0xMTAyNjY1A+0W5oij4/f6e\ni64N0hIj+ju/L8C+3VVs23iIqvIG3G4/ZouBmDgrZosU7v1RIKCRmRXPlIIcVIMMogghRG/UrXnY\nt23b1vL/e/fuDX5UQohuMRhVckemMTgvmb07Ktn27SGqK+1UV9qxWE3ExFkxmQ2hDjNslZTuxuV2\nkJ83PtShBI2qKpTtr+WzZTsomDcMi1WmfhRCiL6k3aGYrKyslv9/6623GDJkyAl/3n777U4/0PLl\ny8nPzycvL4/Fixe3uc3q1auZMGECo0ePbjnRtTeQXjH9SK6/YzIZGD42g4vmj2Pa7DzSMmMJBDRs\n5XZqq5vweU/916/e2MN+Mi63g/977Te8+s//wekKr/7vU8m3waDSUOdkxTvbqLHZgxhV3yWfJ/qS\nfOtHcq0vPfLdqd9OH3vssTbX//KXv+zUg/j9fu666y6WL1/O9u3bef3119mxY0erberq6rjzzjtZ\ntmwZW7du5a233urUvoXo70xmIyMnZHLh/PFMmZlDclo0Pk8AW7md+hoHfl/756D0R/l543ls4fNo\nmsYvnrqVLdvXhzqkoFFVBY/Hx5qPdrF3V1WowxFCCBEkHU7ruHLlSjRN46KLLuKDDz5odVtxcTG/\n+tWv2L9//0kf5Msvv+Sxxx5j+fLlADz11FMAPPjggy3bPPPMM5SXl/P44493uC/pYReiY44mDzs3\nHWLXlnLq61z4fQGiYsxEx1ikv/k423dt5JU3/sD4MWcy/7I7Qh1OUGkBjezhKUw4IyukV8sVQgjR\nOd3qYQe46aabUBQFt9vNzTff3LJeURTS0tL405/+1KkAysrKGDRoUMvywIEDWbduXattioqK8Hq9\nnH322TQ2NnLvvfdy7bXXdmr/QojvREaZmXjmEPJGpbP920MUbavA3uDCYfcQFWMhKsaCKgUcACOH\nT2TRwqUcLj/5wENvo6gKe3dW0ljn4sw5uZhMcl6DEEL0Vh0W7CUlJQBce+21vPrqq91+kM5c4MXr\n9bJx40Y+//xzHA4HU6dOZcqUKeTl5Z2w7Z133tnSYx8bG8uYMWOYPn068F0fkZ7LW7Zs4Y477gjZ\n4/en5b/85S8hP969ZTkmzorXcIjkbDfZ5sHs3VnJlq1fowFjRk8iKsrM7r2bARieOw74rof66PKn\na94ma8DQdm+X5eAuBzvfRfu2sHNPgCa7mxnnDuPbzRuA8Hh9hsOyfJ5Ivvvq8rE91eEQT19f7m6+\nt2zZQkNDAwClpaWtBseP16krnR47Jzs0X91UVVUKCgpOdlcA1q5dy6JFi1paYp588klUVWXhwoUt\n2yxevBin08miRYsAuOWWW5g3bx7f//73W+0rHFtiCgsLWw6A6FmS6+6rrrSz9esySvbYcNg9gEZM\nnJWIKHO7X6p37dnUUvz1N4FAAEVRdL2ibE/lW9M0DEaVMwqGkjEwLuj7763k80Rfkm/9SK71Fax8\nn/KVTgsKCvjPf/4DNBfW8+fP5+qrr+aJJ57oVACTJ0+mqKiIkpISPB4Pb7zxBhdffHGrbS655BIK\nCwvx+/04HA7WrVvHyJEjO7X/UJM3hX4k192XlBrNjHnDmPe9MQwblUZEpJnGOhdVhxtxNnnavGpq\nfy3WAf6z/hP+/H+/oK6+WrfH7Kl8K4qC3xfgv58VsWPToR55jN5IPk/0JfnWj+RaX3rku1MF+7Zt\n25gyZQoAS5cuZeXKlaxbt45nn322Uw9iNBpZsmQJ5557LiNHjuSqq65ixIgRPPfcczz33HMA5Ofn\nM2/ePMaOHcsZZ5zBrbfe2msKdiF6C0VRSMuMZdZFI5h76Shy8lMxW4zU1zqxVdhxOb1tFu790ZTJ\nsxmYmcPjv7uDr75ZE+pwTpmiKCiqwraNh1i7qpiAX2YPEkKI3qJTLTEJCQnYbDZKSko455xzKC4u\nRtM0YmJisNv1ne9XWmL6N8l1cGkBjdK9NWz5+iAVZfW4nL5WV03tzy0xR+3bv5P/e+03ZA3M5Yff\nu4uoqNgeeyy98h3wBYhLjGTGvOFYrMYef7xwJZ8n+pJ860dyra+waYmZNm0ad911Fw888ACXXXYZ\n0DytY0pKyikHJ4QIHUVVGJybxHnfG0PBvOEMyIoHmvvda21NMoc7kD04n0d/8hdiYxJ49c0/hjqc\noFCNKvV1Tla8s5VaW3hdPEoIIcSJOjXCbrPZePrppzGbzfz0pz8lOjqaDz/8kKKiIu677z494mwR\njiPsQvQVXo+Pou2VbP+mjJoqB16Pj4goMzFxVgxGmcPd5/dhNPSdEWlN01AVhXFnDCJneGqowxFC\niH6toxH2ThXs4UQKdiF6nsvpZefmw+zcdJj6Wic+ufhSnxYIaAwemsikadkyR78QQoTIKbfEuFwu\nHnroIXJycoiNbe7fXLFiBUuWLAlelL3YsfNvip4ludaHNcLE+DOySBrSxISpWcQlROByeKk83Ii9\nwUUg0Ku+5/eopqYGPB53UPZ1dB51vamqwv491axcth23yxuSGEJBPk/0JfnWj+RaX3rku1MF+/33\n38/WrVt57bXXUNXmu4waNYpnnnmmR4MTQoRWRKSZ02fkcOH8cYyZPJDoWCtNjR6qDjfgsLtlRhmg\ncP0n/PLpH1FSujvUoZwS1aBSV9vc126raAx1OEIIIY7RqZaY9PR09uzZQ3R0NAkJCdTW1gIQFxdH\nfX19jwd5LGmJESJ0bOWNbN5wkNK91TjtHhRVITY+AkuEUdcLDIUTTdNYv3EV/3jnL8ycdiEXnPPD\nXt3nfvRCeaMmDGD4mPRQhyOEEP3GKbfEWCwWfD5fq3VVVVUkJyefenRCiF4jOT2Gsy/I55xLR5OT\nn4LZYqSuxkF1pR2P23fyHfRBiqJwxqRZ/OKnz7KvdBdP/uEeyg6XhDqsbjv6xWvL1wf5cuUe/DJf\nuxBChFynCvYrrriCG264gb179wJw+PBh7rrrLubPn9+jwfUW0iumH8m1vtrKt6IoZGbFM/fS0Zx9\nQT4DhySgKgrVlU3U2prwef0hiDT04uOSuPe2J5hx5gV8u/W/3dpHqHrY26KqCgf31/HZe9twNAWn\nRz/cyOeJviTf+pFc6ytsetifeOIJsrOzGTt2LPX19eTm5pKRkcGjjz7a0/EJIcKUqipkD0vhvCvG\nMn3uMNIyY/D7AlSVN1Jf4+iXI7OKolBw5gVcMPcHoQ4lKAwGBXujm0/f2cbhg/q2PwohhPhOl6Z1\n1DStpRXm6MmnepMediHCk8vpZcemQ+zc3DwVZMCnERVrISrGIlMF9nKapoEGw8ekM2rigH57voIQ\nQqp6uIUAACAASURBVPSkU+5hP0pRFFJTU0NWrAshwpc1wsSEKYO58KrxjD89i5h4K067zChzVGnZ\nHpocvXP2FUVRUFSFHZvLKVxRhE+ugCuEELqSyjsIpFdMP5JrfXUn3zFxVqacPZTzrxjL8LHpRESZ\naahzYStvxOX09tvCfdPWL3nsNwvYsfubdrcJpx72thgMCuWH6lnxzlbs9a5Qh3PK5PNEX5Jv/Uiu\n9RU2PexCCNFVSanRzDw/n7mXjCJ7WAomk5Fam4OayqZ+OaPMRedey3VX3c//vbaYf777HF6vJ9Qh\ndYvBoOJ0ePjs/e0c3FcT6nCEEKJf6FIPeziQHnYhep+AP0DJnmq2fHWQyvIGPG4/1kgjsXERGIz9\na9yg0V7Pq//8Hyqryrj52gcZlJkT6pC6LRDQGJqfwvjTs1DkPAUhhDglHfWwGxYtWrToZDsYP348\nTqeTnJwcoqOjgx1fl+zbt4+MjIyQxiCE6BpFVUhIjmJofipR0RaaGt04Gj3YG9xogMls6DcnMlrM\nViaPL8BstqCgkJqcGeqQuk1RFGoq7VQebmDgkAQMhv715UsIIYLp8OHD5OS0PYjTqU/XRx99lC++\n+IKcnBzOO+88/v73v+Ny9f7+xWCRXjH9SK71Fex8m8wGRk7I5MKrxjJhSvOJqQ67B9vhRpxNnn7T\n364oCtNOP5dR+ZNbrQ/3Hva2qAaV6ko7n7y9jbrqplCH0yXyeaIvybd+JNf6Cpse9ssvv5x33nmH\nAwcOcMkll/DMM8+Qnp7OjTfeyMqVK3s6RiFEHxMZbeH0ghzOv2Isw0anYYkwUV/r7NdXTO3NVIOK\n2+1l1Yc7Kd5ZGepwhBCiz+lyD7vD4eDtt99m8eLFlJaWkpqaiqIo/PnPf2bu3Lk9FWcL6WEXom/R\nAhoH9tXw7foDVJbV4+7H/e0AG779ghHDJhAVGRPqULpF82sMGprI5GlDUKVFRgghOu2U52HXNI3l\ny5dzzTXXkJGRwauvvsqDDz5IeXk5RUVFPPXUU1x77bVBDVoI0T8oqkLW0CTO+/4YzpyTR0p6DD5P\ngKrDjTTWuwgE+kebDDR/1haXbD/p9I/hTDEolO6p5rP/z959h0dVpg8f/54zfSa9QEIqIUDoHaki\na2FVUAQUrD9XLFjWVXGNBVzLogsuiroLou+ua19ZRFgLiIogqCtFgdBreu+Zmpk58/4xyUhMAgGS\nSSZ5PteVi8zMyZl7nhxO7nnmfu7zyUHsNmd7hyMIgtAptChhj4mJYf78+QwaNIj9+/fzxRdfcOON\nN2IwGABvyUxaWlqbBtqRiVox/xFj7V/+HG+NRkX/oT2YOmdIl61vP3J8L7Onz+OWOQ952z+uW4nT\nFXjtH2W1THWljY0f76O4oLq9w2mWOJ/4lxhv/xFj7V8dpob9s88+Y//+/aSnpxMfH9/kNps3b27N\nuARB6KKMJq2vvr3vqfXtRV2nvn1g2kj+9MeVlJQVsGjpfRQW57Z3SGdNliWcTjdbNx7lwO78LvGG\nSxAEoa20qIY9IiKC8vLGF8jo1q0bxcX+XWAkatgFoeuor2/fsz2HolPq24NDDai7QH27x+Phhx1f\n0r/vCMJCI9s7nHOmuBViE8IYc1GvLrkuQRAEoSXOu4bd6Wxch+h0OnG73ecXmSAIwml09fp2SZIY\nN/qygE7WwdtFpiC7ko1r92OuFi2BBUEQztZpE/aJEycyceJEbDab7/v6rz59+jB27Fh/xdmhiVox\n/xFj7V8dZbzVp9a3j00kNMyA1VxLSUE11k5U3x6IfdhbSlbLWC0OvvrvAXJONv7Etj10lOO7qxDj\n7T9irP3LH+OtPt2Dc+fOBWDHjh3cfvvtvj+KkiTRvXv3ZqftBUEQ2oLRpGX0hSn06teNPT/mkH28\njOoKG9YaByHhBrS6057SOg1FcbPh61VMnngVBr2pvcNpMUmSUBQPP245QX5WJSMnJIsSGUEQhBZo\nUQ37oUOHOkwXGFHDLggCeOvbc7Mq2PNjDoV5VTjsLvQGNcFhetRqVXuH16aczlr+/fFy9h/axdyb\n0umdMrC9QzprbrcHU5CWcb/pRVhk4LzpEARBaCunq2FvNmF/5513fL3V//GPfyBJUpM7uO2221op\nzJYRCbsgCKdyuRSO7S8iY1cu5SUWXC6FoGAdphAdstz0eauz2LPvB95etYzxF0zhqik3o1Zr2juk\ns+LxeJBlibTBsaQNjm3274wgCEJXcE6LTj/44APf9++8806zX4KoFfMnMdb+FQjjrVbLpA2JZeqc\nIYwYn0RouAGbpa6+3RxY9e1nW8M+ZOBYnvzja+TmneD5l/9AdU1FG0XWNiRJwuOBfT/ls2X9Yb+3\n7QyE47szEePtP2Ks/atda9g///xz3/eix7ogCB2dwahl5ISe9Errxp7tOWQeK6W60obF7CAkzIBO\n3znr20ODw/n9Hc/y095tBJlC2jucc6JSSZQWm/lizT5GTkgiNiG8vUMSBEHoUJotiVEUpUU7kGX/\nLhgSJTGCIJyJx+MhL6uSPduzKcjx1rfr9GpCwvSoNZ27vj2QeTwe8EBSaiTDxyYhq8SCVEEQuo7T\nlcQ0O+WkVp95NkqSJNGLXRCEDkeSJOKTw4mND+XYwWIyduZSXmKmpLAGU7COoBB9p69vD0SSJIEE\nmUdKKSsyM+6S3gSH6ts7LEEQhHbX7PTFiRMnzvh1/Phxf8baYYlaMf8RY+1fgT7eKrVM30ExTJ0z\nhJETkgmLMGK3OinJr8ZidnS4+vbW7sNeVV3OW/9+EbOlulX329ZktYzZ7OCr/+7n6IGiNnueQD++\nA40Yb/8RY+1f7VrDnpyc3OZPLgiC4A96g4bh45JJqa9vP1KKudKOtaaWkHA9On1gdVdpKaMhCIPe\nxNNL7uL/5jzEwH6j2jukFqtfkLrnxxwKcqoYO7kXGq0oZxIEoWtqtob9jjvu4I033gDwtXds9MOS\nxNtvv9120TVB1LALgnA+PB4PBTlV7NmeTX52JXabC51eRUiYodPWtx86upt/vv8Cg/tfwLVX3YFO\nZ2jvkM6K4lbQGTRccGEK3XoE5sJaQRCEMzmnto4pKSm+73v16kVqaiq9evVq9NVSGzZsIC0tjd69\ne7N48eJmt9uxYwdqtZo1a9a0eN+CIAgtJUkSPRLDuOyagVw4pS+x8SEobigprKGqworibtmC+0CS\n1nsoTz3yOo5aO8++eC9OZ217h3RWZJVMrcPF1o1H+OmHrE75OxIEQTidFl3p9Hy53W769u3LV199\nRVxcHKNGjeKDDz6gX79+jba79NJLMRqN/O53v2PmzJmN9tURZ9i3bdvGhAkT2juMLkGMtX91hfF2\n2J0c3F3AgT35VFfYUBQPwaF6jEFav1/I5/CxPfRNHdKmz1FQmE1sTGKbPkdbUlwKQaF6xl6cSmjY\n+X1S0BWO745EjLf/iLH2r9Ya73OaYf+1r7/+mttvv50rrriCO+64g6+++qrFAWzfvp3U1FSSk5PR\naDTMmTOHdevWNdru1VdfZdasWURHR7d434IgCOdDp9cwdEwiU2cPYeDwOEzBOsxVdkoKarDbnB1u\nYer5CuRkHbwLUi1mB5v+e4CDu/M73e9HEAShKS1K2JcuXcr1119PZGQkV155JREREdx444389a9/\nbdGT5OXlkZCQ4LsdHx9PXl5eo23WrVvH3XffDRBQl6gW72L9R4y1f3Wl8Q4JMzD+0t5MuWYgKWnR\naHVqKkqtlJdYcNb6p31tW8+un04gJb6SJOEB9v+cxzefHcRuc57TfrrS8d0RiPH2HzHW/uWP8W7R\npf+WLl3Kpk2bGDhwoO++W265hUsuuYSHH374jD/fkuT7gQce4C9/+UtdZwDPaf943HvvvSQmemeJ\nQkJCGDRokG+w6lvriNvitrgtbp/t7e+++w6AS68ex8mjpax6/zOqCqwkxKZhMGrJLz2MSiX7Euv6\nNoyBfluj0bJq7UomjZtKRHh0u8fT0ttHT2agHPdQU2VnyOhEcosOAR3neBK3xW1xW9w+3e2MjAyq\nq71td7Ozs5k7dy7NaVENe1xcHMeOHcNg+KVe0GazkZqa2mimvCn/+9//eOqpp9iwYQMAzz//PLIs\nk56e7tsmJSXFl6SXlpZiNBp54403uOqqqxrsS9Swd21irP2rq493rcPF4YxCDvycR2W5DbdLwRSi\nwxSsa5MLL/mjhr0piqKw+btP+O+Gd7jikjlcMukaZDmwOuYoboXYhDBGT0pB08JuP139+PY3Md7+\nI8bav1prvM+phl1RFN/XU089xe23386RI0ew2WwcPnyYO++8k6effrpFAYwcOZKjR4+SmZlJbW0t\nH374YaNE/MSJE5w8eZKTJ08ya9YsVqxY0WgbQRAEf9Lq1AwaGc/UOUMZekECwWF6rOZaSgqqsZpr\nA6qM5HRkWeY3E6/m8QdfYfe+H1jy6nwKi3PbO6yzIqtk8nMq2fBRBkX5Ve0djiAIQqtqdoZdls9c\n3i5JEm53y2o7169fzwMPPIDb7Wbu3Lk89thjrFy5EoC77rqrwba/+93vmDZtGjNmzGi0n444wy4I\nQtdQVmxm744cso6VYbXUolLLhIR1rgsvKYrCpm3r+O7HL1g4/+8BN9Pu8XjAA0m9oxg+JhFZ1eLe\nCoIgCO3qdDPszSbsmZmZLdq5v6+IKhJ2QRDak8fjIS+rgr3bcynI/eXCS8FhhhaXYgQCl9uFWqVu\n7zDOmeJSMIXoGXdxL0LDje0djiAIwhmdU0lMcnJyi76EXxYSCG1PjLV/ifFuTJIk4pMjmDJjIBOn\n9