{ "metadata": { "name": "", "signature": "sha256:6d349ea64b8e4405dbdbcc86fe0989fa84f5bb12221f16825b5fd46491d78f8e" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction to PyMC\n", "\n", "While Markov chain Monte Carlo is a powerful method for fitting Bayesian models, they can be difficult to apply generally, as most commercial statistical analysis packages do not implement it. This has been an impediment to the growth of Bayesian methods. PyMC is a python module that implements Bayesian statistical models and fitting algorithms, including MCMC. Its flexibility and extensibility make it applicable to a large suite of problems. Along with core sampling functionality, PyMC includes methods for summarizing\n", "output, plotting, goodness-of-fit and convergence diagnostics.\n", "\n", "PyMC 2.3 provides functionalities to make Bayesian analysis as painless as possible. Here is a short list of some of its features:\n", "\n", "- Fits Bayesian statistical models with Markov chain Monte Carlo and\n", " other algorithms.\n", "- Includes a large suite of well-documented statistical distributions.\n", "- Uses NumPy for numerics wherever possible.\n", "- Includes a module for modeling Gaussian processes.\n", "- Sampling loops can be paused and tuned manually, or saved and\n", " restarted later.\n", "- Creates summaries including tables and plots.\n", "- Traces can be saved to the disk as plain text, Python pickles,\n", " SQLite or MySQL database, or hdf5 archives.\n", "- Several convergence diagnostics are available.\n", "- Extensible: easily incorporates custom step methods and unusual\n", " probability distributions.\n", "- MCMC loops can be embedded in larger programs, and results can be\n", " analyzed with the full power of Python.\n", " \n", "Before we dig into PyMC in detail, let's look at a simple hierachical linear model of a house's price as a function of age, to give you a flavor for what Bayesian models look like when implemented in PyMC. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "\n", "# Data\n", "age = np.array([13, 14, 14,12, 9, 15, 10, 14, 9, 14, 13, 12, 9, 10, 15, 11, 15, \n", " 11, 7, 13, 13, 10, 9, 6, 11, 15, 13, 10, 9, 9, 15, 14, 14, 10, 14, 11, 13, 14, 10])\n", "price = np.array([2950, 2300, 3900, 2800, 5000, 2999, 3950, 2995, 4500, 2800, 1990, \n", " 3500, 5100, 3900, 2900, 4950, 2000, 3400, 8999, 4000, 2950, 3250, \n", " 3950, 4600, 4500, 1600, 3900, 4200, 6500, 3500, 2999, 2600, 3250, \n", " 2500, 2400, 3990, 4600, 450,4700])/1000.\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "from pymc import Normal, Gamma, deterministic, MCMC, Matplot\n", "\n", "# Constant priors for parameters\n", "a = Normal('a', 0, 0.0001)\n", "b = Normal('b', 0, 0.0001)\n", "\n", "# Precision of normal distribution of prices\n", "tau = Gamma('tau', alpha=0.1, beta=0.1)\n", "\n", "@deterministic\n", "def mu(x=age, a=a, b=b):\n", " # Linear age-price model\n", " return a + b*x\n", "\n", "# Sampling distribution of prices\n", "p = Normal('p', mu, tau, value=price, observed=True)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example will generate 10000 posterior samples, thinned by a factor\n", "of 2, with the first half discarded as burn-in. The sample is stored in\n", "a Python serialization (pickle) database." ] }, { "cell_type": "code", "collapsed": false, "input": [ "M = MCMC(locals(), db='pickle')\n", "M.sample(iter=20000, burn=10000)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\r", " [-------- 21% ] 4368 of 20000 complete in 0.5 sec" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\r", " [---------------- 43% ] 8660 of 20000 complete in 1.0 sec" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\r", " [-----------------63%---- ] 12675 of 20000 complete in 1.5 sec" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\r", " [-----------------82%----------- ] 16557 of 20000 complete in 2.0 sec" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\r", " [-----------------100%-----------------] 20000 of 20000 complete in 2.4 sec" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "Matplot.plot(b)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Plotting b\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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rI0cCI0bE/z3ffLPp4duyxQST55xj1tv/C+ecA5xwgikZcdllZgjeBrBuQYZ/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\nC8AYzzZlAGoBLAOwDsDxSV5LnSQJtVKta+zxsNY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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Coal mining disasters\n", "\n", "Recall the earlier example of estimating a changepoint in the time series of UK coal mining disasters." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import matplotlib.pyplot as plt\n", "from pymc.examples.disaster_model import disasters_array\n", "\n", "plt.figure(figsize=(12.5, 3.5))\n", "n_count_data = len(disasters_array)\n", "plt.bar(np.arange(1851, 1962), disasters_array, color=\"#348ABD\")\n", "plt.xlabel(\"Year\")\n", "plt.ylabel(\"Disasters\")\n", "plt.title(\"UK coal mining disasters, 1851-1962\")\n", "plt.xlim(1851, 1962);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We represent our conceptual model formally as a statistical model:\n", "\n", "$$\\begin{array}{ccc} \n", "(y_t | \\tau, \\lambda_1, \\lambda_2) \\sim\\text{Poisson}\\left(r_t\\right), & r_t=\\left\\{\n", "\\begin{array}{lll} \n", "\\lambda_1 &\\text{if}& t< \\tau\\\\ \n", "\\lambda_2 &\\text{if}& t\\ge \\tau \n", "\\end{array}\\right.,&t\\in[t_l,t_h]\\\\ \n", "\\tau \\sim \\text{DiscreteUniform}(t_l, t_h)\\\\ \n", "\\lambda_1\\sim \\text{Exponential}(a)\\\\ \n", "\\lambda_2\\sim \\text{Exponential}(b) \n", "\\end{array}$$\n", "\n", "Because we have defined $y$ by its dependence on $\\tau$, $\\lambda_1$ and $\\lambda_2$, the\n", "latter three are known as the *parents* of $y$ and $D$ is called their\n", "*child*. Similarly, the parents of $\\tau$ are $t_l$ and $t_h$, and $\\tau$ is\n", "the child of $t_l$ and $t_h$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PyMC Variables\n", "\n", "At the model-specification stage (before the data are observed), $y$,\n", "$\\tau$, $\\lambda_1$, and $\\lambda_2$ are all random variables. Recall from the discussion of subjective probability that the Bayesian interpretation of probability is ***epistemic***, meaning random variable $x$'s probability distribution $p(x)$ represents our knowledge and uncertainty about $x$'s value, rather than some random generative process. Candidate\n", "values of $x$ for which $p(x)$ is high are relatively more probable, given what we know. Random variables are represented in PyMC by the classes Stochastic and Deterministic.\n", "\n", "The only Deterministic in the model is $r$. If we knew the values of\n", "$r$'s parents, we could compute the value of $r$\n", "exactly. A Deterministic like $r$ is defined by a mathematical\n", "function that returns its value given values for its parents.\n", "Deterministic variables are sometimes called the ***systemic*** part of\n", "the model. The nomenclature is a bit confusing, because these objects\n", "usually represent random variables; since the parents of $r$ are random,\n", "$r$ is random also.\n", "\n", "On the other hand, even if the values of the parents of variables\n", "switchpoint, disasters (before observing the data), early_mean\n", "or late_mean were known, we would still be uncertain of their values.\n", "These variables are characterized by probability distributions that\n", "express how plausible their candidate values are, given values for their\n", "parents. The Stochastic class represents these variables.\n", "\n", "First, we represent the unknown switchpoint as a discrete uniform random variable:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from pymc import DiscreteUniform, Exponential, Poisson, deterministic\n", "\n", "switchpoint = DiscreteUniform('switchpoint', lower=0, upper=110)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "switchpoint" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "markdown", "metadata": {}, "source": [ "DiscreteUniform is a subclass of Stochastic that represents\n", "uniformly-distributed discrete variables. Use of this distribution\n", "suggests that we have no preference *a priori* regarding the location of\n", "the switchpoint; all values are equally likely. \n", "\n", "Now we create the\n", "exponentially-distributed variables early_mean and late_mean for the\n", "early and late Poisson rates, respectively:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "early_mean = Exponential('early_mean', beta=1., value=3)\n", "late_mean = Exponential('late_mean', beta=1., value=1)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we define the variable rate, which selects the early rate\n", "early_mean for times before switchpoint and the late rate\n", "late_mean for times after switchpoint. We create rate using the\n", "deterministic decorator, which converts the ordinary Python function\n", "rate into a Deterministic object." ] }, { "cell_type": "code", "collapsed": false, "input": [ "@deterministic\n", "def rate(s=switchpoint, e=early_mean, l=late_mean):\n", " # Create a vector of Poisson means\n", " out = np.empty(len(disasters_array))\n", " out[:s] = e\n", " out[s:] = l\n", " return out" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The last step is to define the number of disasters disasters. This is\n", "a stochastic variable but unlike switchpoint, early_mean and\n", "late_mean we have observed its value. To express this, we set the\n", "argument observed to True (it is set to False by default). This\n", "tells PyMC that this object's value should not be changed:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "disasters = Poisson('disasters', mu=rate, value=disasters_array, \n", " observed=True)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Why are data and unknown variables represented by the same object?