CE2PhRFgdLCGirLrbjP46I+9YsqO4JATtbB2/7RanHw9ScH2f9THh6l8dyUOL79S4y3/4ix9i9/\njHeLz8jr1q1jy5YtlJWVoSiKr/PL22+/3WbBCYIgdFQqtUyfATEk9Yri0N4CDu7Op7LCSkl+DUGh\nOkxBOqQ2WJjanlwuJxWVpURHxbZ3KC1S/3fqwO58ck6WM2piTyK7BbVzVIIgCGevRcV9Tz/9NHfd\ndReKorBq1SqioqL44osvCAsLa+v4AoJYie0/Yqz9S4z3men0aoaMTuDK2UMYMiqB4FA9lhoHxQU1\n2KxntzC1Pfuwt0RWzlEWvXQfX337MYpy7p8k+Juq7mJLmz8/xA+bjuGsdQHi+PY3Md7+I8bav/wx\n3i1q65iYmMhnn33GoEGDCAsLo7Kyku3bt/Pss8/yySeftHmQpxI17IIgdGQlhTXs2Z5DzolybNZa\nNBoVIeF6NNrALjGpV1icy5sf/BWVrOLWOQ/RLTquvUM6K263gk6nZsCwOFLSogPqIn2CIHRu51TD\nfqqqqioGDRoEgFarpba2ltGjR7Nly5bWizKAiVox/xFj7V9ivM9edEwwF0/tx+Qr04hLCgcJSovM\nVJadub69I9WwNyemWzzpv1/KsEHjeG7Z/Xz25fsoin+uBNsaVCoZl0vh5/9l8fKS96iqtLV3SF2G\nOJ/4jxhr/+owNewpKSns37+fAQMGMGDAAFasWEF4eDgRERFtHZ8gCELAkWSJ5N5RxCWFczijkP0/\n5VFRbqWkoIagED2mYG1Az+zKsopLL5rJsMHj+X77l0hS4LVOlFUyVrODr9btJ6lXFMPGJKJSB97r\nEASha2hRScxnn31GUFAQkyZN4scff+SGG27AbDazfPlyZs6c6Y84fURJjCAIgcZcbSdjZy5HDxRj\nqbEjSRIhYQZ0BnVAJ+6dhdulYDBqGTI6noSUyPYORxCELuqc+rB3VCJhFwQhUBUXVLP7x2xyT1Zg\ntzrR6FSEhBnQaDtP//ZAprgVIrsFccGkFIxBuvYORxCELua8a9gBjhw5wp///GfuueceFi1axJEj\nR1otwEAnasX8R4y1f4nxbl3dYkO45KoBXHRFGj0Sw8ADpUU1VJVbUdxKQNSwt0RJWQFvvPM8lVVl\n7R3Kaf16vGWVTHmJhS8+3sfeHTko59FTX2hMnE/8R4y1f/ljvFuUsL///vsMHz6cjIwMgoKC2Lt3\nL8OHD+e9995r6/gEQRA6FVmWSOkbzRXXDeaCi1KIiDbhsLvq2kA6z6oNZEcVGhxBVEQMTy25i83f\nfRpQLSAlWcLjgcMZhWxYs4+8rPL2DkkQBKFlJTE9e/bkrbfe4sILL/Tdt3XrVm6++WYyMzPbMr5G\nREmMIAidSXWljYwduRw7VIy1xoGskggOM6DTB359e17BSd768CVkSeaW2Q/SIyapvUM6Kx6PB4/b\nQ1iUiRHjkgiPMrV3SIIgdGLnXRJjNpsZO3Zsg/vGjBmDxWI5/+gEQRC6sJAwA+Mv7c2UawaSkhaN\nRqOiotRKeYkFZ23gtEtsSlxsTx69/yVGD5/MSysexWoLrL8ZkiQhq2WqKqxs+vQgWzcewWatbe+w\nBEHoglqUsD/00EM89thj2GzefrVWq5XHH3+cBx98sE2DCxSiVsx/xFj7lxhv/4mJD8UYVcmkBvXt\ndf3bXYFTUvJrsqziNxOvZtET/8Jo6Fgz1C1dMyBJEpIsUZRfzYbVGezclhnwb6bagzif+I8Ya/9q\n1z7sCQkJDW4XFhby8ssvEx4eTkVFBQCxsbE8/vjjbRuhIAhCFyHJEr3SupHQM8Lbv/3nPKrKbZQU\n1GAK0WEK1iHLgVkmo9UGftcVWZbwACePlpCfXUFq/+6kDYpBVon+7YIgtK1ma9g3b9585h+WJCZN\nmtTaMZ2WqGEXBKGrsNQ42LcrlyP7i7BUO/DgITjMgMGoCfj69nrbf/qGYYPHo1Fr2zuUs+Z2KhiD\ntQwcHkdir8hO8zsRBKF9iD7sgiAIAays2Mye7TlkHy/DaqlFpZa9F17St+hi1R1Wba2D199eRF5h\nFnOuuZshA8a0d0jnxO1SCA03MmxsItExwe0djiAIAeq8F53W1tby5JNP0rNnT3Q6HT179uTJJ5+k\ntlYsvgFRK+ZPYqz9S4y3fzU33pHdgph8ZRoXX9WfpF6RqOv6hZeXWHA5A7eWWqvVcd/tz3DjzPtY\ntXYlL7/+BEUluX57/tbqe69Sy9RU29iy/jCbPz+EucreKvvtbMT5xH/EWPtXh+nDnp6eztdff83K\nlSvZs2cPK1euZNOmTTzyyCNtHZ8gCIKAtwQxoWcEv505iIlT+hATF4Li9lBS6L3wkjuAL/IzsN8o\nnk5/nb69BvP8sj9w8MjP7R3SWZMkCVklUVZi5ou1+/hh0zHRUUYQhFbTopKYuLg49uzZQ1RUlO++\n0tJSBg8eTH5+fpsG+GuiJEYQBAEcdicHdxdwcE8+VRU2FMVDUIgOU5AOKUAXpgJUVpVhNAQF/CJV\nRfGgkiVi4kMZOiYRgzHwavQFQfCv05XEBHYBpCAIQhel02sYOiaRlLRoMnblcfxgEZYaB5aaWoLD\n9AG7MDUsNLK9Q2gV9R1l8rIrKcytEom7IAjnpUUlMddeey1XXXUVGzZs4ODBg6xfv56rr76aa6+9\ntq3jCwiiVsx/xFj7lxhv/zqX8Q4JMzD+4lQunzmY3gNi0Bs1VFfYKC0yY7c5CbC+As3KzjuGxVrT\nqvtsrRr20zk1cd+wOoMfvum6pTLifOI/Yqz9q137sJ9qyZIl/PnPf+a+++4jPz+fHj16cP3117Ng\nwYK2jk8QBEFogejYYC6e2o/crAoyduRSkFtJRakVrU5FSJgejTawP1Dds+9/bNq6jssvns3kiVcF\nXBtIX+Ke5Z1xj40PY+iYRPQGTXuHJghCADhjDbvL5WLu3LmsXLkSvV7vr7ia1VwNu8fjobi4GLfb\nHZAfAwudg8fjQaVS0a1bN3EcCu3G7VY4ebiEjF25lBaaqa11oTdqCA41oFYH7kV+8gpOsubTf5Jb\ncJLpl9/KBSMmI8uq9g7rnNTXuMcmhjH0ApG4C4LQCn3YY2Njyc7ORqNp/xNKcwl7UVERwcHBGI3G\ndohKEH5htVqpqamhe/fu7R2K0MXVOlwc2VfEgZ/zqCiz4nIpmIK1BAXrAvrqnEeOZ/DRJ/+P0JAI\n7rntT+0dznlR3AoqlYoeiWEMuSBBJO6C0IWddx/2Bx98sMP3XXe73SJZFzoEo9GI2x24vbFPJeog\n/au1x1urUzNwRBxTrx/KiPFJhEUYsFudFBfUYK52BGx9e59eg3j0D8u4YeZ957Uff9Swn4mskvHg\nIedkGevratxrqmztHVabEOcT/xFj7V8dpob9lVdeoaioiBdffJHo6GjfR/2SJJGdnd2mAbaUKD8Q\nOhJxPAodidGkZeSEnvTu352MnbmcOFzi7ShjdhASqkcfgB1lJEnqNB1loC5x93jIy6okP6uSsEgj\nfQfFEJcYHtBtOgVBaB0tKonZvHlzs49ddNFFrRjOmTVXElNQUEBsbKxfYxGE5ojjUejIivOr2bsj\nh5yTFdistajUMiGherR6dcAl7r/mqLXzyYZ3uHTyLEKDw9s7nHPm8XhQ3ArGID2JKRGkDY4J+IXD\ngiCc3nn3Yfd3Ui4IgiC0nW49Qrh4Wn9yTpazd2cuRXlVlNd1lAkO06MN4MRQUdy4FTdPPj+Xiy+c\nzmUXzUKvD7xySUmSUKlVOOxODu0t4PihYqK7BzNwRByhEYH3egRBOD8tqmF3OBwsXLiQ1NRUjEYj\nqampLFiwALvd3tbxdQqHDx/m6quvJjk5mZEjR/LZZ5/5HsvOziYyMpLExETf19KlS32Pr169mv79\n+zN06NAGNVInT57kt7/97RlrUAsLC7n//vvp378/SUlJjBkzhsWLF2O1WgGIjIwkMzOzdV+w0GmI\nOkj/8ud4S7JEYq9ILp85iAun9KVHYigAZUUWKkotuFyBuQ7DoDcxe/o8Fj68nOLSfB5fdCtff7sW\np7PxGqyOUMPeEiq1jKJ4KMyv4st1+/ly3X4yj5aiKIG1BkGcT/xHjLV/dZga9rvvvpsjR47w6quv\nkpiYSHZ2NosWLSIvL48333yzrWMMaC6Xi5tuuonbbruNtWvXsm3bNm644QY2b95Mr169fNtlZWU1\n+ija5XLxzDPPsHnzZnbv3k16ejrfffcdAI8++ijPPffcaT++rqioYMqUKYwZM4aNGzcSHx9PXl4e\ny5cvJysri379+rXNixYEIWCo1DK9B3QnuXckh/cVceDnfCpKLZQU1GAK0mEK0aEKwI4yUREx3H7T\no2TnHePjz96kR0wS/foMa++wzoskSUgqiepKGzu2nmTfT3nEJ4XTb2gPdPrA/VREEIQza1ENe0RE\nBMePHyc8/Jd6wPLycnr16kVFRUWbBvhrgVbDfvDgQaZMmdJgce6sWbMYMWIEjz32GNnZ2QwbNozi\n4mJUqob9hIuLi7n55pv54osvsNvtpKamkpuby7p169iyZQsvvvjiaZ970aJFbNiwga1btza7TWRk\nJLt27SI5Ofm8XqfQUEc9HgXhTKyWWg7uzudwRiHVlTYUxUNQiA5jkA5ZLH7scNxuBbVaJqpbMH0H\nxRAdGxzw6xAEoas67xr22NhYrFZrg4TdZrPRo0eP1omwja15e1er7WvGLSPOex+KonDw4MEG9w0Z\nMgSAyZMn8/TTTxMREUFUVBQVFRXk5+ezd+9e+vXrh9ls5sUXX2TdunVnfJ4tW7YwderU845XEISu\nw2jSMmJ8Mqn9u7P/pzyOHyzGXOPAUuMgOFSPwaTtNAmh1WYBPBgNQe0dyjlTqWQ8HigurKYwrwpT\nsI4eiWGkDY4VPd0FoRNp0eecN998M5dffjmvv/4669evZ+XKlVxxxRXccsstbNq0yfclNJaamkpU\nVBSvvvoqTqeTTZs28f3332OzefvsRkZGsmnTJvbu3cs333yD2WzmzjvvBECWZf76179y6623snz5\ncpYtW8bzzz/PnXfeSUZGBldffTWzZs3i0KFDTT53RUUFMTExfnutQucj6iD9qyONd2i4gXEXp3L5\nrEGkDY7BYNJSU2mnpKAGu9UZsD3cT/XVlo94/M//x8efvYnZUt3e4ZwX7yJVGbvNydEDRXz+n71s\n+vQg2cfLUNxKe4cHdKzju7MTY+1fHaaG/bXXXgPg+eef993n8Xh47bXXfI+BdyFkR9Qas+LnSqPR\n8O6775Kens7LL7/MsGHDmD59OjqdDgCTyeSbXY+Ojmbx4sX069cPi8WCyWTiwgsvZOPGjQDs27eP\nvXv38uyzzzJkyBA2bNhAbm4u999/v2+bU4WHh1NYWOi/FysIQqcTFRPMRVekkZ9dScbOXPKzK6ks\ns6LWygSHGtDqVAE74943dQhjR17K+q//zROLbmXCmMu5LMDbQQK+NQcVZRZ+3HKCPds1dIsNod/Q\nWELCDO0cnSAI56JFNeytZcOGDTzwwAO43W5uv/120tPTGzz+3nvvsWTJEjweD8HBwaxYsYLBgwc3\n2CbQatibMmXKFG688UZuueWWRo8VFxfTr18/MjMzCQ4O9t3v8XiYOnUqS5YsITo6msmTJ7N//34c\nDge9evUiNze30b6ee+451q9fz7ffftvsH1RRw942Aul4FISWUtwKmcfK2Lcrl+L8ahwON1qtClOI\nDl2A93Avqyjmi02r+HHXJp557B8Bn7T/mqJ4wOP95CQxNZKUvtFoNKoz/6AgCH5zuhp2vy39d7vd\n3HfffWzYsIEDBw7wwQcfNKrjTklJ4dtvv2Xv3r0sXLjQVxoS6A4cOIDdbsdqtfK3v/2NkpISrr/+\negB27drF0aNHURSF8vJyHn30USZOnNggWQd45513GDp0KAMGDCAiIgKbzcbhw4fZtm1bs8n2Pffc\nQ01NDffcc48voc/Pz2fBggWNxl4QBOFMZJVMSt9oLr92MBMv60NcYhiSLFFRaqW0yBzQpTKR4d24\nYeZ9PLfgrU6XrAPIsoSskqiptrNnew6ff7iHbRuPUlpYE7C/M0HoSvyWsG/fvp3U1FSSk5PRaDTM\nmTOn0cLJsWPHEhrq7QV8wQUXNDlrHIg+/PBD+vfvT1paGlu3bmXNmjVoNN7FQFlZWVx33XUk7DHM\nZQAAIABJREFUJSUxYcIEDAYDb7zxRoOfLysrY+XKlTz22GMAqNVqlixZwvTp03n44YdZvHhxk88b\nFhbGhg0b0Gg0XHrppSQlJTFjxgxCQ0Pp2bMnQEDPiAltT9RB+legjLdGo6Lv4FiunDOESZf3JaFn\nOGq1TGW5ldJCMzZLbUAkgU31YTcZg5vYEhwOW0C8ppZQq2Xcioeigiq++fwQ61dnsHNbJtWVtjZ9\n3kA5vjsDMdb+1WFq2FtDXl4eCQkJvtvx8fH8+OOPzW7/j3/8gyuuuMIfobW5p59+mqeffrrJx2bM\nmMGMGTNO+/ORkZG+/uv1Zs2axaxZs8743DExMbzyyivNPl5aWnrGfQiCIDRFo1HRu393UvpEk3W8\njAO78ynOr6aqwkZNlZ2gED0Gk6ZTTAx8/tW/2b3vey658BouGHExWq2uvUM6b96FqhJ2m5PMY6Vk\nHi0hONRAbEIovQd0x2DUtneIgiDU8VvCfjYn7G+++YZ//vOfjZLUevfeey+JiYkAhISEMGjQoAYX\nIRKEjqL+XfeECRMC8nb9fR0lns5+u/6+jhLP2dxO6RtNXtEhHFQTq0qkMLeKPRk7ARg8cARGk5Yj\nJ/YC3sWe8MsMd3vdrr+vJdtPv+JWDIYgtv5vA2s+e5OJYy4nIb4XIUFhHeb1nM9tWZY4fMz7+0mt\nGsSxA0XkFh0mOjaYWbOvQKNVd+njO9BuT5gwoUPF09lvn+t4Z2RkUF3t7VCVnZ3N3LlzaY7fFp3+\n73//46mnnmLDhg2At+OMLMuNFp7u3buXGTNmsGHDBlJTUxvtpzMsOhU6P3E8Cl2ZR/GQm1XBwT35\n5GdVYrPWggdMoXqMJm3AX4CpqCSXTd+uY8fuLSx64k0MelN7h9Rm3E43Gq2a0AgjKX2jiE+OQKUO\nvCvfCkIg6BCLTkeOHMnRo0fJzMyktraWDz/8kKuuuqrBNtnZ2cyYMYN33323yWRdEAT/EnWQ/tVZ\nxluSJRJ6RnDpVQOYMmMgfQbGYAzSYal2UJJfTU2VHXcH6A3eVA17S3SPjuf6mfey+E/vdupkHUCl\nUaF4PJSXmvlxywk+W7WHrRuPUJhbhUc5u/m+znJ8BwIx1v7VqWrY1Wo1f/vb35gyZQput5u5c+fS\nr18/Vq5cCcBdd93FM888Q0VFBXfffTfg7WG+fft2f4UoCIIgtCJJloh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mDqFv6hB6JvVt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BCiCzp37hxlZWUkJCR433O73Xzve9/zSZeSkuJ9HhUV5fM6MjKS2tpa7+s+ffp4n2dk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\nAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The *95% credible interval*, or 95% CI, painted in purple, represents the interval, for each temperature, that contains 95% of the distribution. For example, at 65 degrees, we can be 95% sure that the probability of defect lies between 0.25 and 0.75.\n",
      "\n",
      "More generally, we can see that as the temperature nears 60 degrees, the CI's spread out over [0,1] quickly. As we pass 70 degrees, the CI's tighten again. This can give us insight about how to proceed next: we should probably test more O-rings around 60-65 temperature to get a better estimate of probabilities in that range. Similarly, when reporting to scientists your estimates, you should be very cautious about simply telling them the expected probability, as we can see this does not reflect how *wide* the posterior distribution is."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### What about the day of the Challenger disaster?\n",
      "\n",
      "On the day of the Challenger disaster, the outside temperature was 31 degrees Fahrenheit. What is the posterior distribution of a defect occurring,  given this temperature? The distribution is plotted below. It looks almost guaranteed that the Challenger was going to be subject to defective O-rings."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 2.5)\n",
      "\n",
      "prob_31 = logistic( 31, beta_samples, alpha_samples )\n",
      "\n",
      "plt.xlim( 0.995, 1)\n",
      "plt.hist( prob_31, bins = 1000, normed = True, histtype='stepfilled' )\n",
      "plt.title( \"Posterior distribution of probability of defect, given $t = 31$\")\n",
      "plt.xlabel( \"probability of defect occuring in O-ring\" );\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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nERcXh/DwcKSlpSE0NBRxcXEAgJSUFGzbtg0pKSlISkrCvHnzIIQAAMTExCAh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\n5n8BRf137Q3kmtoAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Is our model appropriate?\n",
      "\n",
      "The skeptical reader will say \"You deliberately chose the logistic function for $p(t)$ and the specific priors. Perhaps other functions or priors will give different results. How do I know I have chosen a good model?\" This is absolutely true. To consider an extreme situation, what if I had chosen the function $p(t) = 1,\\; \\forall t$, which guarantees a defect always occurring: I would have again predicted disaster on January 28th. Yet this is clearly a poorly chosen model. On the other hand, if I did choose the logistic function for $p(t)$, but specified all my priors to be very tight around 0, likely we would have very different posterior distributions. How do we know our model is an expression of the data? This encourages us to measure the model's **goodness of fit**.\n",
      "\n",
      "We can think: *how can we test whether our model is a bad fit?* An idea is to compare observed data (which if we recall is a *fixed* stochastic variable) with artificial dataset which we can simulate. The rational is that if the simulated dataset does not appear similar, statistically, to the observed dataset, then likely our model is not accurately represented the observed data. \n",
      "\n",
      "Previously in this Chapter, we simulated artificial dataset for the SMS example. To do this, we sampled values from the priors. We saw how varied the resulting datasets looked like, and rarely did they mimic our observed dataset. In the current example,  we should sample from the *posterior* distributions to create *very plausible datasets*. Luckily, our Bayesian framework makes this very easy. We only need to create a new `Stochastic` variable, that is exactly the same as our variable that stored the observations, but minus the observations themselves. If you recall, our `Stochastic` variable that stored our observed data was:\n",
      "\n",
      "    observed = mc.Bernoulli( \"bernoulli_obs\", p, value = D, observed=True)\n",
      "\n",
      "Hence we create:\n",
      "    \n",
      "    simulated_data = mc.Bernoulli(\"simulation_data\", p )\n",
      "\n",
      "Let's simulate 10 000:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "simulated = mc.Bernoulli( \"bernoulli_sim\", p)\n",
      "N = 10000\n",
      "\n",
      "mcmc = mc.MCMC( [simulated, alpha, beta, observed ] )\n",
      "mcmc.sample( N )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  10000 of 10000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 57
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 5)\n",
      "\n",
      "simulations = mcmc.trace(\"bernoulli_sim\")[:]\n",