\n", "\n", "Since its represented by a Stochastic object, disasters is defined\n", "by its dependence on its parent rate even though its value is fixed.\n", "This isn't just a quirk of PyMC's syntax; Bayesian hierarchical notation\n", "itself makes no distinction between random variables and data. The\n", "reason is simple: to use Bayes' theorem to compute the posterior, we require the\n", "likelihood. Even though disasters's value is known\n", "and fixed, we need to formally assign it a probability distribution as\n", "if it were a random variable. \n", "\n", "Remember, the likelihood and the probability function are essentially the same, except that the former is regarded as a *function of the parameters* and the latter as a *function of\n", "the data*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Parents and children\n", "\n", "We have above created a PyMC probability model, which is simply a linked\n", "collection of variables. To see the nature of the links, we can examine any node's parents attribute:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "switchpoint.parents" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 11, "text": [ "{'lower': 0, 'upper': 110}" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The parents dictionary shows us the distributional parameters of\n", "switchpoint, which are constants. Now let's examine the parents of disasters and rate:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "disasters.parents" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 12, "text": [ "{'mu': }" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "rate.parents" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 13, "text": [ "{'e': ,\n", " 'l': ,\n", " 's': }" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are using rate as a distributional parameter of disasters\n", "(*i.e.* rate is disasters's parent). disasters internally\n", "labels rate as mu, meaning rate plays the role of the rate\n", "parameter in disasters's Poisson distribution. Now examine rate's\n", "children attribute:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "rate.children" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 14, "text": [ "{}" ] } ], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because disasters considers rate its parent, rate considers disasters its child. Unlike parents, children is a set (an unordered collection of objects); variables do not associate their children with any particular distributional role, so an index is not required. Try examining the parents and children attributes of the other parameters in the model.\n", "\n", "The following **directed acyclic graph** is a visualization of the parent-child relationships in the model. Unobserved stochastic variables switchpoint, early_mean and late_mean are open ellipses, observed stochastic variable disasters is a filled ellipse and deterministic variable rate is a triangle. Arrows point from parent to child and display the label that the child assigns to the parent." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from pymc import graph, MCMC\n", "graph.dag(MCMC([switchpoint, rate, early_mean, late_mean, disasters]))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 15, "text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "code", "collapsed": false, "input": [ "!dot MCMC.dot -Tpng -o images/dag.png\n", "from IPython.core.display import Image\n", "Image('images/dag.png')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "png": 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7kpkpoGDDRi0bwqXem8osSxz+B3D2NMODH3WlEwMBPjrx+0iYoNCXbVzqxb6v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\nusB0RowYYczyww8/tIG+ZcuWplWL6cXIkSOF+yjowJBQumH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"prompt_number": 16, "text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As the examples above have shown, PyMC objects need to have a name assigned, such as switchpoint, early_mean or late_mean. These names are used for storage and post-processing:\n", "\n", "- as keys in on-disk databases,\n", "- as node labels in model graphs,\n", "- as axis labels in plots of traces,\n", "- as table labels in summary statistics.\n", "\n", "A model instantiated with variables having identical names raises an\n", "error to avoid name conflicts in the database storing the traces. In\n", "general however, PyMC uses references to the objects themselves, not\n", "their names, to identify variables." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Variables' values and log-probabilities\n", "\n", "All PyMC variables have an attribute called value that stores the\n", "current value of that variable. Try examining disasters's value, and\n", "you'll see the dataset we provided for it:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "disasters.value" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 17, "text": [ "array([4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6, 3, 3, 5, 4, 5, 3, 1,\n", " 4, 4, 1, 5, 5, 3, 4, 2, 5, 2, 2, 3, 4, 2, 1, 3, 2, 2, 1, 1, 1, 1, 3,\n", " 0, 0, 1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0,\n", " 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2, 3, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2,\n", " 0, 0, 1, 4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you check the values of early_mean, switchpoint and late_mean,\n", "you'll see random initial values generated by PyMC:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "switchpoint.value" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 18, "text": [ "array(60)" ] } ], "prompt_number": 18 }, { "cell_type": "code", "collapsed": false, "input": [ "early_mean.value" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 19, "text": [ "array(3.0)" ] } ], "prompt_number": 19 }, { "cell_type": "code", "collapsed": false, "input": [ "late_mean.value" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 20, "text": [ "array(1.0)" ] } ], "prompt_number": 20 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, since these are Stochastic elements, your values will be\n", "different than these. If you check rate's value, you'll see an array\n", "whose first switchpoint elements are early_mean,\n", "and whose remaining elements are late_mean:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "rate.value" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 21, "text": [ "array([ 3., 3., 3., 3., 3., 3., 3., 3., 3., 3., 3., 3., 3.,\n", " 3., 3., 3., 3., 3., 3., 3., 3., 3., 3., 3., 3., 3.,\n", " 3., 3., 3., 3., 3., 3., 3., 3., 3., 3., 3., 3., 3.,\n", " 3., 3., 3., 3., 3., 3., 3., 3., 3., 3., 3., 3., 3.,\n", " 3., 3., 3., 3., 3., 3., 3., 3., 1., 1., 1., 1., 1.,\n", " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", " 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n", " 1., 1., 1., 1., 1., 1., 1.])" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "To compute its value, rate calls the function we used to create it,\n", "passing in the values of its parents.\n", "\n", "Stochastic objects can evaluate their probability mass or density\n", "functions at their current values given the values of their parents. The\n", "logarithm of a stochastic object's probability mass or density can be\n", "accessed via the logp attribute. For vector-valued variables like\n", "disasters, the logp attribute returns the sum of the logarithms of\n", "the joint probability or density of all elements of the value. \n", "\n", "Try examining switchpoint's and disasters's log-probabilities and\n", "early_mean 's and late_mean's log-densities:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "switchpoint.logp" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 22, "text": [ "-4.709530201312334" ] } ], "prompt_number": 22 }, { "cell_type": "code", "collapsed": false, "input": [ "late_mean.value = 5" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 23 }, { "cell_type": "code", "collapsed": false, "input": [ "disasters.logp" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 24, "text": [ "-318.0083429843733" ] } ], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "early_mean.logp" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 25, "text": [ "-3.0" ] } ], "prompt_number": 25 }, { "cell_type": "code", "collapsed": false, "input": [ "late_mean.logp" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 26, "text": [ "-5.0" ] } ], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Stochastic objects need to call an internal function to compute their\n", "logp attributes, as rate needed to call an internal function to\n", "compute its value. Just as we created rate by decorating a function\n", "that computes its value, it's possible to create custom Stochastic\n", "objects by decorating functions that compute their log-probabilities or\n", "densities (see chapter :ref:\\chap\\_modelbuilding\\). Users are thus not\n", "limited to the set of of statistical distributions provided by PyMC." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using Variables as parents of other Variables\n", "\n", "Let's take a closer look at our definition of rate:\n", "\n", " @deterministic(plot=False)\n", " def rate(s=switchpoint, e=early_mean, l=late_mean):\n", " ''' Concatenate Poisson means '''\n", " out = empty(len(disasters_array))\n", " out[:s] = e\n", " out[s:] = l\n", " return out\n", "\n", "The arguments switchpoint, early_mean and late_mean are\n", "Stochastic objects, not numbers. If that is so, why aren't errors\n", "raised when we attempt to slice array out using a Stochastic object?