      "print simulations.shape\n",
      "\n",
      "plt.title( \"Simulated dataset using posterior parameters\")\n",
      "figsize( 12.5, 6)\n",
      "for i in range(4):\n",
      "    ax = subplot( 4, 1, i+1)\n",
      "    plt.scatter( temperature, simulations[1000*i,:], color = \"k\", \n",
      "        s = 50, alpha = 0.6 );\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "(10000L, 23L)\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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gL4vDhw87fGxI7pw/+OCDaNeuXb3Px8TEWMZpDho0CHl5ebh16xYAoLKyEnv2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\nU48AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Note that the above plots are different (if you can think of a cleaner way to present this, please send a pull request and answer [here](http://stats.stackexchange.com/questions/53078/how-to-visualize-bayesian-goodness-of-fit-for-logistic-regression)!).\n",
      "\n",
      "We wish to assess how good our model is. \"Good\" is a subjective term of course, so results must be relative to other models. \n",
      "\n",
      "We will be doing this graphically as well, which may seem like an even less objective method. The alternative is to use *Bayesian p-values*. These are still subjective, as the proper cutoff between good and bad is arbitrary. Gelman emphasises that the graphical tests are more illuminating [7] than p-value tests. We agree.\n",
      "\n",
      "The following graphical test is a novel data-viz approach to logistic regression. The plots are called *separation plots*[8]. For a suite of models we wish to compare, each model is plotted on an individual separation plot. I leave most of the technical details about separation plots to the very accessible [original paper](http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf), but I'll summarize their use here.\n",
      "\n",
      "For each model, we calculate the proportion of times the posterior simulation proposed a value of 1 for a particular temperature, i.e. compute $P( \\;\\text{Defect} = 1 | t, \\alpha, \\beta )$ by averaging. This gives us the posterior probability of a defect at each data point in our dataset. For example, for the model we used above:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "posterior_probability = simulations.mean(axis=0)\n",
      "print \"posterior prob of defect | realized defect \"\n",
      "for i in range( len(D) ):\n",
      "    print \"%.2f                     |   %d\"%(posterior_probability[i], D[i])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "posterior prob of defect | realized defect \n",
        "0.44                     |   0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "0.26                     |   1\n",
        "0.29                     |   0\n",
        "0.35                     |   0\n",
        "0.39                     |   0\n",
        "0.19                     |   0\n",
        "0.16                     |   0\n",
        "0.26                     |   0\n",
        "0.82                     |   1\n",
        "0.59                     |   1\n",
        "0.26                     |   1\n",
        "0.07                     |   0\n",
        "0.39                     |   0\n",
        "0.91                     |   1\n",
        "0.39                     |   0\n",
        "0.12                     |   0\n",
        "0.26                     |   0\n",
        "0.04                     |   0\n",
        "0.10                     |   0\n",
        "0.06                     |   0\n",
        "0.12                     |   1\n",
        "0.10                     |   0\n",
        "0.79                     |   1\n"
       ]
      }
     ],
     "prompt_number": 65
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next we sort each column by the posterior probabilities:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ix = np.argsort( posterior_probability )\n",
      "print \"probb | defect \"\n",
      "for i in range( len(D) ):\n",
      "    print \"%.2f  |   %d\"%(posterior_probability[ix[i]], D[ix[i]])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "probb | defect \n",