\n", "\n", "Whenever a variable is used as a parent for a child variable, PyMC\n", "replaces it with its value attribute when the child's value or\n", "log-probability is computed. When rate's value is recomputed,\n", "s.value is passed to the function as argument switchpoint. To see\n", "the values of the parents of rate all together, look at\n", "rate.parents.value." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fitting the model with MCMC\n", "\n", "PyMC provides several objects that fit probability models (linked collections of variables) like ours. The primary such object, MCMC, fits models with a Markov chain Monte Carlo algorithm:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from pymc.examples import disaster_model\n", "M = MCMC(disaster_model)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 27 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case M will expose variables switchpoint, early_mean,\n", "late_mean and disasters as attributes; that is, M.switchpoint will\n", "be the same object as disaster_model.switchpoint.\n", "\n", "To run the sampler, call the MCMC object's sample() (or isample(),\n", "for interactive sampling outside of the IPython notebook) method with arguments for the number of iterations, burn-in length, and thinning interval (if desired):" ] }, { "cell_type": "code", "collapsed": false, "input": [ "M.sample(iter=10000, burn=1000)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\r", " [----------- 31% ] 3147 of 10000 complete in 0.5 sec" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\r", " [-----------------60%--- ] 6053 of 10000 complete in 1.0 sec" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\r", " [-----------------91%-------------- ] 9139 of 10000 complete in 1.5 sec" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\r", " [-----------------100%-----------------] 10000 of 10000 complete in 1.6 sec" ] } ], "prompt_number": 28 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Accessing the samples\n", "\n", "The output of the MCMC algorithm is a trace, the sequence of\n", "retained samples for each variable in the model. These traces can be\n", "accessed using the trace(name, chain=-1) method. For example:\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "M.trace('switchpoint')[1000:]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 29, "text": [ "array([39, 39, 39, ..., 41, 41, 41])" ] } ], "prompt_number": 29 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The trace slice [start:stop:step] works just like the NumPy array\n", "slice. By default, the returned trace array contains the samples from\n", "the last call to sample, that is, chain=-1, but the trace from\n", "previous sampling runs can be retrieved by specifying the correspondent\n", "chain index. To return the trace from all chains, simply use\n", "chain=None.\n", "\n", "A node's chain can be accessed directly using its trace attribute:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "M.early_mean.trace()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 30, "text": [ "array([ 2.60698391, 2.60698391, 2.60428494, ..., 2.79480505,\n", " 2.72259973, 2.69514232])" ] } ], "prompt_number": 30 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sampling output\n", "\n", "You can examine the marginal posterior of any variable by plotting a\n", "histogram of its trace:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.hist(M.trace('late_mean')[:])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 31, "text": [ "(array([ 20., 151., 706., 1645., 2300., 2042., 1255., 623.,\n", " 215., 43.]),\n", " array([ 0.55752905, 0.63378676, 0.71004447, 0.78630219, 0.8625599 ,\n", " 0.93881762, 1.01507533, 1.09133304, 1.16759076, 1.24384847,\n", " 1.32010619]),\n", " )" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 31 }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "PyMC has its own plotting functionality, via the optional matplotlib\n", "module as noted in the installation notes. The Matplot module includes\n", "a plot function that takes the model (or a single parameter) as an\n", "argument:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from pymc.Matplot import plot\n", "plot(M)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Plotting switchpoint\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " late_mean\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " early_mean\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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pcvkPPnwkR6EsWhS8T54cvB9+ePBIkVz07Fnzc6l6qF54Ibf06Xqoct3/UDYN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\njIGJiD2Ury57SZL2mUoGRs8kGRRdinpExI+A18ZsrhX7EuC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K4ONB/luZKlYuk31x9eOet//+jiLlJxPLRjYxtnJV3nMlyscq6IUgE8Km9sLa\nv+KKagU4V//A558PL2c+VnUT87UpT6zfkyXOo3wMvgzyPpYB55LKIh8H/0N3/Hjn73ch6Zt/+cWJ\nc9SpU8393gf6mjXV+8IGhOeec/56I7xHDR5R4Q3cdtNx881O1O6oqTH/ffEHTo0z8M6d6wQlVXVC\nTtx2W7UPljfmkb8uf9uffgq3315zX7aWkXQkMf319NPhx/zJgL3tuRH/w2Tw36NsZP3gg+rt+fNr\n1vGnPwVbrMLaCbqf06dnbjk6LiCXwp131t4Xdb1uHLGw/1uj7jFs2DDztylDrN+TJXKoVtU3gdBH\np6p+nUpyGkPFcM8J3u931na59VZYtCj4mMsNN1Rvhw1Q117rTJelCyfg54cfgve71xA3P93pp2c+\ntbRgQc32vvgiXA6Xt992rEpr1jghJz76qPqYV1GIsljddlvt3I1Bip3fgpUp3mvMB6++Gn5sr73S\nn+veI1chzlUJdK/VrWfixJpBTt376w8n4fLuu87q1AceqLl6058KKi7ePn/nnfByYWFLJk1y/t59\nd3btG4Zh1EeKEnk9LHZR2MAVFn7BW95rXUn35u+fLvMOLuPGwcknB7eVK6q1EyAn5azctGntKa8o\nR/0ox/Cg+E9B8l57bXiAzzgWq0ysLYWeXnKvN45VMg6PPFJ7X5DF6t//Dj5/zz2TkcPl1Vch3Uuq\nK0+Y7166EB8HHmiWLMMwypOiOK97V6f586b5ycT/xyUThcXr5xQUtiCTaZl0vPkmHHtsZufExatU\n+f3LvEpBJharIPIZ+DHOysR8KVZxV/tFlfP7zPl58cXa9eTqYxV1Xrp79vbb8eqPY1UM+t/xT8Ma\npY/52pQn1u/JUmCL1XDAXYpewfTpFVWJZyHzgTNsisIduP78Z7g4wp3e65/z00/OW/YWW0TL9MYb\n8eWEYCtdEopKmHz9+zt/H344+Lh/1VqbNsHl5s6ttgZmO/DHoUkTJ3ekN2ZYPhS5TOrMZeo2CHcq\n17taNV9BOl1WroR27cKPpwuhIFLth+YnfDq9MvWp7aNnlD7mZ1OeWL8nS5KKVYxhYTgAZ58N994b\nb8XWt9/CTTcFHwtSKubPr3ZyX7Eiun4vL70UnBQ6CDdKdi7EjY+UjrBVdW++Gd4eONGx41BRAYsX\nO9thilWYpSZTRfmTTzIrH5ePP662nrgyudcE8NlnweeFrS7NFa/fVxIWq3TyLVmS/r56ffD8iMD2\n2wcfC08NxTRSAAAgAElEQVRFVJH6wLnnwp132luwUfcYM2Y8r7/+36zObdu2DffeW4SkpkbJEKlY\neTLIN09lkB8GNAJQ1ftEZGvgfWAzYL2InA+0V9XQNXAdOgTvd51hvXide/14B5Rf/9oZ4F9+GTp3\nTn9NcRg1yqmnV6/c64qLariFIIw99ohftkePav+duIEivQpImAIYJnPSCkm29bVvX729fLmzkq5L\nl+p9YQsQ9t8/t3ajmD27Zt3eYKGZkC5VUL6mby0foFFfUT2OefO6ZrTIqZr/MWfOA9x7b9JSGXWJ\nSMVKVQMWZ9c4/hUQMpGUX7xKl9dqksRDf8gQJyhmPgmSM2xFWC51Rh1Lp7zGrTuIUoxldPHFtSPy\nFxPvPWrZMrs6lizJvv1CBSU16gaun015Tw11SH2yYSYQkNC1xLF+T5airApMijCF4Le/za1ed9B4\n7bXc6onTzmOPVcfXEsksbUgQ6cJSeO+Xd3l9XAUonz5WQXLkY/DORqnKp4Lorfvcc7Or46STwo9l\nk1TbJddVfaWoWBvpsYG1PLF+T5aiprQJW1Yel7iWllJFpKaztmrNIJ7ZcNVVmZ+TLhWNl0JaKVTj\n5XosBO4iiXxcvz+NUV0hzr0wxcowjHKkqIqVN4lyNtTVB7frSC0CG3hshj/+GB4zKAnC7lfcAI+Z\nWqxyUXznzoWRvlj+Uf3tWv7yRa6/1yCKvcLZpgINwzCSpaiKVa4EDdwzZxZejkxp3tz5+8MPNeN4\nZTsVFJcwRSeughoW3iKMoEjx6Xj44epprWymHZ96KvNzik2+p1eLiXfhg1E3sHhG5Yn1e7LUaR+r\nIIUg3ylSkuSbbwrbXphiFdeXJqkI5GF8/bWTH/HhhzNP7BsVaLZUqatW1112iS6z3375l8NIFvO1\nKU+s35OlTr8vx5lqeuIJJxRDKRInjlch8AasTEchrStBMcjGjQsvHxbCo9QJy0VZKLp3L277hmEY\n9Y06bbGKo1gdfXT+5ciWCy8sbHu5WkdydayPy3/+k3levC+/zI8shmEYhpEJddpitTI0BKkRRK6K\nVaEclgs9RWoYhoP52pQn1u/JEify+mjgd8BSVe0YUuYO4EBgFTBIVaclKqWRCLkqVmPHJiJGJHXV\n78gw6jrma1OeWL8nSxyL1RhgQNhBETkI2FlV2wJDAAvmX6LkqrC8+24ychiGYRhGfSVSsVLVN4F0\n68YOBR5KlX0PaCoiWyUjnpEkdcUSNHBgsSUwDMMwjOxIwseqNbDQ830RsE0C9RoJU1dDEhiGURjM\n16Y8sX5PlqRWBfrdmuuIbaS8mD+/2BIYhlHKmK9NeWL9nixJKFaLgTae79uk9gUw3LNdkfoYhlF/\nqEx9DMMwypMkFKvngHOAR0WkN/C9qi4JLjo8geYMwyhdKqj5wmTTC4ZhlBeRPlYiMgF4B2gnIgtF\n5FQROUNEzgBQ1ReAz0RkLnAfcFZeJTYMw8AJBSMiS0RkRsCxi0VkvYg08+y7UkQ+FZHZItLfs7+b\niMxIHbu9UPKXIuZrU55YvyeLaIGWiomImuuVYZQbgqrmJbSsiOwDrATGeWPsiUgbYBTQDuimqt+K\nSHtgPNADZ8HNJKCtqqqITAbOUdXJIvICcIeqvuRrSwv1rDRyp0WLHfjmm9eAHWKe4f5Ec+3jmWyz\nzdEsXDgzx3qMUkAku+dXnY68bhhG+ZImFMytwGW+fQOBCaq6RlUXAHOBXiLSEthUVSenyo0DDsuT\nyIZhlAGmWBmGUW8QkYHAIlX90HeoFU4oGJdFOJYr//7Fqf2GYRhZUaeTMBuGYbiIyEbAVcD+3t1J\n1T98+PCq7YqKCioqKpKqumRw/Wxs+X15Yf3uUFlZSWVlZc71mI+VYRh5JH8+VgAisj3wD1XtKCId\ncXynVqUOu6FfegGDAVT1xtR5LwHDgM+B11V1t9T+44A+qnqmrx3zsSog8+bN45prbmDduuzOnzjx\nMX75ZQbmY2XkQrY+VmaxMgyjXqCqM4CqdFoiMp9q5/XngPEicivOVF9bYHLKeX2FiPQCJgMnAXcU\nQXzDw9KlS5k48XVWr746yxr2BJonKZJhxMYUK8Mw6iSpUDB9gC1FZCFwjaqO8RSpMj+o6iwReRyY\nBawFzvKYoM4CxgIbAi/4VwQaxaFx461Yvfq0YothGBljipVhGHUSVT0u4viOvu83ADcElJsKdPTv\nL0fM16Y8sX5PFlOsDMMwDMAG1nLF+j1Z4kReH5CKVPypiFwecHwLEZkoIh+IyHsisnt+RDUMwzAM\nwyht0ipWItIQuAsYALQHjhOR3XzFrgL+q6qdgZOBsk4JYRiGYRhG+RJlseoJzFXVBaq6BngUJ4Kx\nl92A1wFUdQ6wvYi0SFxSwzAMI69YzrjyxPo9WaJ8rFoDCz3fF+HEhPHyAXAE8JaI9AS2w4kf83VS\nQhqGYRj5x3xtyhPr92SJsljFiZZ2I9BURKYB5wDTgCzDuhmGYRiGYdRdoixWi4E2nu9tqJlXC1X9\nATjV/Z4KyvdZcHXDPdsVqY9hGPWHytTHMAyjPIlSrKYAbVNpI74AjgFqxI4Rkc2B1ar6i4icDryh\nqiuDqxuem7SGYZQ4FdR8YTK/jbqExTMqT6zfkyWtYqWqa0XkHOBloCHwoKp+LCJnpI7fh7NacKyT\nC5CPAAuVaxiGUQexgbU8sX5PlsgAoar6IvCib999nu3/AO2SF6282WorWLKk2FIYhmEYhpEJkQFC\njeLTtm2xJTAMwzAMIw51XrHq0aPYEuSfBnW+lwzDqAtYPKPyxPo9Wep8rsC+feH994stRX5p2DDz\nc9q1gzlzkpfFMIz6i/nalCfW78lS520hGifSVh1EpHo7G8XKe75hGIZhGIXBFKs6QDZTgeVwXwzD\nMAyj1Chrxaqiwvl7ySWJiJI3NshiwnaTTTI/Z6ONMj/HMIz6g/nalCfW78lSkj5WnTrBySfnX+Fx\nlbJe/uyHBaBLF5g2Lfy4dyovG4vVZps59XfpEv+cjTaCVasyb8swjPqB+dqUJ9bvyVKSFquePeHi\ni+OVratTXumUKj/Z+Es1aAB77JHZOXX1XhqGYRhGqRCpWInIABGZLSKfisjlAcebi8hLIjJdRD4S\nkUG5CpXJAJ+EMhBUxxln5F5vGEOHRpfJ1WKVjTJmDu+GYRiGkRtph2wRaQjcBQzASV1znIjs5it2\nDjBNVffASRJ2i4jkNMW4fn38srkoVm47QXVsuGH29UZxzz2ZlTeFp/CcdFL4sQsvLJwchlFIzNem\nPLF+T5YoW0hPYK6qLlDVNcCjwEBfmS+BzVLbmwHLVHVtpoJstVX1tqvo3HBDprVkxsqQVNFQnspM\ns2bJ13nUUcnXGYdOnYL3nxYzk+XOO4cfa9Qoc3kMoy4wbNgw87cpQ6zfkyVKsWoNLPR8X5Ta52UU\nsLuIfAF8AJyfq1CuYnXiifHLZsN22zl/GzSAV17Jvp58k62PVaYceWTm50RRLAV18mTYe+/a++Mu\nVPjll/Bj5ah0u9x4Y7ElMAzDKG2iht84astVwHRVbQXsAdwtIpsGFx3u+VSGN1ogHytXsWrSBDp3\nzr6efOAdvHMdyG+7LfM280Xfvtmf26JF/LJNmsDgwdm35SpWxXiJ+/BD2GKLwrd70UXRZX7966gS\nldT8PzcMwygvohSrxUAbz/c2OFYrL3sCTwCo6jxgPtAuuLrhnk9FaKNBypJ/leAHH4SXzYRHH4X+\n/ZNRKho0cHxzkp4qykShCKJVq+rtgf6J3Dzj758gK1Icfvwx83NyybF4yCHhdYjk3ifpyEduyDFj\n8tdukybebxWYYlV3MV+b8sT6PVminMynAG1FZHvgC+AY4DhfmdlAP+BtEdkKR6n6LFNBvIqNOxgH\n7XMJ86HJBFU45hhnO4nBbIstYNw4mDQJvvwy9/pcxoyBZ56pvb9FC/j66+BzwhTFdNe57baZyxaF\nv9+22Sa7erIJXhrVp716wXvvBR/bZx/n7047BR/Pp3VPJPnQF1tvHV3GbfNXv4Kffopfd79+8Pzz\n2clllBbmZ1OeWL8nS9qhJ+WEfg7wMjALeExVPxaRM0TEDUhwA9BdRD4AJgGXqeq3YXVuuy289lr6\nB3FQbrymTcNkTHcF8fEPlCK5Kxq5DL7eczff3Pm7/fY1y3gtUX4lYscdg+tKd7/+8IeMRMyKXNpw\nZZ85028lqYlrTQq7/+5vKSoHo2rwb0Aks75t0ya6jJd8WKwy4bHHwo8F/X7K2efMMAzDT+QjXFVf\nVNV2qrqzqv4lte8+Vb0vtf2Nqh6iqp1VtaOqjg+ra8oUmD/f8bM56KDwNoNSuFx2We19994LF1wQ\ndQXBTJoE11xT/d0/mInA4YfHq2v16upzvH/vvz872fy49fXpU3O/d5Dzyx+mwKRTrAoxoDdoAC+9\nlN25u+ziKE3t26cfzF2FKex63P1xFIKePTOTMYhM/aU22yy6TKbE6Vv3t5GP9g3DMMqFgr4bN2gQ\n/oD3DnLXXlv7eJMmzoA8e3b1vjPPDJ6qiZomfP992G8/2HLLmrJly69+VfO7ey1/+EN2ztp+y5RL\nOqXIryREWWPS8ZvfZH+uH1fmU06p3nfAAfHP96bkeeUVmDu3Zr1eXMuQmycxqE8HDKitAKcjyDK2\n0065W2nSKZdeS6TL3/5We99118Vvz5X3hReq9516avzzXdq2jV92l10yr98oLuZrU55YvydLyaS0\ncX1vVKFly+ptLwcc4Dys33wzfV1Rg1737tHnZDpwPvEEPPJI7f3r1mVWTzrSKVaNG9f8HqZcBtXh\nT9h87rnpz8nG3ylMWUzHe+/B7bdXf99442prStB19Ojh/HX7zqs4u3in5bJRppcuja+QHHecE5/t\n0Ufh2GMza8d/fUcfXTv8iOtg72fkyNr73GttnQqWMnNm9RTzXnvVLJvut+/6nrl07hxefs6c8HqS\nQERGi8gSEZnh2XeziHwsIh+IyNMisrnn2JWpDBKzRaS/Z383EZmROna7v51ywuIZlSfW78lSUMXK\nH9LAOx149NG1ywdFYBeJXlkW9KDv0QN288eM9xA0FZgJRx7prC70E6ZYRS1bD2o/rn9Unz7h8gfd\n04MPdix46dr28u23mQ+a2Vh4evYM961z8VoE3Tbcvtx//+BFBH6LVZx4aS4bbhjfx+qyy+Crr5zf\n3Z//HF4uTmwt1dr97/9+ySVwxx3VK2jdtEz7718tr3tO+/bV2+7fww6LlsNPgwZF9bEag5MVwssr\nwO6q2hn4BLgSQETa4yy+aZ865x6RKsnvBU5T1bY4i3X8dRqGYcSm4FOBXjp0SF8+W2tP0IO+RQs4\n4YTab+dh54jA+TmHOoW3367e7tzZWTUIwQmSb7klfV3du9ecXvEOrF6lNd1AF6ScTZjg+JzFOR+c\n6bG4U41xFhcsX579+d5Vhg0aOEqlqyCIVK+G80aA9ytWDz8cLaP/XL/lJoq2bcOV0Xfeqb0vk0UZ\nBx/s/N1zz5rWRjfsR7Nm1f3lrffII53wG66y7V7TxhvXrL9Dh5pTsl6K6biuqm8C3/n2vaqq7uvD\ne4D7CxkITFDVNaq6AJgL9BKRlsCmqjo5VW4ckIWKaRiG4VAyU4FBD+hsFauw1XxXXw1vvRV8LMhi\ntcMO2bUfNti89lr6HHSusuW1iHhzFrZuXXNwdgfJHXeEQYPg0EOD28908PP7jMUpGzbVt802zgCf\nbiownbN0lILhPS4ClZXB0cE/+qh621WYg6YCoxJku/cyyMIaVtbF9Z3yr4gVcfwFM+VXv4Kbb4ZR\no4Lb89KrlzNd7e3bvfZywnj4rZj+vlq1Kty3qsRXBJ4KuF5lragZg8/NIuHfv5ja2SXKBvO1KU+s\n35OlZBSrINZmnHHQ4aCD4Pvva/oCRQ0A2SojUVY3L1Grw4Lid916a3S9G2zgnBPHZ8jNB3jggeFl\nmjSBn3+OrsvL8ccH77/5ZieKeVgcpaj7nElC7nR1LVtWvX3VVfHazrQNP2FKYb9+tff5p6mjpv3A\nUbQvuaT63ob9hkUcherII2HXXZ2VuV7899hfT11M7yMiVwO/pFulbNTGfG3KE+v3ZCkZxSpo9VVc\ni1WzZs50iNfHZvPNM4uAHuZj5bUkBDmnB+EdbM45J3h/XEf0AQHeHu6qSX8dQWX9dOzo/P3Tn/I7\nKPbsCUuW1Haq93LssfDJJ+nrycRilU6xPOggRx5ILr5YUnXE8acL+i37Fx1EtePit0hFKVbp+mCb\nbUpPuRKRQcBBwAme3f4sEtvgWKoWUz1d6O5fHFTv8OHDqz6VlZVJimwYRglQWVlZ4/88W6IirxeE\n77933qj9TrxxFav//c+x2ninzTIlbFD2KnzHH+9YYKZPT1+Xd6C5807YdFP4y1/Sn/PnP0Pv3s62\na4GCmoOgu++Pf3QUI/+Ad8YZwVNKYelgwgbMOANlkHJw+unV01J9+kQ76O+4I+y8s7O91141/dFc\nwixWfsfrKLkbNqwtj798nNWOSVisgupIV2+PHs50qbe+KH+8uHVDzXt82GG1p2bXroWzzoJ2vkRV\nS5c69+yEEygZUo7nlwJ9VNUbP/45YLyI3Ioz1dcWmKyqKiIrRKQXMBk4CbgjqO5cHrSGYZQ+FRUV\nVFRUVH3Pdno00mIlIgNSy5M/FZHLA45fIiLTUp8ZIrJWRCLWctVk880dBcZdLu8Slk7Ez8YbO+fn\nEoU9zIrg1ukqWHGmaA4/vOYquyFDotv705+c67jllmglLKou//c1a2rLm+nUaBy8qzVvuCGzc/3t\nuYE5oxQr73npLFZxpkmPPDK6jNveypXRZdPJks6S58edvvUSNK3cvHnN766sbgDbMLz3eOJER7F3\nQzaceaajVPXpU72y0Z22bNGipqO767v2+9+nby8pRGQC8A7QTkQWisipwJ3AJsCrqWfSPQCqOgt4\nHCeDxIvAWapV/71nAQ8AnwJzVTXLELZ1H/O1KU+s35MlrcVKRBoCd+HkAlwMvC8iz6nqx24ZVR0J\njEyVPxi4QFW/T0K4qKmOMJLwnXEHYvfR6+ZOc78PGRIeWf2222p+jwoZ4OWii5y/Z59dc/8uu0DX\nrtXfBw1yVmoFrVxMN5UTR7FKd8yNgB+kzHnb8UfPD1JA01mb3njD+Ru2+jAsFEcYYcmUM8U9J2qa\nuXnz8EUUIuB5KQqU5dprYcUKGDYsnpxr14bfqyDFzEtQ35x1lmNBDVpFe/31cMQR1d9d+bp1i5Yz\nSVTVn7cUYHSa8jfgpODy758KdExQtDqL+dmUJ9bvyRI1FdgT5w1uAYCIPIqzbPnjkPLHAxMSky5L\n3ACgcaeJgo6HlXfrvO++5FLWpGvHxb9Uf8wY52+ckBBeJSTX3IrpoqYfcYSj8CWBu3qta9fgcASX\nXgo33VRzXzqrVFT/77efY2l85ZX05byrAnff3bHOzJvnKLnTplWXC0qOHddaCNWpmoYNC5729ONX\nqkaPdq7p9tvT51WEYCV1ww3DQ5MElY2SzzDKhdWrV/D0009nff5+++3H5ptvHl3QKFmiFKvWwELP\n90VAYDhDEdkIOADHrJ4YTZs6Plhx6N7d8cvyByLNBf9gsWpV+uPZ1pvp8Uzb2mCDmqsss3U43nff\n4P0iji/ZfvvBv/4VLEM6wuQRCU6xc+ON1YrVsGEwYkTmU4HHH189leXG8QpTrNq0gYULq+XcYAPn\nd+be06D8ln789+DBB+G005ztOP0RZHkMY/Dg6u2gTANeohSvKK691lE0O3d2gpEaRvmyKatW9WDw\n4L9ndfZPP03i/fffolNUXjajpIkaDjIZ3g8B3ko3Deh1/qyoqOCyyyoiAy1utFF8xeqZZ4IHnx12\ncGJYZYLfx8olyRQ16WjeHBYtii4H0YNy2IC8447w2Wfx6vSXDWvz3nujV/oFyRLl6J6O4cMdxSrd\nsyhomuyww2pb2NIpeEHHmzeHzz93rJfffJNesfD/lgYPrp4mDlOUttoqOtNAOuIo6P/8Z/ogrX78\nL9M77VTtD3nVVZUMHVoJOP1i1C1cPxubGsqWbVm9+ulIv8YwNtusOAqV9XuyRClW/iXKbagZTM/L\nsURMAwatqnGjRofx5JNOCpU4tPaF9XMHlYsvrl5xF5cwxcprmXj88ZqRv6PqyoRJkzKPJRXWXlhI\nghdfrL3SK4zHHqu9uCCozbZtM0vUmxTr1mXmN/bSS7UVhHS4/e6v59VXHR+mnXYKjqbvJSisgeur\nFKawf/VV8P4kQxy0bFmdnzMOffuGK/0VFRW0b1/B7NmuwmsOsXUJG1jLE+v3ZIlaKzUFJ3fW9iLS\nGCfX1nP+QqlEp78Fnk1awN/8Bn73u9zqyCbZrsugQeFRsY86Kniays8mm8AVV9Tc5w6MYcvmt9yy\nOlJ3pngH3YMOcpRXV7nyWm78qUuCzg/bl2t093QE5feLIipnnT+P4wEHZCaza5Hxn+NfnZcuQXg6\n61GcJM3eIKzF9GcSqf0SYxiGYTiktVip6loROQd4GWgIPKiqH4vIGanj96WKHga8rKpZGkDzQ5Ay\nERd3AO3RI72lJg4NG9YOoeDK5l8dljT+9CkuIs5y+bCI6VFKRxyfIi9bbZX++O23O+lkvGEq4pCp\nb1KSZYNIJ0+6urfayrF4pYuRFnUPS4ULLoj26zIMw6ivRA6PqvoiTtwX7777fN8fAh5KVrTkyMQy\n0aCBM2WTSb68YpOJcuEd3Bs3Do4m36BBbSXA30br1jB1avXKsSgZunatHU/J20arVs7nb3/LzN8q\nF2tkJjRo4PhQBdGxY7zgtJmk5wmiUP59ubLPPpknqTZKA/O1KU+s35OlJCKv55u4OQefecaJav7R\nR/HCGCRBPqZ0gpSN7bZzcr7FWfLfqFHt+F1B5b1xteIEvIyjrJ5xRnQZl//8J3l/rhYtgveLONOz\nQXz4Yby6mzYNzhPocuedTuiGTGUzjKSwgbU8sX5PlpLJFZhPwhIA+xk4sHqKK0wJKPVYPZMnw9ix\ntfdPneooAHHkb9DAmb7s2jV6Kf6jjzoxpdy4S4Wkd+9wZSdbrr7aSZGULen84ho1cpzdw9h7bzjl\nlPDjbvofwzAMo3Sp1xYrV4nIJH1IXcRrTQrzB3OdrN17EhU5vEEDRxkLasPLwIHOJxtKUUlt3NiJ\nWeUnrlKzww6leV2GYRhGYajXipXLnnsWW4L8seWW2QVEtfhz8Vmxom753BlGtpivTXli/Z4s9Vqx\nci0HQQlrS4VcrRuLF2e26jGTtCpett++OvluUmy2WbL15YtNNy22BIZRGGxgLU+s35OlLBSrUq4z\n21hVLrmmI4lL06Ywa1Zy9X36aXiSYiMaN66WYRiGUVrUa8UqG6KsE9nExEpHq1aF9ckpFf8fc8TO\nnpEjoU+fYkthGIZhBBGpWInIAOA2nAChD6jqTQFlKoD/AxoB36hqRbJiZsc++2SWAw3gqafS5yZ8\n9dXM6ywlbFqr7lOo2F1G+WG+NuWJ9XuypFWsRKQhcBfQDydv4Psi8pyqfuwp0xS4GzhAVReJSPN8\nCpwJL74YXcZPixbp4wVtt1328ngpluVo6FAYMKA4bRuGUdrYwFqeWL8nS9S7b09grqouUNU1wKOA\nf3H98cBTqroIQFVD4lMXnoYNk5+6q+tssEFxkiQbhmEYRjkQpVi1BhZ6vi9K7fPSFmgmIq+LyBQR\nOSlJAesrSSYtTpqkrHKGYRiGUW5E+VjFmbBqBHQF9gM2Av4jIu+q6qe5CmcUnlJxbjcMo/CYr015\nYv2eLFGK1WLAG4e6DY7VystCHIf11cBqEfk30BmopVgNHz68aruiooKKiorMJa4nmAJjZEuchM/F\norKyksrKymKLYWSJDazlifV7skQpVlOAtiKyPfAFcAxwnK/Ms8BdKUf3JkAv4NagyryKlWEYmfPB\nB8kHak0S/wuT+yZsGIZRLqRVrFR1rYicA7yME27hQVX9WETOSB2/T1Vni8hLwIfAemCUqiYYStIw\nDBdLRWQYhlHaRMaxUtUXgRd9++7zfR8JjExWNMMwDKOQmK9NeWL9niwWed0wDMMAbGAtV6zfk8Vi\nOBuGYRiGYSSEKVaGYRiGYRgJYVOBReLII6Fp02JLYRiGUY352pQn1u/JIlqggEoiooVqyzCM0kBE\nUNUSzjMQD3t+FZb//Oc/HHjgRSxf/p8Ctej+RIvbx5tt1ok33/w7nWz5b0mQ7fPLpgINw6iTiMho\nEVkiIjM8+5qJyKsi8omIvJJKEu8eu1JEPhWR2SLS37O/m4jMSB27vdDXYRhG/cIUK8Mw6ipjgAG+\nfVcAr6rqLsC/Ut8RkfY4AY7bp865R6QqY+e9wGmq2hYnILK/TsMwjNiYYmUYRp1EVd8EvvPtPhR4\nKLX9EHBYansgMEFV16jqAmAu0EtEWgKbqurkVLlxnnPKjhEjRli0/DLE+j1ZIp3XU29vt+FEXn9A\nVW/yHa/ASWvzWWrXU6p6XcJyGoZhxGErVV2S2l4CbJXabgW86ym3CGgNrKFm/tPFqf1liTkvlyfW\n78mS1mKVyv93F47pvD1wnIgEZSp7Q1W7pD4loVQVOhFsfW+vGG1ae3W7vWKT8jY3j3PDMApKlMWq\nJzA3ZTpHRB7FMal/7CtXcqt+KisraySDtfbqXpvWXt1ur0gsEZGtVfWr1DTf0tT+xUAbT7ltcCxV\ni1Pb3v2Lgyr2JpH3J5s2avP2228zc+bMrM6dN29ewtIYRjSVlZWJvIBGKVatgYWe74uAXr4yCuwp\nIh/gPJAusSTMhmEUieeAU4CbUn+f8ewfLyK34jzX2gKTVVVFZIWI9AImAycBdwRV7FWs6itJxjMa\nN+4xxoyZwgYbdMjq/F9+GZizDEY8LI6Vg/+FKVu/syjFKo4Z/b9AG1VdJSIH4jzIdslKGsMwyhoR\nGYfjZP5ijLITgD5AcxFZCFwD3Ag8LiKnAQuAowFUdZaIPA7MAtYCZ3kCU50FjAU2BF5Q1ZcSvag6\nRJh8MIIAACAASURBVJIDqyqsWXMsa9acl1idRn4od4UqadIGCBWR3sBwVR2Q+n4lsN7vwO47Zz7Q\nTVW/9e03XwfDKEMyCbAnIk1wwiL8DngHZ8HMj/mSLS4WIDRzhgw5j1GjdgbqgmJlAUKN2mQbIDTK\nYjUFJ67L9sAXOA+843wNbwUsTZnUe+Ioa9/6K6oP0ZcNw8g7WwI7AstxVvWNxnnuGIZh1AnSKlaq\nulZEzgFexgm38KCqfiwiZ6SO3wccCQwVkbXAKuDYPMtsGEb95WLgHlWdB5Ca4jMKhPnalCfW78lS\nsFyBhmEYUYjIIar6j9T271T1+WLLBDYVmA02FZg5NhVYWpRsrkARGZDKzfWpiFyeQz0FzQsmIm1E\n5HURmSkiH4nIeflsU0R+JSLvich0EZklIn/J9zV6yjcUkWki4g5o+byvC0Tkw1R7kwvQXlMReVJE\nPk7d11557MN2qetyP8tF5Lw8X9+Vqd/oDBEZLyJN8v2bEZHzU2U/EpHzU/uSarOPp6l90slhGIZR\nkqhq3j4404dzge2BRsB0YLcs69oH6ALM8Oz7K3BZavty4MbUdvtUW41Sbc+l2jo3GeiZ2n4BGBDS\n3tbAHqntTYA5wG55bnOj1N8NcKJE753P9jztXgQ8AjxXgPs6H2jm25fP9h4CTvXc180LdE8bAF/i\nxE7KS3upcz4DmqS+P4YTYiCf97MDMAP4Fc7/96vATkm1meqv/YB9gTH5fD5l+PxRIzNOP/1chdvV\nWR9Y6h9Sn+LKsdlmHfWDDz4odtcZKVL/9xk/L/JtsaoKMKqqawA3wGjGaIHzgqnqV6o6PbW9Eico\naus8t7kqtdkYZ9D6Lp/tAYjINsBBwANU28PznW/Nb1rNS3sisjmwj6qOBsdnUFWXF+D6APrh/PYX\n5rG9FTgpWTYSkQ2AjXAWmeTz+nYF3lPVn1R1HfAG8PsE2zwPJ1zLrsAFITIYecJyxpUn1u/JEpkr\nMEfiBBjNhYLkBRNnVWQX4L18tikiDXDigu0E3KuqM0Uk39f4f8ClwGaefflsU4FJIrIOuE9VR+Wx\nvR2Ar0VkDNAZmIozWBfid3MsMCG1nZf2VPVbEbkF+B+wGnhZVV/N82/mI+B6EWkG/ISjlE9J8Bq3\nxbEqNgHOB/4cIoeRB8x5uTyxfk+WfCtWmuf6qxtSVclDrCwR2QR4CjhfVX8QqTa2JN2mqq4H9khZ\nWl4Wkb6+44m2JyIH44TKmCZOMu0gmZK+r3up6pci0gJ4VURm57G9DYCuwDmq+r6I3AZckcf2ABCR\nxsAhOFNiNUiyPRHZCUdR3B4nPMETInJivtpL1TdbRG4CXgF+xJnmW5dgmxcBt+AoXoZhGHWOfE8F\n+vNztaHmW2quLBGRrQEk4bxgqTob4ShVD6uqmxojr20CpKarnge65bm9PYFDxQnqOgHYV0Qezmeb\nqvpl6u/XwESc6eJ8tbcIWKSq76e+P4mjaH2V5z48EJiaukbyeH3dgXdUdZmqrgWeBn6T7+tT1dGq\n2l1V++BMV3+S4DV+pKofqeocVZ0TJoNhGEapkm/FqirAaOot/hicnF1J4eYFg9p5wY4VkcYisgPV\necG+AlaIszJMcPKCPeOvFCB1/EFglqrelu82RaS5u5JKRDYE9gem5fMaVfUqVW2jqjvgTF29pqon\n5fEaNxKRTVPbGwP9cRyh89JeqtxCEXFTLPUDZgL/yNc9TXEc1dOAbr35aG820FtENkyV64eTsiWv\n1yciv0793RY4Ahif4DX2FZF/iMgTIvJEmAxGfjBfm/LE+j1hsvF4z+SD8/Y+B8dp9coc6pmA45j7\nC47f1mCgGTAJ5435FaCpp/xVqTZnAwd49nfDGcznAnekaW9vYD3OVMe01GdAvtoEOuL4V00HPgQu\nTe3P2zX62u9D9arAfF3jDqnrm47jq3Nlvq8Rx7fqfeADHIvO5nlub2PgGxzHbApwfZfhKIszcJzG\nG+X7NwP8O9XmdKBvkteIswK3R2p7m6SfRzk8f9TIDFsVmPnHVgWWFmS5KtAChBqGUTKIyCjgF1U9\nW0TuUdWzii0TWIDQbLAAoZljAUJLC8lTrkDDMIxCspLqsCqriymIYRhGNuQ98rphGEYGfAPsmQoj\nsb7YwpQb5mtTnli/J4tZrAzDKBlU9XoR2RVooKqzii1PuWHxjMoT6/dkMcXKMIySQUTc1ZQbpvwb\noiLcG4ZhlBSmWBmGUTKo6nFQFe7kwiKLYxiGkTGmWBmGUTKIyO44S7MaAbsXWZyyw/Wzsamh8sL6\nPVlMsTIMo5Q4MvX3Z+COYgpSjtjAWp5YvyeLKVaGYZQSUzzb24jINqr6fNGkMQzDyBBTrAzDKCX+\nALyNMx24N+lTBxmGYZQcplgZhlFKzFbVkQAi0kJVHyq2QOWE+dqUJ9bvyWKKlWEYJYWIPIhjsVpS\nbFnKDRtYyxPr92QxxcowjFLiamAb4HscB3bDMIw6haW0MQyjlLgNGKaqK4A7iy2MYRhGpphiZRhG\nKbEe+Dy1/X0xBSlHLGdceWL9niw2FWgYRinxM9BeRM4Ftii2MOWG+dqUJ9bvyWKKlWEYJUEqjc2T\nQHNAgHuKK5FhGEbm2FSgYRglgaoq0FdVX1TVF1R1XbZ1iciVIjJTRGaIyHgRaSIizUTkVRH5RERe\nEZGmvvKfishsEemfyAUZhlGWmGJlGEZJICIDgYEi8i8ReUJEnsiynu2B04GuqtoRaAgcC1wBvKqq\nuwD/Sn1HRNoDxwDtgQHAPSJSls9G87UpT6zfk6VgU4EiooVqyzCM0kFVJWbRAaq6l4jcq6pDc2hy\nBbAG2EhE1gEbAV8AVwJ9UmUeAipxlKuBwARVXQMsEJG5QE/g3RxkqJOYr015Yv2eLAV9K1PVevEZ\nNmxY0WWw67BrqQufDNlWRH6X+nuQiByU5XPmW+AW4H84CtX3qvoqsJWqukFHlwBbpbZbAYs8VSwC\nWmfTtmEYRlmauw3DKEmewHFcfxxokfpkjIjsBFwAbI+jNG0iIid6y6ij9aXT/MzCbhhGVtiqQMMw\nSgJVHZtQVd2Bd1R1GYCIPA38BvhKRLZW1a9EpCWwNFV+MdDGc/42qX01GD58eNV2RUUFFRUVCYlb\nOljOuPLE+t2hsrKSysrKnOuRLMz12TUkooVqK99UVlbWi4dqfbkOsGspVUQEje9jlVSbnYFHgB7A\nT8BYYDKwHbBMVW8SkSuApqp6Rcp5fTyOX1VrYBKws/eBVZ+eX4ViyJDzGDVqZ+C8YosSA/cnWtw+\n3myzTrz55t/p1KlTUeUwHLJ9fpnFKgvqy6BXX64D7FqMalT1AxEZB0zBieT+X+B+YFPgcRE5DVgA\nHJ0qP0tEHgdmAWuBs0yLMgwjW0yxMgyj3qGqfwX+6tv9LdAvpPwNwA35lsswjPpPpPO6iIwWkSUi\nMiNNmTtSwfU+EJEuyYpoGIZhFAKLZ1SeWL8nSxyL1RicLPPjgg6mlkTvrKptRaQXcC/QOzkRDcMw\njEJQ7s7L5Yr1e7JEWqxU9U3guzRFDsUJtoeqvgc0FZGt0pQ3DMMwDMOolyQRx6o1sNDzfRHOcmXD\nMAzDMIyyIinndf9yRFtRYxiGUceweEbFZ+3ataxduzarc0WEhg0bZnye9XuyJKFYxQquB+URYM8w\nypmkAuwZxcEG1uLy888N6d69Z1bnqq7nkksu4+abb8z4XOv3ZElCsXoOOAd4VER64+TlWhJU0KtY\nGYZR//C/MNlKI8OIz88/T8vh7BtR/T4xWYzsiVSsRGQCTkb45iKyEBgGNAJQ1ftU9YVUwtS5wI/A\n4HwKbBiGYRiGUapEKlaqelyMMuckI45hGIZRLMzXpjyxfk8Wi7xuGIZhADawlivW78mSRLiFRBg7\ndix333136PFRo0YVUBrDMAzDMIzMKRnFSiR9Aun777+/QJIUh/Xr19f4bjlgDcMwDKPuUTKKlZcT\nTjiBiooK9tlnHxYuXMjEiROZM2cOffv2ZcKECXz22WcMGDCAvn37ctFFFwXWsWDBAvbcc0+OPfZY\nOnXqxLPPPsshhxzCHnvswdy5cwHHSvbb3/6Wvfbai9dffx2AkSNH0rdvX7p168akSZMAGDRoEEOH\nDqV///4cfvjhtdr6+9//XnXO3//+dwC+/vprDj74YCoqKjjppJMAePTRR+nduze/+c1veOWVVwBn\nFdXll1/OgAEDeOihhzj22GM59NBDeemll5K9qYZhGBFYzrjyxPo9YVS1IB+nqXDGjh2rd911l6qq\nrlq1SlVVJ06cqFdffbWqqnbv3r2q7FFHHaWfffaZqqoOHTpUp0yZUqu++fPn62677abr16/XV155\nRXv06KGqqs8++6xec801umzZMh0wYICqqq5cuVIrKipqtL1kyRLt06ePqqoOGjRIH374YVVVPeaY\nY/TDDz+s0ZZ7zqpVq7Rr166qqnrhhRfq008/XVVm7dq12rlzZ/355591xYoVVddTUVGhr732WtU9\nOPnkk9PeJ8OoS6T+7wv2nMnXJ+r5ZdTm9NPPVbhdQevAh9Sn2HLk8vmLXnzx5cXu9npFts+vknNe\nX79+PZdeeikzZsxg9erVdOzYsVaZOXPmcOqppwKwcuVKBgwYQLdu3WqVa9++PSJCy5Ytad++PQCt\nWrVi0qRJzJs3j5kzZ9K3b18AvvnmGwDGjRvH+PHjadCgAV999VVVXV26dAGgTZs2fPddzdSJL730\nEnfccQeqyrx58wCYPXs2f/zjH6vKfP3112y77bY0btyYxo0b06hRI9atWwdAjx49qsp17949wztm\nGIZhGEapUHKK1fTp01m+fDlvvPEGTz31FP/85z+Bmj5Y7dq1Y+TIkWy77bYAVQqKH+853m1VZccd\nd6RTp05V9bspBO666y4+/PBDli5dyj777BN6vpfrr7/+/9u7+2g56jrP4+8Pl4eAkMQYDprkuiAQ\nE2Z9ICsEJcJFWYgeBUQPD44MBFbCzmKYEVcSdjx0nNEJLjMLM+COGx4Oh4OwDmScMIMksOQi6/BM\nEsEkQMQgIUN4kugigWT47h9VNzQ3fW/37VvV3dX1eZ1T59ZT1+9Xt7qrv/37fauKe++9l4jgwAMP\nBGD69Oncc889fOELXyAi2HfffXnmmWd44403eOONN3jzzTd3PHpgl13e7pGtHjczM7Ni6ajAShLT\npk3jmWee4bjjjmPatGk7AppjjjmGk046iTlz5nDppZdy3nnnsXXrVnp6erj22mvp7e3daVsDr601\n/p73vIfTTjuNo48+mp6eHj70oQ9xxRVXMGvWLI488kiOOOII9tlnnyHrWe3kk09m1qxZzJgxgwkT\nJgCwYMECzjrrLK644gp6e3u54YYbmD9/PkcddRS77LIL3/nOdxratplZq/h+RuXk454tDW59ya0g\nKVpVlpl1BklEROF/Lfj8NXLnnjuPxYsPAua1uyoNGHiLFvkYL+LCC1/lsstG/qxAq63Z81dHtVg1\n68knn2Tu3LnvmHfjjTcyadKkNtXIzMzMyqgrAqupU6fuuF2CmZmZWbs4U9rMzADfz6isfNyz1RUt\nVmZmNnpOXi4nH/dsucXKzMzMLCMOrMzMzMwy4sDKzMwA59qUlY97tpxjZWZmgHNtysrHPVt1W6wk\nzZa0TtJTki6qsXyipDskrZL0uKSzcqmpmZmZWYcbNrCS1ANcCcwGDgFOlzR90GrnAysj4qNAH/BX\nktwSZmZmZqVTr8XqcGB9RGyIiG3AzcCJg9b5V2BsOj4WeDkitmdbTTOzxkkaL+kWSWslrZE0U9IE\nSXdKelLScknjq9ZfkLbKr5N0XDvr3k7OtSknH/ds1WtZmgw8WzW9EZg5aJ3FwN2SNgH7AKdkVz0z\ns6ZcAdweEV9KW9DfBfw34M6I+F6a1jAfmC/pEOBUklb5ycBdkqZGxFvtqny7ONemnHzcs1WvxaqR\nJ1JeDKyKiEnAR4GrJO0z6pqZmTVB0jjgkxFxLUBEbI+ILcAJwPXpatcDJ6XjJwI3RcS2iNgArCdp\nrTczG7F6LVbPAb1V070krVbVPgF8ByAifinpV8AHgYcHb6xSqewY7+vro6+vb8QVNrPO1d/fT39/\nf7urcQDwoqTrgI8AjwB/AuwXEZvTdTYD+6Xjk4D7q16/kaTlysxsxOoFVg8DB0vaH9hE0lx++qB1\n1gHHAj+TtB9JUPV0rY1VB1Zm1n0G/2BqU97GrsAM4PyIeEjS5STdfjtEREgarkW+kdb6rjNwvNw1\nVC4+7tkaNrCKiO2SzgeWAT3ANRGxVtLcdPkPgO8C10laTdK1+M2IeCXnepuZDWUjsDEiHkqnbwEW\nAM9Lem9EPC/pfcAL6fLBLfNT0nnvUIYWd3+xlpOPeyKrFndFtOaHmaRoVVlm1hkkERFqQ7k/Bf5T\nRDwpqQLslS56OSIulTQfGB8RA8nrPyTJq5oM3AUcVH3C8vlr5M49dx6LFx8EzGt3VRow8BYt8jFe\nxIUXvsplly1qd0W6RrPnL99vysy60deAGyXtDvwSmEPS6v4jSecAG0ivYI6INZJ+BKwBtgN/7CjK\nzJrlwMrMuk5ErAYOq7Ho2CHW/y5JWkOpOdemnHzcs+XAyszMAH+xlpWPe7bqPivQzMzMzBrjwMrM\nzMwsIw6szMwM8DPjysrHPVvOsTIzM8C5NmXl454tt1iZmZmZZcSBlZmZmVlGHFiZmRngXJuy8nHP\nVstzrCqVih/GbGbWgZxrU04+7tlqeYuVo2IzMzPrVr4q0MzMapo161heeGFLU6/dvPkZ4M+yrZBZ\nATiwMjMzYOdnxq1atYrXXrsJGN/kFt+fTcUsV35WYLYcWJmZGTDUF+uhwMRWV8VayAFVtnxVoJmZ\nmVlG6gZWkmZLWifpKUkXDbFOn6SVkh6X1J95Lc3MzMwKYNiuQEk9wJXAscBzwEOSlkbE2qp1xgNX\nAcdHxEZJbjM2Mysg59qUk497turlWB0OrI+IDQCSbgZOBNZWrfNl4NaI2AgQES/lUE8zM8uZv1jL\nycc9W/W6AicDz1ZNb0znVTsYmCBphaSHJZ2RZQXNzMzMiqJei1U0sI3dgBnAp4G9gPsk3R8RT422\ncmZmZmZFUi+weg7orZruJWm1qvYs8FJEvA68LumnwEeAnQKrgUfZVCoV+vr66Ovra67WZtaR+vv7\n6e/vb3c1rEnOtSknH/dsKWLoRilJuwJPkLRGbQIeBE4flLw+jSTB/XhgD+AB4NSIWDNoWxERSGK4\nMs2se6Sfd7W7HqM1cP4qm733nshrr62j++9jNfAWLfIxXsS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vJxf5JOe+/nr+5YWx//5w773OY/f9atkSevTIvq1IKp+o0K7AdAHn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\ndEz/qzm5RkJ7FQKsYh0ajzstM+vGZNuOtyszsxGLiLYTMAP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"text": [ "" ] } ], "prompt_number": 32 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The upper left-hand pane of each figure shows the temporal series of the\n", "samples from each parameter, while below is an autocorrelation plot of\n", "the samples. The right-hand pane shows a histogram of the trace. The\n", "trace is useful for evaluating and diagnosing the algorithm's\n", "performance, while the histogram is useful for\n", "visualizing the posterior.\n", "\n", "An alternative visualization of posterior quantities is to use the summary_plot function to create forest plots of stochastic or determinsitic nodes. This will display the posterior median, interquartile range, and posterior credible interval (defaults to 95%) in a layout that makes it easy to compare multiple nodes." ] }, { "cell_type": "code", "collapsed": false, "input": [ "Matplot.summary_plot([M.early_mean, M.late_mean])" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Could not calculate Gelman-Rubin statistics. Requires multiple chains of equal length.\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 33 }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a non-graphical summary of the posterior, simply call the summary method." ] }, { "cell_type": "code", "collapsed": false, "input": [ "M.early_mean.stats()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 34, "text": [ "{'95% HPD interval': array([ 2.49124983, 3.60405374]),\n", " 'mc error': 0.00756500947969721,\n", " 'mean': 3.0527065227383434,\n", " 'n': 9000,\n", " 'quantiles': {2.5: 2.5172050574749441,\n", " 25: 2.8605823290604975,\n", " 50: 3.0380496362489353,\n", " 75: 3.2300775101774053,\n", " 97.5: 3.6363693972833957},\n", " 'standard deviation': 0.28702076399829468}" ] } ], "prompt_number": 34 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Imputation of Missing Data\n", "\n", "As with most textbook examples, the models we have examined so far\n", "assume that the associated data are complete. That is, there are no\n", "missing values corresponding to any observations in the dataset.\n", "However, many real-world datasets have missing observations, usually due\n", "to some logistical problem during the data collection process. The\n", "easiest way of dealing with observations that contain missing values is\n", "simply to exclude them from the analysis; this is called a **complete case analysis**. However, this results in loss\n", "of information if an excluded observation contains valid values for\n", "other quantities, and can bias results. An alternative is to ***impute*** the\n", "missing values, based on information in the rest of the model.\n", "\n", "For example, consider a survey dataset for some wildlife species:\n", "\n", " Count Site Observer Temperature\n", " ------- ------ ---------- -------------\n", " 15 1 1 15\n", " 10 1 2 NA\n", " 6 1 1 11\n", "\n", "Each row contains the number of individuals seen during the survey,\n", "along with three covariates: the site on which the survey was conducted,\n", "the observer that collected the data, and the temperature during the\n", "survey. If we are interested in modelling, say, population size as a\n", "function of the count and the associated covariates, it is difficult to\n", "accommodate the second observation because the temperature is missing\n", "(perhaps the thermometer was broken that day). Ignoring this observation\n", "will allow us to fit the model, but it wastes information that is\n", "contained in the other covariates.\n", "\n", "In a Bayesian modelling framework, missing data are accommodated simply\n", "by treating them as unknown model parameters. Values for the missing\n", "data $\\tilde{y}$ are estimated naturally, using the posterior predictive\n", "distribution:\n", "\n", "
\n", "$$p(\\tilde{y}|y) = \\int p(\\tilde{y}|\\theta) f(\\theta|y) d\\theta$$\n", "