        "0.04  |   0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "0.06  |   0\n",
        "0.07  |   0\n",
        "0.10  |   0\n",
        "0.10  |   0\n",
        "0.12  |   1\n",
        "0.12  |   0\n",
        "0.16  |   0\n",
        "0.19  |   0\n",
        "0.26  |   1\n",
        "0.26  |   0\n",
        "0.26  |   0\n",
        "0.26  |   1\n",
        "0.29  |   0\n",
        "0.35  |   0\n",
        "0.39  |   0\n",
        "0.39  |   0\n",
        "0.39  |   0\n",
        "0.44  |   0\n",
        "0.59  |   1\n",
        "0.79  |   1\n",
        "0.82  |   1\n",
        "0.91  |   1\n"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can present the above data better in a figure: I've wrapped this up into a `separation_plot` function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from separation_plot import separation_plot\n",
      "\n",
      "figsize( 11., 1.5 )\n",
      "\n",
      "separation_plot(posterior_probability, D )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 80
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The snaking-line is the sorted probabilities, blue bars denote defects, and empty space (or grey bars for the optimistic readers) denote non-defects.  As the probability rises, we see more and more defects occur. On the right hand side, the plot suggests that as the posterior probability is large (line close to 1), then more defects are realized. This is good behaviour. Ideally, all the blue bars *should* be close to the right-hand side, and deviations from this reflect missed predictions. \n",
      "\n",
      "The black vertical line is the expected number of defects we should observe, given this model. This allows the user to see how the total number of events predicted by the model compares to the actual number of events in the data.\n",
      "\n",
      "It is much more informative to compare this to separation plots for other models. Below we compare our model (top) versus three others:\n",
      "\n",
      "1. the perfect model, which predicts the posterior probability to be equal 1 if a defect did occur.\n",
      "2. a completely random model, which predicts random probabilities regardless of temperature.\n",
      "3. a constant model:  where $P(D = 1 \\; | \\; t) = c, \\;\\; \\forall t$. The best choice for $c$ is the observed frequency of defects, in this case 7/23.  \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 11., 1.25 )\n",
      "\n",
      "# our temperature-dependent model\n",
      "separation_plot(posterior_probability, D )\n",
      "plt.title(\"Temperature-dependent model\")\n",
      "\n",
      "# perfect model\n",
      "# i.e. the probability of defect is equal to if a defect occurred or not.\n",
      "p = D\n",
      "separation_plot( p, D)\n",
      "plt.title(\"Perfect model\")\n",
      "\n",
      "# random predictions\n",
      "p = np.random.rand( 23 )\n",
      "separation_plot( p, D)\n",
      "plt.title(\"Random model\")\n",
      "\n",
      "# constant model\n",
      "constant_prob = 7./23*np.ones(23)\n",
      "separation_plot(constant_prob, D )\n",
      "plt.title(\"Constant-prediction model\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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      },
      {
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       "output_type": "display_data",
       "png": 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7EEREREREJNv/AXNxXnG3rmkWAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 91
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the random model, we can see that as the probability increases there is no clustering of defects to the right-hand side. Similarly for the constant model.\n",
      "\n",
      "The perfect model, the probability line is not well shown, as it is stuck to the bottom and top of the figure. Of course the perfect model is only for demonstration, and we cannot infer any scientific inference from it."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Exercises\n",
      "\n",