\n", "\n", "This describes additional data $\\tilde{y}$, which may either be\n", "considered unobserved data or potential future observations. We can use\n", "the posterior predictive distribution to model the likely values of\n", "missing data, assuming values are missing completely at random.\n", "\n", "Consider the coal mining disasters data introduced previously. Assume\n", "that two years of data are missing from the time series; we indicate\n", "this in the data array by the use of an arbitrary placeholder value,\n", "None:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "x = np.array([ 4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,\n", "3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,\n", "2, 2, 3, 4, 2, 1, 3, None, 2, 1, 1, 1, 1, 3, 0, 0,\n", "1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,\n", "0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,\n", "3, 3, 1, None, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,\n", "0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 35 }, { "cell_type": "markdown", "metadata": {}, "source": [ "To estimate these values in PyMC, we generate a *masked array*. These are specialised NumPy arrays that contain a matching True or False value for each element to indicate if that value should be excluded from any computation. Masked arrays can be generated using NumPy's ma.masked_equal function:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "masked_values = np.ma.masked_values(x, value=None)\n", "masked_values" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 36, "text": [ "masked_array(data = [4 5 4 0 1 4 3 4 0 6 3 3 4 0 2 6 3 3 5 4 5 3 1 4 4 1 5 5 3 4 2 5 2 2 3 4 2\n", " 1 3 -- 2 1 1 1 1 3 0 0 1 0 1 1 0 0 3 1 0 3 2 2 0 1 1 1 0 1 0 1 0 0 0 2 1 0\n", " 0 0 1 1 0 2 3 3 1 -- 2 1 1 1 1 2 4 2 0 0 1 4 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1],\n", " mask = [False False False False False False False False False False False False\n", " False False False False False False False False False False False False\n", " False False False False False False False False False False False False\n", " False False False True False False False False False False False False\n", " False False False False False False False False False False False False\n", " False False False False False False False False False False False False\n", " False False False False False False False False False False False True\n", " False False False False False False False False False False False False\n", " False False False False False False False False False False False False\n", " False False False],\n", " fill_value = ?)" ] } ], "prompt_number": 36 }, { "cell_type": "markdown", "metadata": {}, "source": [ "This masked array, in turn, can then be passed to one of PyMC's data\n", "stochastic variables, which recognizes the masked array and replaces the\n", "missing values with Stochastic variables of the desired type. For the\n", "coal mining disasters problem, recall that disaster events were modeled\n", "as Poisson variates:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "disasters = Poisson('disasters', mu=rate, \n", " value=masked_values, observed=True)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 37 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here rate is an array of means for each year of data, allocated\n", "according to the location of the switchpoint. Each element in\n", "disasters is a Poisson Stochastic, irrespective of whether the\n", "observation was missing or not. The difference is that actual\n", "observations are data Stochastics (observed=True), while the missing\n", "values are non-data Stochastics. The latter are considered unknown,\n", "rather than fixed, and therefore estimated by the MCMC algorithm, just\n", "as unknown model parameters.\n", "\n", "The entire model looks very similar to the original model:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def missing_data_model():\n", "\n", " # Switchpoint\n", " switch = DiscreteUniform('switch', lower=0, upper=110)\n", " # Early mean\n", " early_mean = Exponential('early_mean', beta=1)\n", " # Late mean\n", " late_mean = Exponential('late_mean', beta=1)\n", " \n", " @deterministic(plot=False)\n", " def rate(s=switch, e=early_mean, l=late_mean):\n", " \"\"\"Allocate appropriate mean to time series\"\"\"\n", " out = np.empty(len(disasters_array))\n", " # Early mean prior to switchpoint\n", " out[:s] = e\n", " # Late mean following switchpoint\n", " out[s:] = l\n", " return out\n", " \n", " masked_values = np.ma.masked_values(x, value=None)\n", " \n", " # Pass masked array to data stochastic, and it does the right thing\n", " disasters = Poisson('disasters', mu=rate, value=masked_values, observed=True)\n", " \n", " return locals()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 38 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we have used the masked_values function, rather than masked_equal; The result is the same." ] }, { "cell_type": "code", "collapsed": false, "input": [ "M.early_mean.summary()" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\n", "early_mean:\n", " \n", "\tMean SD MC Error 95% HPD interval\n", "\t------------------------------------------------------------------\n", "\t3.053 0.287 0.008 [ 2.491 3.604]\n", "\t\n", "\t\n", "\tPosterior quantiles:\n", "\t\n", "\t2.5 25 50 75 97.5\n", "\t |---------------|===============|===============|---------------|\n", "\t2.517 2.861 3.038 3.23 3.636\n", "\t\n" ] } ], "prompt_number": 39 }, { "cell_type": "code", "collapsed": false, "input": [ "M_missing = MCMC(missing_data_model())\n", "M_missing.sample(5000)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "\r", " [-------------- 38% ] 1946 of 5000 complete in 0.5 sec" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\r", " [-----------------77%--------- ] 3862 of 5000 complete in 1.0 sec" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\r", " [-----------------100%-----------------] 5000 of 5000 complete in 1.3 sec" ] } ], "prompt_number": 40 }, { "cell_type": "code", "collapsed": false, "input": [ "Matplot.plot(M_missing.disasters)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Plotting disasters_0\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " disasters_1\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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DUeQjonJZonIJgnCXWjZLVKbvM5N4zUVru/My0djoRFR4WhkTUYaRH+YP1XFI\n0hI1R1UP9KxQXUSkf1SiQnXnZXqhFOKFU2hLVJxRWy3NK44lKmp/sEx/f6lZojL5REXRWhGVjyUq\nU1iLllqSWmuJypZvlEN6uO6ZyrXuPMMwOhqJPfZUNfhKXReIdH8udndea0RULmEWJ9+W+kRlI19L\nVK5pSDJZRIJ1T8InqtBz7iXpE5WvJaolIip8/YplicrmWB7VnRcVbiOffNsSEekiIo+LyGQR+YeI\ndBaRS0RkqohMFJFKL90pIvKyiDwpIt3aut6GYZQHSUcsP1pEZgHfqer8qDSZXjZR3XnN84/OL46I\nao1vUtjiEjeYYrD8fMtN0rE8KCzy6c6LiikVTJ9PPYIU2ycq6jtI2hIV1Z2X654uNUtUJp+ouCKq\nRC1Rw4HXVXUo8BpwMlDtTUv1NjDCi3F3NjAIuMdbN4wWYz5RHYdEH3uq+oSq7gF8IyKHRqUJvmwO\nOii1vno13HZb8xfDIYe4pQi8/XZqXcQNUQ+Ozhs/3u3v0gWee86l9bsnLrkEhg5N5fvRR7ktI37o\nAb9cn2AdV6xwYmL8+Og8Xnopen82li7NHoPJj6kVh7CIijr3z39212C77dy2/5K84YZUmquuSq1/\n+aVb9u7t4lQFr98tt8C226bnP3JkermPPBK//hUV8Mwz2dOIuNAQY8c2j8UEcMIJ0flmEiG33AI3\n3pi9zF/+0i1POcUto4S1fz3nzEm/Rhtu6Jb+/SXi7uOFC932kiXZy/7qq+ZlJkEmS1Qw6OYzz8Ct\nt0af/847JWmNWgL08NY3BLYB/IDAk4D9ge2BWaraGNhnGC3G4kR1HJKMWN45sLkc6Nw8VS1vvlmL\nH2wzzOTJ+VluVqxI786b7D0a16xxQS2DTJ8OdYEio2IHgQt+6bN0qRNh3ULG/WAdu3bNHpXaZ4cd\ncqcBOPnkeOnCdO+evv2738G++7q6xu3i+uCD3Gl+8IPU+t57p2JG+bz0Enz4Yfq+hx+G+++PV4cw\nqi6+VC4WLYLHH09tB7+zKEHqTyI8ahQsX55+LJvwDVsle3iv57Al6uab4Xvfc9tdu6aLi6VL4e67\nndgPdo36916cKOp+G8AF9PzFL5ofP+YYt9xgA7fcaSe3zNadF+UTFRRRft18gRjExRIruWCb04C9\nROQdYG9gLuBf4eU4gdXDWw/uMwzDyEmCM4oxXER+gZs3bz7wz+ZJatl998yBKcNTZsRx2g525wXF\nQkv/pYeL/27wAAAgAElEQVTzqKrKHuKgc+d43Vpx65NEvcFZiPx59JKcNy74As6nrq2xUMQR1uFI\n6HG641SdRSpsfclWXqdO6WVl8okKfx/h+nTu7ARZ0L/JF2i5fM2inNq7dGmezhdlfvv87Xx9ooLC\n0V9fZ51Mtaumtra6aasEujTGAE+r6tUicjFQBfh/ObrjfDeXRewzDMPISZLBNp8AnsiVLtsLwrcO\nxC8zvTvPf3FVVbU8Bk/QryPTyL/gdlRwwigKLaLC/iidO6cLhXDaJMrJ57sqdDdPuE1xHMOjglXG\naVNFRXN/ubCICl+ncDlVVenzzjU0xBdRYQHX0BAtonxB5IvoXGLav9/DBO9vv+zOEXbmEqU74HWA\n8iXQB9gHuAo4BGepeg/YXUQqAvsiqA2sV3sfw2iO/+fBuvTKi7q6OuqCXVYxSDJO1L7ANUAjzpEz\nooMh/r/sODQ0pHfnBUVUkpaobBGoq6riWaLiCo6kLFGdO2e2RHXqlIyIKpYlKtu5wcCgUXHHMuHX\nvaIif+taWGgHl/56MLZS1Hfv3zdBa1K2ybej6p7LEhUWUVFWpnC+UWmi6hMlolojzgvIROBBERkD\nrAFOBM4SkanAR8A1qlovIhOAqcBSYFR0VrXFqK/RDjDxVJ5UV1dTXV3dtB3Hkp5kd96HwFBVXeMN\nHd5dVd8JJ8plicqnO2/t2nRrUfBlEdcSFS4jyhJVjiIq2J0XPpZrFFXcUWvFElHZ8K+937Ubt7zg\nCLp82xQ12jEcUyuYJpMlyr9//Xyi8ooinK6hIbp7zRdE4WVruvN8okRbKYooVf0KCM+seaX3Caab\niBNchmEYsUmyO29hYHMtENnJle0h63fPxcX/Jx/VndfS7rOwJSpXd15cERW3XUl153Xp4sqMcixv\nzVD0lnbnFYqgiAoSVyi2RETFtUQFywoLl8rK5paofH2igv5YUaIm3I0XxxIVNQghHxFlGIbRkUj8\nsSci/YBNVTVisHl+lqhc+P/ko7rz4oqWcLpCWaKK7VjepUvKOuMf85dJiahSskRl+x6j8P3FwiLK\nF57ZCAvt8H3bUktUUERl81+Ka4kKO5bnskRlivgeV0TFHQVqGO0dixPVcUiyOw8R2Qi4AYiIzON4\n+unM56vCY4+ltqMe1EH23NMtR41yMWq23NJtV1XBBRe4T5i33oKDD07FQPrDH9KPL17sXjKffgrn\nerP/ffwxHH889OrlhnsH4/h06wa77ebWd9wR3nsvdSzYvbFgQfa2gBsu31IRtc8+rp4+G2/s4hN1\n6ZJ6Mfov3+rqzN+DCDz6aOZygi/gO+9MrY8b5162fgyo11+H229318w/LxwfKtPL/IYb4Kc/TW1/\n8UXztAsXwvPPw5gxbnvIkPTjBx8MDzyQuR2+83dYRI0dC3//e+bzAJYtS61XVMBvfwuXX57aN326\nE0j+HHThewzc9zJ1aipEwqhR8MILqbp17+5CIQS56SaXxg/lsPnmqWN+3Kogft7/+59b/ve/bhn0\nZzr7bPc93XsvnHpqeuw2n3DICoDdd4ennnLrftyqddd1bd5+e5g3Dx58sPl5RsegoWEtb4cD7BWA\nbbfdlm7hGDQlgPlEdRySdCyvxPkU/FJVF0Wnqg2sV5NrdMvgwe5hnAv/ZbLIKzVbt8X06S5YpJ/m\n+uuj04UDHj76aLTV6cknU+Vfc016HKVf/xr+9KfMdTn22HTReOCB0SLq449h/fVho41cMMmePd2/\n/mBsqL/+1ZU3cKDb7tvXLV97DUaMSKXr0sWJhMceg5NOggsvhOuuSy/Pt4L06uViYH35JZx2mhNN\nmSw8l12Wbg2aPx/+8hfYbDO3LeLiFQUFSCYmhjxTunZtnmbRItfmIIcc4oTvD37gvqvbb28eP8vH\nH50Xbs8996TWx493Iq221gk7PybWrrvC55+7WE/HHefaGWbPPeG++5rv9wXVzjun7/cFFLjruN12\nTvRssUVq/8SJ8Mor0e3ZZpvm+/bYI33bv7f8YJ/grhHApElOBFdUuLhZxx6bHgw0zOWXO9G1yy6p\nfT17wtKldcybVweAvUc6KpU0NPRi0KDRBS1l1aoPePrpxzj00Mi4zoZRFJK0RJ0ADACuFPfU/Y2q\nhh75tVkzCHejxJ3g1rdY+ednE1HhqTgyBcqMEjOdOjUXUX4gw1zlRhG2tIWdo3223joVMHLzzdPL\n9P/9d+rk1oN1BWeRCr4EN9jAWSL87p8okeGnr6hw1owvv3T5BI/lIixOROIPi8/mg5Ypfz9dt26p\ncrL9Qc3kWB4sa8MNnXANx1nq2tWd37mzE5zhYJ4VFZm74zbayC2zdX01NLjjPXum6hSuZ5io6xFO\n76eJusf8dldUuOsWvMeiEIGttooqrxr/z9Guu8K771qXRsdjE7777u1YQYhbwwYbmHgy2p4kHcvv\nB1oYl9rPI307XxHlvxziiCjfahKOuO0T5VOVaQ62qPVgfXLVJZh/pnP8F2D4Zem/rCsq0o/565WV\n6eX460H/sUz1CkbRDgqrOESJhCSd6zt1an791q6NL2SDcaIyiahMba2qcvdNRYWrR1hE+V2F2cRf\nNhHl+7GJpLqEo9obJI4/kp8m273t1y/OJNu5yizBKWAMoyhYnKiOQ5LdeVsATwO7AOt581DlRVIi\nKpvFI85Ex3GO+7RGRIVf0pksUcG04XN80eC/0MN1qapKPycshqJehFFTkWQqPxPhF6hI/GsaxxIV\nVUZ9fXwR1diYElAtEVHffZeKXh4lxDMJDH9/Lsfx4PX2LVP5WqIypYn6Hvzfml+/OCIq3Iao77y1\niMjdwP2qGjEDgmGUJiaeOg5Jjs5bCgwDMnht5KalIsp/0cexRPnEjQqdiyiB4pOvJSqbiMo0WbL/\n0hPJLKKyWaKiXr7BEWNhEZXpxZhpapxgKIGWWqKirklDQ+ssUcHReUHiBOwMC9eo0ZmtsUT5oslP\nl2/sqkxkE1F+G6IsUS0tMyFL1JnApiLyoIhcKCLrJZKrYRhGAiQmolR1taq2as6p8IM7TugASL3o\n/fOz/ctP2hIVlXfcPPLpzsskonJ154VFRdiilK3bLWjZybc7L9yOfCxRcdJlEgJx5wn0r3WUNdAn\nU1uD1zyTkMh0bhyLXjAsRXCKmWJYovLpzmtN0NY82Bjoi5vfbiHwt0RyNQzDSIBEQxy0lqQcywvV\nnZfrn3W2F3Lc9PmKN/+FnskSlanLJY6IWrMmviUqk4AMir8ku/P87rgg+VqiwlO++Pt9clmi/O68\nKDJ1vwUth5kId+eFr2UUcURUNp8of18+lqgw+f6JiMnFwM2qOs+VIZ8kkqthFBDzieo4lJSICscu\nevbZeOf5I83mzHHL4Ci1MH4MpJ/8JHuegwe7Zc+eLiYRZB7J5+PH5fHJNLwe3It4xx3T902enApR\nkInwy3LnneGTT9z+4Gg/X/x06pQeu+rTT93Sv2ZRI9hOPNEt6+tTcZ56944u3yf8Yvbz8K9ZOGRE\nNsLhZcIhGCAVIyzI3LnZv/sgF1/slkcfnb4/KB78axgehfaON5lRRUV0kEv/WJSvVByxM3y4C2kB\nLn//PvK/iyiiYqr5Iyp9dtvN3Qsffwz/+AcceWTqmB97yhdawRhU223n7s1cvBOa5ClXvK2Y1AUE\n1JGqmiXSnGGUBiaeOg6Fmqghw3/m2sCnjk03dYEAx41LT7ViBXz0UWr74IMzFzRnTvMX2UUXpW8H\nhcITT2TOKyogZjhmUSb+/GcXgHDJEvcy+fpruPRSePXVlDBavBg++8yl+ewzuOQSFz4AYD3P02P5\n8sxlLF6c/rJctgwmTHDrIk7wvfGGa0e3bm7pWwf8QKQ+++/vlv36ORHmB2QMsnYtXH21e+n++Mcu\n6KUvAoLX6re/zVzncHuyXf/WMn26e+EHee01t3znHRcode5cd919/Bf/Rx/BppumiyhfZPzsZ+mB\nL/3vrFMnqKuDa69tXpdOnVKxug48MH1/HFascMtgXKjPPkutH3BAevrevV0bPvggFVfLn0ezosJ9\nX/ffD7Nnu313350qI4j//V5zjRPcy5a5IJ+Z+PhjmDHDXdf//AegjvTfeasJhlEdlESGhmEYSZF0\nsM1ngT2B50Tk/6nqa+mpatO2+vZ1wfoWL/YqU+msH+utl94ts+uuqcB/YXbc0b3cg/j/4oPb33yT\nuw3BwIY+68V0Y91hB7fceON0C8A++8C227oI3pts0vw8P25QRYV7ia9e7YTS6tWp6+ETPr97d1i5\nMn1f//7R7dlii3ThE/SPCVtafFRdGb51p2fPlCgLtrFfv+jzowgGekya3Xdvvs+/Zn5U+e22gz59\nUsf967DNNu679q1H666b3m0XrPfGG7v7qaLCiZeo9vvxliBd5Oc75U5YFPqERbFIKuDmVlulWx83\n3DB1LwTjP0V1l/v1W3/95r+jKLbe2n3AL7+a9CC6rY4TtamIHAwo0LO1mRmGYSRJknGi6oFD8jkn\n7JcTfMEEfXlyvXhy+Sq1xjej0HPe+aim4g/5y2LE2ck1Yi5sOfHrFPx+4gbRhNKYpDZY9+A1jut/\nFBRXkDkwq0/weL7zy7XkHsjmzxT0eco0qrClFGjuvJ8Bo3DW7YtypDWMksB8ojoOSc+ddy2wN/CG\nquZ84IWdnKNGl4XX49Ujfbs1o4TiDstPYiRSZaXrYslHlLSWXM774RdjOCgjFLe+SRC0coZFVDAk\nQyaCo/Mg+h4JOq0Hr3HUvRwUb3HJdr9lyyv4fUaJqNYIoQKJ/m2ADYAuwIXA/xWkFMNIEBNPHYfE\n7AIishcuyOZgoLOIDMhZeEX0MlO6TOQSMC21ElVUZBIZdYmV4eNbotasaR5WoHDU5RRR4WsflT6f\nF29Cw94jqIudMpuI8r/HbPdcME4URH/3+Yio5k7hdZkLj0E24R8sP2lLVIHu118ATwEPADalsWEY\nJUWSnSv7As9765OA/XMWnqU7LypdS2mpwKmqyvRCqkusjOD5fjdeMGxBYanLaWkL1yGT1SUupSCi\nMnXndeoUr37h7ryoaxIMcRAUUVGCs7klry5nHbLdG1ExunyCoSqy+USVEO+o6juqOkdV57R1ZQzD\nMIIk2Z3XA/jAW18G7JbrhHB3XqYXQ2stUS19cWcWUcmVES5v7drS6s4LE3U9ym2OtEyxpCoqUvPg\nZfve87VEBS0+8SxRrSOboC+kJapADBWRauA7AFU9oW2rYxi5MZ+ojkOSImoZ4EdG2gDIGb3cH3nk\nv5R69kwfRbfRRm5oeTjeTZjwSzH8Uurb141M+/zz9P3rrZca3RYV76dPn8xxgCB9hFS2UXybbZb5\nGDjR1K1bqt477QTz57vyv/oq+7lxgkt27epGCM6Y0fxYtvZFiaMogRc3SrhflyDdu2cP69Baouob\nvD/8+Ffg2uELkN2y/AXo3duFHvCvfbhNfl7+yMD330/tj/q+evaERYsylxfFpptmPrbVVqnYZpAa\ntefXC1xcqPCoViiYc3hrOAnYRVVfF5EM40izIyI/An6Es7yPBk4BjgY+Ak5T1XoROQU4Dzd91ShV\njTGe1zCiMfHUcRBNqH9FRPoDZ6vqOSJyE3CHqk4PHC9YR45hGKWLqrbYVikiE4A1qnq+iNysqufl\neX4vYKyqnuFtb4Z7Nh0pIr/CWc8fB17ExWY4HthGVf8cykddlIX2iv8VlU8bN9jgUB5++Fcceuih\nbV0Vo50iIjmfX0mGOHhTRL4TkSnAm0EB5R0vs04fwzBKgBWAb49d1YLzDwM6icgk4H+4WHZ13rFJ\nOKvUf4FZqtropZvQqhobhtFhSDTEQZywBoZhGHmwBBgkIlcDLRm+0ROoUtVDROQKnKuB34G8HOfL\n2SNin2G0GPOJ6jiU1Nx5hmEYQVT1jyKyM1ChqhGTE+Xka2CKt/4SMADwXeq7e8eD/pz+vghqA+vV\npEdmN4wUJp7Kk7q6Ourq6vI6pyhjcUTkWhGZIiLji1FeSxGRLUTkDRFZJSIV3r5LRGSqiEz0prZB\nRE4RkZdF5EkR6ebtGyYi/xGRlzw/jDZFRPb16jhVRK7x9pVdW0RkN69+U0TklnJtRxAR+bmITPXW\ny7ItItJHRBaKyGQRedbbl3hbROR+oAa4XET+0YKq/gfwJ+bpD3xCaj6+Q4BpwHvA7t5v3t8XQW3g\nU92CqhiGUcpUV1dTW1vb9IlDwUVUS4JwtiFLgWHAK9DkhFqtqoOAt4ERIlIFnI2bDPUebx3gt8Ch\nwKXAb4pc7yg+BIZ6dd9MRAZTnm2Zo6oHevdPFxEZSHm2AwAR6YKbX1JFZFPKuC3A86o6VFWHF+q3\noqonq+rJwLGkLEqxUdW3gFUiMhk3m8IDwBRPxPYD/uFNWTUBmAqMAW7LtxzDMDomxbBE5R2Es61Q\n1dWq6pvyBWf6r/O2/bpvj+eE6u8TkXWBVaq60pt0OWeMrEKjqgtV1Yt6xFpcneq87bJpi/eC81kX\nGEgZtiPAT4C7KPP7y2OoZyG8CCdQ6rz9ibXFs0TuihM8LWq3ql7iib2RqrpWVa9U1UGqOtq/v1R1\noifWj7LwBkZrGTt2bJNflNG+KYZPVN5BOEuIuE6owX0AJRNtR0T6AZvi/Dx8x9yyaouIHA38EZiB\nG6nlh8Ist3ZUAUNU9WZxQbhy1btk2wIsAHYA1uBCBHQD/GhXSbbleG+5Gri+1bU2jCJgPlEdh2JY\novIOwlkiKNEOp7n2Qeol36aIyEbADcCPKeO2qOoTqroH7uW7kjJtB66r6L7Adjl/J2tUdZWqNuDm\ntptHYdoy3fvMArYSkSOTaYFhGEbrKYaImgYc7K0fTEanzZJDcA/vnE6oqvotsK6IrCci++DizrQp\nnmPvROCXqrqIMm2LiARjjvvWjLJrh8eOwLki8k+cRXYAZdoWEVk/sHkgMJfCtOUMYBdgZ299k+Ra\nYRiG0ToK3p2XKwhnKeEJj2dxjr/PApeRckL9CLjGmyLCd0JdCozyTv8j8AIuIOCpxa57BCfgXtJX\nel1Hv6E82zJcRH6BE7XzcSO1Ni/DdqCql/rrIjJFVf9PRH5Vjm3BxW76Pa6bbYqqvub5RyXdlnf9\n6OEisqmq3lWIxhhGklicqI5DYtO+GIZhJI2I/AnYDNe9vlBVL2ujeti0LyWGTftiFBop5rQvhmEY\nBeAyYCucP9XqNq6LYRhGGkUJtmkYhtFCxgM1qrocN0jCMAyjZCiaJcqZww3D6Gi0cvLxRpyPFZTP\nyF6jg2M+UR2HolqiVLVdfGpqatq8DtYOa0s5fBJgNbCriPwU2DCJDA2j0NTU1JiA6iDkFFEi8jdv\njqxZWdJcLyLvi8hbItI/2SoahtERETes9BFchPd5wDltWyPDMIx04nTn3YHzRbg76qCIHAFsr6o7\niMi+wC3AfslV0TCMjoiqqogMVdUr27ouRmkyd+5cNtmksKHDNtxwQ/r06VPQMozyJaeIUtWpItIn\nS5Kjcf8UUdVXRaSHiPRU1YXJVLH0qK6ubusqJEJ7aQdYW9ojInIMcIyIHIaLM4WqntC2tTJKhVWr\ntuPSS28Hbi9YGWvXLuXII4fw8MORNoSMmE9UxyFWnChPRD2pbuqN8LEngT+p6n+87UnAr1V1Riid\nJuQjYRhGmRAnzkqWc29R1XP9ZdJ1y7MuFieqQ3I3I0ZM4rHH8hNRRvugmHGiwoVE/hJra2ub1qur\nq+0ft2G0M+rq6qirq0squ228ufK28dwGUNVnksrcMAyjtSRhiboVqFPVB7ztd3Ez1S8MpTNLlGF0\nMFppiTqN0B8ybaNpX8wS1VExS1RHpliWqCeAC4AHRGQ/4Ov27A9lGEZxUNU727oOhtESzCeq45BT\nRInI/bjZ2TcRkU9wE8BWAajqbar6jIgcISJzgZXA6YWssGEYhmGUMiaeOg5xRuedHCPNBclUxzAM\nI3lE5OfAcao6SEQuwY0q/gg4TVXrReQU4DzcKMBRqvpNG1bXMIwywebOMwyjXSMiXYA9ARWRTYFq\nVR0EvA2MEJEq4GxgEHCPt24YhpGToouo4Ag9wzCMIvATXCw7AQYAdd7+ScD+wPbALFVtDOwzjBYz\nduzYJr8oo31TdBFlN5ZhGMXCszINUdXJ3q4ewHJvfbm3HbXPMFqMzZ3XcYjjWD4cGA90Av6iquNC\nxzcBJgKbe/n92UbVGIZRIowB7gtsLwO28ta7A197+7qH9kVQG1iv9j6GYbQXWhLnLmucKBHpBMwB\nDgE+A14HTlbV2YE0tUAXVf2NJ6jmAD1VtT6Ul6qqH3chr0oahlGetCZOVELlXwF8DxcAaV/cH8J9\nVPUHIvIr4APgH8CLwFDgeGAbVf1zKB+LE9UhsThRHZkk4kTtA8xV1Q+9DB8AjgFmB9J8DvTz1rsD\nX4YFlGEYRlugqpf66yIyRVX/T0R+JSJTcaPzrvFG500ApuKNzmuj6hrtBIsT1XHI5RPVC/gksP2p\nty/IBGA3EVkAvAVcGLfwTE7mTz31VNNNeM4558TNLpK77rqLtWvXtiqPMNdddx0HHXQQxxxzDN98\nYyOhDaMcUNXB3vJKVR2kqqP9P3yqOlFVD1TVoyy8gdFazCeq45BLRMWx7f4/YKaqbokzm98kIt3i\nFB7HyfzWW2+Nk1VG7rzzTtasWRMrbZxuxiVLlvDkk0/y73//mxNPPJGbbrqpVfWLU5fGxsaClGEY\nhmEYRsvJ1Z33GbB1YHtrnDUqyAHAHwFUdZ6IzAd2AqaHM/MtT7W1tc0mH162bBknnngiIkKPHj3Y\nZZddABgwYADTp0/nd7/7HS+99BJdunThiiuuoE+fPpx00knU19fTs2dPHnzwQebPn8+YMWNYZ511\n2GmnnTj11FOZOXMmhx9+OMcddxyjR4/mzDPPZPny5WyxxRbcfffdTJkyhauvvpqqqiqOOuoopkyZ\nwrx586isrOSOO+6gd+/eafV8/fXXGTJkCADDhw/n1FNPTTuuqnz/+99n7dq1dO7cmUcffZRu3bpx\nxx13cPvtt7POOuvw29/+loEDBzJ69Oi0urz88stpdbnhhhsYPHgwS5YsYeLEiTm+KsNoexKegNgw\nDKO0UdWMH5zImgf0AToDM4FdQmmuAWq89Z44kbVRRF7qzUCsPsH1q666SidMmKCqqpdeeqmOHTtW\nVVUHDBigqqr77ruvNjQ0qKpqY2OjrlmzRuvr61VV9cILL9QXXnhB//rXv+rNN9/clEZVtbq6Wleu\nXKmqqhdffLG+9NJLqqo6btw4feSRR7Surk4HDx6sqqpr167VAw44oKlOfh5B7rvvPh0/fnxkep9v\nv/1WVVWvvfZanTBhgi5atEj3339/Xbt2bVO+V111ld52222qqvr73/9e77777rS6qKpuu+22Om/e\nvGb5G0a54P3Gsz5nyuEDKGg7/qDtv40t+dylI0aMyfu+r62t1dra2rzPM0qLOM+vrN156vwFLgCe\nA/4HPKiqs0XkbBHxo/peDgwQkbdwgep+papL8xVzDzzwAHvvvTcAAwcOxNU/xdixYzn99NM555xz\nWLRoEUuWLOGHP/wh1dXVPPPMM3z++eeMHDmS+fPnM3r06EjLzezZs6mpqWHo0KE89thjLFzo5kke\nMGAAAJWVlZx//vmMGTOGiy66iG+//bZZHj169GD5chdSZtmyZWy00UZpx1esWMEZZ5xBdXU1f/vb\n31iwYAHz589n7733prLSGf5EhHnz5jFw4MCm9r7//vtpdQHYcMMN6du3b76X0jAMw2hDzCeq45Az\n2Kaq/lNVd1LV7VX1T96+21T1Nm99iTpnzD1VdQ9VvS97jtHMmDGDN954A3BdZmEGDx7MXXfdxZAh\nQ7j99tu5//77Oeqoo6irq2P48OE0NjZSWVnJlVdeycSJExk3bhyqSlVVFfX1brDgzjvvzOWXX87k\nyZOZNm0aZ511lrsIFe4yNDY2MnLkSO655x569uzJ3//+92b1GDhwIFOmTAHgueee46CDDko7/vzz\nz9O3b1/q6uo47bTTUFW222473njjjaZ6NDY2sv322/Pqq68C8Nprr7Hjjjum1SW8bhiGYRhGaZEz\n2GYxeeihh3jooYfYYostmiwwIi5Ew4gRI1izZg0NDQ3ccsst1NfXM2bMGJ588km6du2KiPDEE09w\n4403As5fSUQ4+uijGTlyJMcffzyXXXYZZ555ZtM/hCuvvDKtjOXLlzNixAhEhIqKCu69995mddxk\nk0048sgjOeigg9hoo42apdlvv/24/PLLefPNN+nZsye9e/dm44035owzzuDAAw9kvfXWa6rHKaec\nwgMPPMDmm2/Ob37zG15++eWmugTrZRiGYRhG6ZE12GaiBUUE28y0bhhG+6Ctg20mhQXb7KjcTWXl\n2ay33oZ5nfXznztvl2uvvS1W+qoqWLx4Qd61MwpLnOdXyYmo2trakpmk+L333uPss9MndL/33nvZ\ncsst26hGhlFemIgqF0xERfMtGWcBSgwFtjIjQgmSiIjKNXeel6YauBaoApaoanVEmlgiyixShtF+\nMBFVLpiIajsUqLD3XgnSahEVc+68HsDLwGGq+qmIbKKqSyLyMhFlGB0ME1HlgomotsNEVKkS5/mV\na/hX09x5qroW8OfOCzIKeFRVPwU3Wq+lFTYMwzCMcqe2diy1tbln5DDKnyTmztsB2EhEJovIdBEZ\nk1TlSsU3yjAMwzDiUltbQ22txYnqCCQxd14VsBdwBHAY8DsR2aG1FYN4c+sZhmEYhmG0BUnMnfcJ\nzpl8FbBKRKYAewLvhzPLNneeYRjlj82dZxhGRyKXY3klzrH8YGAB8BrNHct3Bm7EWaG6AK8CJ6rq\n/0J55e1YXophDwzDiI85lpcL5lieJL4/VLwuPXMsL1WSCnFwOKkQB39V1T/58+b5U7+IyC+B04FG\nYIKqXh+RT4tFlI3YM4zyxERUuWAiqu0wEVWqlGWwTRNRhtF+MBFVLpiIajtMRJUqSYQ4KDmsW88w\nDAbQpzsAACAASURBVMMwjFKg7CxRZpUyjPKhrS1RIrIvcA3O1eB1Vf2FiFwCHA18BJymqvUicgpw\nHrAUGKWq34TyMUuUERvziWoftMvuPBNRhlE+lICI6gl8paprRGQicDvwa1U9UkR+BXwAPA68CFQD\nxwPbqOqfQ/mYiDIKhImoUiWR7jwRGS4i74rI+yLy6yzpBopIvYgc15LK5ot16xmGkQtVXaiqa7zN\ntcBuQJ23PQnYH9gemKWqjYF9hmEYOckqory5824EhgO7AieLyC4Z0o0DniX1l6agWCBOwzDiIiL9\ngE2Br4Hl3u7lQA/vE95nGIaRk1zBNpvmzgMQEX/uvNmhdD8FHgEGJl3BOFgcKcMwMiEiGwE3ACcA\nA4CtvEPdcaJqmbce3BdBbWC92vsYRnPy84kySoWWBAvOFWzzeOAwVT3T2x4N7KuqPw2k6QVMBIYB\nfwOeVNW/R+SVqE+U+UkZRulTAj5RlcATQI2qvi4imwF/U9UfBHyi/oHziRqK+US1aS06JuYTVaok\n4RMV51sdD1yq7g4QitSdF4VZowzDCOFbn64UkclAX2CKiEwF+gH/UNV6YAIwFRgD3NZWlTUMo7xI\nYu68vYEHRARgE+BwEVmrqk+EMyv03Hljx441IWUYbUipzZ2nqvcD94d2vwJcGUo3EWdRNwzDiE2r\n584Lpb+DNuzOC+4zPynDaHvaujsvKaw7z8gHixPVPija3HmBtCUjosxPyjDaHhNR5YKJqLbDRFSp\n0q6DbcbdZxYpw2g7TESVCyai2g4TUaVKu5w7L1+C8aRMTBmGYRiGkRTt3hJl1inDaDvMElUumCUq\nSVriE9W3b/+C1qmiAsaP/z1HHnlkQctpT1h3njmgG0abYiKqXDAR1XYo8GbBS+na9bfcdtsoRo8e\nXfCy2guJiSgRGU7KufwvqjoudPwU4Fe4X+I3wLmq+nYoTUmKKBNUhlE4TESVCyai2jvrrz+aW24Z\nbiIqDxLxiZJ48+d9AAxW1X7A73