      "1\\. Try putting in extreme values for our observations in the cheating example. What happens if we observe 25 affirmative responses? 10? 50? "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2\\. Try plotting $\\alpha$ samples versus $\\beta$ samples.  Why might the resulting plot look like this?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#type your code here.\n",
      "figsize(12.5, 4 )\n",
      "\n",
      "plt.scatter( alpha_samples, beta_samples, alpha = 0.1 )\n",
      "plt.title( \"Why does the plot look like this?\" )\n",
      "plt.xlabel( r\"$\\alpha$\")\n",
      "plt.ylabel( r\"$\\beta$\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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4N2xoOvaXotRbvPUxu1JvR9uLmixtK+pkm7IR/WAwyPe+9z2uueYaPM9jzZo1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\n"
      }
     ],
     "prompt_number": 90
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### References\n",
      "\n",
      "-  [1] Dalal, Fowlkes and Hoadley (1989),JASA, 84, 945-957.\n",
      "-  [2] German Rodriguez. Datasets. In WWS509. Retrieved 30/01/2013, from http://data.princeton.edu/wws509/datasets/#smoking.\n",
      "-  [3] McLeish, Don, and Cyntha Struthers. STATISTICS 450/850 Estimation and Hypothesis Testing. Winter 2012. Waterloo, Ontario: 2012. Print.\n",
      "-  [4] Fonnesbeck, Christopher. \"Building Models.\" PyMC-Devs. N.p., n.d. Web. 26 Feb 2013. <http://pymc-devs.github.com/pymc/modelbuilding.html>.\n",
      "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. <https://plus.google.com/u/0/107971134877020469960/posts/KpeRdJKR6Z1>.\n",
      "- [6] S.P. Brooks, E.A. Catchpole, and B.J.T. Morgan. Bayesian animal survival estimation. Statistical Science, 15: 357\u2013376, 2000\n",
      "- [7] Gelman, Andrew. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 2 Apr. 2013.\n",
      "- [8] Greenhill, Brian, Michael D. Ward, and Audrey Sacks. \"The Separation Plot: A New Visual Method for Evaluating the Fit of Binary Models.\" American Journal of Political Science. 55.No.4 (2011): n. page. Web. 2 Apr. 2013."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.core.display import HTML\n",
      "def css_styling():\n",
      "    styles = open(\"../styles/custom.css\", \"r\").read()\n",
      "    return HTML(styles)\n",
      "css_styling()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<style>\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
        "    }\n",
        "    div.cell{\n",
        "        width:800px;\n",
        "        margin-left:16% !important;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    h1 {\n",
        "        font-family: Helvetica, serif;\n",
        "    }\n",
        "    h4{\n",
        "        margin-top:12px;\n",
        "        margin-bottom: 3px;\n",
        "       }\n",
        "    div.text_cell_render{\n",
        "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
        "        line-height: 145%;\n",
        "        font-size: 130%;\n",
        "        width:800px;\n",
        "        margin-left:auto;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    .CodeMirror{\n",
        "            font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n",
        "    }\n",
        "    .prompt{\n",
        "        display: None;\n",
        "    }\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 300;\n",
        "        font-size: 16pt;\n",
        "        color: #4057A1;\n",
        "        font-style: italic;\n",
        "        margin-bottom: .5em;\n",
        "        margin-top: 0.5em;\n",
        "        display: block;\n",
        "    }\n",
        "    \n",
        "    .warning{\n",
        "        color: rgb( 240, 20, 20 )\n",
        "        }  \n",
        "</style>\n",
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
        "                           extensions: [\"AMSmath.js\"]\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
        "                }\n",
        "        });\n",
        "</script>"
       ],
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "<IPython.core.display.HTML at 0x50f8f98>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}