EzpZcdvv+UCSnDMAzDMHIRx7G8af48VV0L+PPnNaGq01R1mbf5\nKqm5qcqSKGf0oLAykWUYhmFkorZ2bJNflNG+iSOiegGfBLY/9fZl4ifAM62pVCnhC6qgsIqyWJmw\nMgzDMMA5lNvkwx2DOCIqdie5iAwFfgz8usU1KiPiCisTWIZhGIbR/ogjouLMn4eI9MNN4nm0qn4V\nlVFQVJTS/FpJEiWs8ukeNMFllDN1dXVNAzTsXjaM0mLFihUsXbq0oJ/ly5e3dTOLSpxpX3LOnyci\n2wAvAaNV9ZUM+ZT86LxSqkPwJWQvJKNcsdF55YKNzkuS/OJEFYeqqrOpqHi4oGU0Nq5lv/0OYMqU\n5wpaTrFIMsRB1vnzROQvwLHAx94pa1V1n1AeJqJaWQcTU0a5YSKqXDARZSTBc+yzzzW8+mrHEVGx\npn1R1X+q6k6qur2q/snbd5t6ExCr6hmqurGq9vc++2TP0WgJcbsFk96XzzmGYRiG0VHo8BHLrQ7J\n1ivoD2PiyjBLVLlgligjCcwSZRitIq4zfTmRlJUu6ZhjxS7PMIx4WJyoDoSqFuXjilL1l5nW22qf\n1aG49aqpqUlbtgVRdYjaV4xrk6sO2epVrPJaglde0Z4zrfkA1wJTgPERxxS0iJ/JRS4Pbf9ttPIK\nX+azus8+32/VMyMbkydPLljeUcR5fmU96PJgOPAu8D7w6wxprveOvwX0z5AmWKmM6+1JKJRjHdqy\nXtle5rmOt0aElMO1KYU6tOT7KRcRBewF3O6t3wwMCB0v8suppsjltYWIKnYbrbzCl1lYEVXsP92t\nFlG40XhzgT5AFTAT2CWU5gjgGW99X+CVDHkFK5Vxvb2/iEq9DqVar1KoQ6nWqwzqkPU5Uwof4Fzg\neG/9OOCnoeOteNG05FNT5PJMRFl5SZTZ8URUJdlpmjcPQET8efNmB9IcDdyFK+1VEekhIj1VdWGO\nvA3DMEqFHriJ1AGWAbs1T/JYEaszu8jl+bTnNhavvNrat5k8uY5//at9ti9zmc/x2mvP06vX1plO\naBXLly9jwoS/FiTvMBts0CNWulwiKmrevH1jpNkKMBFlGEa5sAzo7q1vAHzdPMlxRawOwENFLg/a\nfxuLU15q/Ma/ilJeira4Z5qXuWBBs0lNEmPFim8KlneQuG3IJaI0ZnnhIYBxzzMMwygFpgFnAw/j\nZme4I3hQ20GYBsMwkieXiIozb144zVbevmaI1AI13rIaUKTp0eSvt9U+q0Np16sU6lCq9SqlOtSR\n+o2XD6r6poh8JyJTgDdVdXpb18kwjNIna7BNiTdv3hHABap6hIjshxsevF9EXpqtLMMw2h/tJdim\nYRhGFFmDbapqPXAB8BzwP+BBVZ0tImcH5s57BvhAROYCtwHnFbjObU5dXV1bVyER2ks7wNpiFA4R\nuVZEpojI+CKVt4WIvCEiq0Sk4AGRRWRfEXlZRKaKyDVFKG83r7wpInJLocsLlPtzEZlahHL6iMhC\nEZksIs8WujyvzB+JyCQReUlEtixCeYd57ZssIgtE5OgCl9dFRB73yvuHiHQucHmVIvKAdz3HZUub\n8weqOebN87Yv8I7vqapvtL4JpU17ecm1l3aAtcUoDCKyF7Ceqg4GOovIgCIUuxQYBrxShLIAPgSG\nquogYDMR2b3A5c1R1QO9a9pFRPoXuDxEpAuwJ8Xz131eVYeq6vBCFyQivYDBqnqIqg5T1QWFLlNV\nn/PaNxT4GJhU4CKHA6975b3mbReSY3Hd+sOAdUWkX6aENu2LYRhGZvYFnvfWJwH7F7pAVV2tqhGj\nAwtW3kJVXeNtrgXqC1xeMP91iRwJmTg/wYXiKVbX8lDP0nZREco6DOjkWaKuL4b10kdE+gILVfXb\nAhe1BBeGBG+5pMDlbQvM8tZnAgdkSmgiyjAMIzM9AH9M9TJSD/J2h/dve1NVfbcIZR0tIrOA71R1\nfoHLqgKGqOrkQpYTYAGwAzAUOERE9ihweT2BKlU9BPgWF8uxWBwH/L0I5UwD9hKRd4C9ve1CMgcY\n4q0PI8vvPqtjeZK4WdANw+holLNjuYicByxW1YdF5Digl6reUKSyJwMHq2pjEcraCBc18QRVXVTo\n8gLlXg88qaovFLCMHwNfqurjIjLV67YsCiJyDrBMVe8vYBnnAg2qeruIfB83ZdHlhSovVHYdcKyq\nflXgck4FNlHVq0XkYmCRqt5TwPIqgPHArrju7n+r6p1RaXOFOEiMcn6QGobRYckaP6oIFPy56Y3C\nngj8shgCSkQ6B7oPlwMFdRIGdgS+5wma3UTkfFW9qVCFicj6qrrC2zwQN7dsIfkPcKa33p9U5P2C\nIiKbA2sKLaA8ugN+OV+SCoxbELw/Lj8DEJHbcIPrIrHuPMMwjAyo6puAHz+qvhjxo7yRQZNwjtDP\nicg+BS7yBGAAcKU3+qlZiJqEGS4idSLyL1xcwX8WsjBVvVRVh6vq4cA7hRRQHoNEZLqIvAx8qqqv\nF7IwVX0LWOVZLvcGHilkeQGOBv5RpLImAid5bTwZuLeQhYnIlt5v4UXgZVX9PGNai91kGIZhGIaR\nP8WIQTJcRN4VkfdF5NeFLi9JRGRrT43+V0TeERHfvLeRiLwgIu+JyPMiUjbOpiLSSUTeFJEnve2y\nbIu4ia4fEZHZIvI/L9ZN2bVFRH7j3V+zROQ+Lx5KWbRDRP7mxcOZFdiXse5eW9/3ngffb5taG4Zh\nJEdBRZSIdAJuxMV02BU4WUR2KWSZCbMW+Lmq7gbsB5zv1f9S4AVV3RF40dsuFy7EBU71TZDl2pbr\ngGdUdRegH/AuZdYWEemD82XYS1X3ADoBJ1E+7biD5vFaIusuIrsCJ+KeA8OBm4s5FNswDKMQFPoh\ntg8wV1U/VNW1wAMUd/hlq1DVL1R1pre+ApgN9ML1Bd/lJbsLGNE2NcwPEdkKOAL4CymH1bJri4hs\nAAxS1b+Bizujqssov7Ysxwn1rp5zb1fc8OiyaIeqTiXl7OmTqe7HAPer6lpV/RCYi3s+GIZhlC2F\nFlG9gE8C2596+8oOz2rQH3gV6KmqC71DC3FxOsqBa4FLgOCQ6XJsy7bAYhG5Q9z0GBNEZD3KrC2q\nuhS4GhfxdwHwtTfUu6zaESJT3bckffLysn0WGIZh+BRaRLULr3URWR94FLhQVb8JHvNmVS75dorI\nD3CxNd4kw7DpcmkLLjTHXsDNqroXsJJQl1c5tEVEtgMuAvrgRMb6IjI6mKYc2pGJGHUvy3YZhmH4\nFFpEfQZsHdjemvR/oyWPF+32UeAeVfWHcy70YmQgIlsARQtO1woOAI4WkfnA/cAwEbmH8mzLp6QP\nHX4EJ6q+KLO2DAD+o/r/2zvzMCuqo3G/NcywCqKiSHBBIirBDYG4oDAgSVAzymcQN4jLh7s/xV2i\nfjPExAhPJCpGjaiIQFRMgoArKDNAABUENxRUBDcURIFRFmGY+v3R3XN77txt7vRdp97n6bndp0+f\nU6dvT3fdOtVV+p2bCuM/OGlFcm0cfqJdT+H3gv3cMsMwjJwlMCVKImc9XgJ0ESerdVMcx9IZQfWZ\nakREgMeAD1TVn8F9BnCBu34B6YuVkTSq+gdV3V9VD8JxXp6jqsPIzbF8A3whIoe4RQOA5cBMcmss\nK4DjRKSFe60NwHH6z7Vx+Il2Pc3AifPSVEQOwkmL8WYG5DMMwwiMwOJEichZQGdVHS1OKP9HVfVd\nETkFJ3x6E+AxVf1LIB2mARE5EZgHvEto6mEkzs1/KnAATkj4IelMGNpQRKQvcIOqni5OuoecG4uI\nHIXjIN8UWAVchHON5dRYRORmHGWjGlgKDAdakwPjEJGncPJLtcPxf/o/YDpRZBeRPwAX4yS4vVZV\no0YBNgzDyAWCVKJuxokG+6I4uYqaqurDgTRuGIZhGIaRZQTpE5Vw1mPDMAzDMIxcJ0glaibQws35\ntB34JsC2DcMwDMMwsoqU5M5zsx6X+ZP2iYi9zmwYjRBVjRhSwzAMI9cJ8u28uFmPVTUvltLS0ozL\nYOOwseTCYhiGkc8UBtWQqq4F+gXVnmEYhmEYRjYTpCWqmYhMd61Rz7lxoQzDMNKCiBwrIgtEZL6I\njHXLNrv3pDki0tYtO9+tN1NEWrtl/UVkoVvP0tEYhpEQQTqWDwQWq2o/nDhK4dnd84bi4uJMixAI\n+TIOsLEYgBOXqp+qngTsIyKHA++qaj9V7a+qm9wMBJcBJwGT3HWA24Ff4aQPGpl+0Q3DyEWCVKI2\nEApr0Nbdzkvy5SGXL+MAG4sBqrpOVXe4mzuBXUBXEZknIl6Q3y7Ae6paDbwKHC8iLYBtqrpFVd8E\nuqVdeMMwcpIglahFwDEi8j7Qw902DMNIKyJyJLC3qn4IHKyqfYA9RKQE2B2odKtW4vzga+srAyfy\nvWEYRlyCVKKGAS+o6uHAi8DQOPUNwzACxU1jNA4nvQwaSpfzHHA4sBlo45a1ATaFlYFjwTIMw4hL\nYG/n4dyENrrr31H7pgRAWVlZzXpxcbFNWxhGnlFRUUFFRUVG+haRQmAycKOqrheRlsBPqroLOBF4\nB/gIOFxECnASPi9S1a1uEuhWOFN5yyO0bfEaDKMRovHi3AUYD2YPYBZQDrwCtA3br4ZhNC7c//t0\nxaQ6F1jv3oPKgeOAt4C5wARCwYWHAgtwsiy0dstOBhYCrwH7RWg75efKAyfZedr68ygtLbX+rL+s\n7jPd/SVy/woyTtRG4NdBtWcYhlEfVPUp4Kmw4h4R6k3GsVj5y17DUaAMwzASJkifKMMwDMOIy6hR\nozI27WsYQRKYJUpEfoMTYwXgUOByVZ0RVPuGYRhG6kinj2ppaSl9+/ZNW3+Q/tAh+d5fJvrMRj/q\nVCUgfh3or6pbfWWair4Mw8heRCS+Y2YOkM77l4hzuux+aRiZJZH7V+DTeSLSGVjnV6AMwzAMwzDy\njVT4RJ0J/CcF7RqGYRh5wKhRoxg1alSmxTCMBhNknCiP3wL/E2mHxYkyjPwmk3GijNyhtLQ00yIY\nRiAE6hMlIvsCT6pqnVAH9fEpeP7553nrrbcoLS3l8ssv5+GHH05apokTJ3LeeedRVFSUdBvh9O/f\nn2XLljF58mROO+20Wvs2b97MrFmzOOusswLrzzByFfOJSqovwHyiDCPTZMIn6nSc9AqB0RAFCuCJ\nJ55gx44d8SuS+E1rypQpjBgxIuK+jRs3MnXq1Drl1dXVCbVtGIZhGEZuEOh0nqo+kuyxmzdv5uyz\nz0ZEaNu2LV27dgWgZ8+eLFmyhDvuuIM5c+bQrFkz7r77bjp16sQ555xDVVUV7du355lnnmH16tUM\nGzaM5s2bc+ihh3LBBRfw9ttvc8opp3DmmWcydOhQLrnkEiorK+nQoQNPPvkk8+bN45577qGoqIiS\nkhLmzZvHqlWrKCwsZMKECRx44IF1ZO3QoUPUcTz00EPMnTuX/v378/e//53zzz+fPn36sGHDBm69\n9VauvvpqduzYQY8ePRg3bhyqytVXX817771HYWEhU6dOpbKykiuvvJKffvqJ7t27M3bs2GRPq2EY\nRtbh+UPZtJ6R6wSqRInI74Hf41i4hqrq2kSPHT9+PIMHD2b48OGMHDnS3yYAs2fPZuHChRQUFKCq\nVFVVMXv2bJo0acKIESOYM2cOn3/+OcOGDeOKK65AVRERjj76aF544QVatmzJjTfeyDXXXEO/fv0Y\nM2YM06ZNo127dlRWVjJ37lyqqqp49NFHWbBgAZCcOf3KK6/k008/5dlnnwVg06ZNXHPNNXTu3Jnt\n27fX+IsMGjSITz75hA8++IAmTZowb968mj6vvPJKHnroIQ466CCuvPJK3nrrLXr0qBN42TAMIycx\n5cnIFwKbzhORjkAfVR2gqv3ro0ABrFq1qkZR6NWrVx0FZtSoUVx00UVcfvnlrF+/ng0bNvC73/2O\n4uJiXnzxRb7++muGDBnC6tWrGTp0KJMnT67Tx4cffkhpaSn9+vVj2rRprFu3DnCsXQCFhYVcddVV\nDBs2jBEjRrB1a/2jNITLvccee9C5c2cAPv30U0499VSKi4tZunQpa9euZcWKFbWCzokIK1eu5OKL\nL6Zfv34sXryYr776qt5yGIZhGIaRWoL0ifoN0EREXhWR+90s6Qlz8MEHs3TpUgAWL15cZ3+fPn2Y\nOHEiffv25ZFHHuGpp56ipKSEiooKBg4cSHV1NYWFhYwZM4bJkyczevRoVJWioiKqqqoAOOyww7jr\nrrsoLy9n0aJFXHrppQAUFDiiVldXM2TIECZNmkT79u35z3+iR2qIZqVq2rQpu3btqtn22gbHv+uG\nG26goqKC7t27o6p07dq1xgrlyXDooYcyceJEysvLWbx4cR3ndcMwDMMwMk+Q03ntgSJVHSAidwNn\nANMSPXj48OEMGTKEqVOn0qFDhxrrjTedN2jQIHbs2MGuXbt46KGHqKqqYtiwYcycOZOWLVsiIsyY\nMYMHHngAgIEDByIinH766QwZMoTBgwdz2223cckll9SYkseMGVOrj8rKSgYNGoSIUFBQwJQpU2rk\nmz8fVKFPH7j44ouZO3cu06dPZ/ny5dx888019Tp06MC2bdsYMmQId911V03bACUlJVx77bUcdthh\nNdONJSUlvPzyy5x00kkUFRUxdepURo8ezeWXX8727dtp0qQJjz/+OPvvv3/9vxHDMIwsxHyijHwh\nsBAHInIFsEtVHxGRXwM9VfUu3371/8PkWpyoPfcEEfjuu0xLYhjZS3icqFGjRlmIg/r3BViIA8PI\nNImEOAhSiToKuERVrxaRW4DPVPVp3/6cy5330UcfcdlllwHgPRe++moKP/vZzzInlGHkEBYnKqm+\nAFOiDCPTpDVOlKq+A2wTkXKgB/CvoNrOFIcccgjl5eWUl5cD5RQWlpsCZRhGQqxZs4YjjjgCgCVL\nlnDttdcG1va9997Ltm3bAmsvnBUrVnD88cfTvHlz7rnnnqj1dtttt4jl//jHP5g0aVLU4+bOncui\nRYsaLKdhZJpAI5bH7CgHLVF+RKBpU/jpp0xLYhi5Q2O2RK1Zs4aSkhLee++9+vYFxLZEHXTQQSxZ\nsoS99tor4Xarq6trvegSi2+//ZbPPvuM5557jj322IMbbrghYr3WrVvzww8/JCyDR3FxMc2aNeOV\nV16p97GGkS7SaokSkU4isk5EykXk5aDazSaaNMm0BIZhZDNvvfUWRx11FEcffTQPPvhgTXlFRQUl\nJSWAY4Xp3r073bt355hjjmHLli38+OOPDBgwoE48uC1btnDaaadx9NFHc8QRRzB16lTGjRvH2rVr\n6devHyeffDIAs2bN4oQTTqBHjx4MGTKELVu2ANCpUyduvfVWevTowbPPPsv9999Pt27dOOqoozj3\n3HOjjmPvvfemZ8+eCaXLuv322zn66KM5/vjjWb9+PeDkSfUsWP4+zzvvPD777DNWrlzJ8uXL6d69\nO//973/rcYYNI7sIOgHxLFUdFnCbWUOCP+IMw2ikXHTRRTz44IOceOKJtd7a9XPPPffw4IMPcvzx\nx7N161aaNWsGwLRp02jdunWtN3pffvllOnbsyAsvvADADz/8QOvWrRk7diwVFRXsueeebNiwgT//\n+c+89tprtGjRgtGjRzN27FjuuOMORIR27drx1ltvAdCxY0fWrFlDUVERlZWVDR7vli1bOP744/nT\nn/7ELbfcwvjx47ntttsQkZpxjB49ulafbdq04fLLL6d169Zcf/31DZbBMDJJ0GpBPxGZJyKRE8vl\nOKZEGYYRjU2bNrF582ZOPPFEAIYNi/x7snfv3lx33XWMGzeOjRs30qRJE6qrqxk5ciRHHXVUTb31\n69dz5JFHMnv2bG699Vb++9//0rp16zrtvf7663zwwQeccMIJdO/enSeffJLPP/+8Zv/ZZ59ds37k\nkUdy3nnnMWXKFJoEYFpv2rRpTRy7Hj16sGbNmjp1ovWZy+4dhuERpFqwFugC9AMGiMgR4RWef96J\ntZSr5KMS9fXXsGRJpqXIfl57DdwZEsNIiGhKwi233MJjjz3Gtm3b6N27NytXrmTKlCls2LChJuAw\nwPbt2+nSpQvLli3jiCOO4Pbbb+fOO++M2OavfvUrli1bxrJly1i+fDnjx4+v2deqVaua9RdeeIGr\nrrqKpUuX0qtXr1qBgZPBP91XUFBQE9gYQuOP1GdFRQWzZs1qUN+GkQ0ENp2nqju8dRF5HjgcqOVR\nWVJSxtVXw1575V6cKMhPJWroUJgzJ7eV23QwYADcfTfcckumJcluwuNENSbatm1L27ZtWbBgAb17\n964VrNfPqlWr6NatG926dWPx4sWsWLGCyspK9tlnnzrWoa+//po99tiD888/n913353HH38ccBy6\nKysr2XPPPTn22GO56qqrWLVqFT//+c/ZsmULa9eupUuXLrXaUlU+//xziouL6d27N08//TRbtmyh\nTZs2UceUrLXIOy5Snz/++CMlJSWBTCcaRqYJTIkSkd1U9Ud3szdwf91ajhJ16KFB9Zpe8tGx3PfD\n0YiDnav4hP848iJTNxYmTJjAxRdfjIjw61//upZ/k7d+3333UV5eTkFBAYcffjinnnoqlZWVlJSU\ncOSRR9Zq77333uOmm26ioKCAoqIiHn74YQAuvfRSBg4cSMeOHXnttdd44oknOPfcc/nJfX34z3/+\ncx0lateuXQwbNozNmzejqlx77bVRFahvvvmGXr16UVlZSUFBAffddx8ffPBBnZAG4ePztr31SH3u\nvvvulJSUMHjwYKZPn84DDzxA7969kzndhpFxggy2eQpwJ/ATME9VR4btV1A+/BAOOyyQLtOKCOyz\nD7g5i/OGPn1CKW2M6IjAH/8Id9yRaUlyi3SGOBCRY4GxQDWwWFWvF5GbgNOBz4ALVbVKRM4HrgS+\nB85T1R9EpD/wJ2A7MExVvwpr24JtGkYjI93BNl9S1Z6q2jtcgfJTXR1Uj+knH6fz7D6dOA10HzFS\nzxqgn6qeBOwjIn2AYnf7XWCQiBQBlwEnAZPcdYDbgV8BtwJR719GMIwaNarRWSmN/CToEAeIyHXA\nme6Nqw65/NA2JapxY0pUdqOqfjvxTqAbUOFuvwqcDywH3lPVahF5FRgvIi2Abaq6BXhTREZHaj/V\nPjyxfJNSxRNPPMF9991Xq+zEE09k3LhxKe3XEg8b+UKgSpSINAOOAqI+ms0SlV2YEpU4uXztNiZE\n5Ehgb2ATztQeQCXQ1l0qY5QBRPR+3Hvv/VIhrjttt5MdO7anpP1YXHjhhVx44YVp79cw8oWgLVH/\nC0wE/hitQi4/tPPRsTyXv490Y0pU9iMiewLjgLOAnoCn+bTBUao2u+vRygAi2hx37PAHhix2lyDY\nTmFh24DaMgwjWZJ5uzjItC9FQF9VLY9VL9se2l9+CV98ARs3wooVsevmiiXq5ZejP/C/+w4++ii0\nvXFj/dvfvBk++CA52SKxYQP8859OuwBvvOHImSg//gheLtMlS2DHjtj1k2X58vrVf/PN0BTgqlXg\nZsQInNdfd/6vKitDMi5ZAjt3BtdH0O2lAhEpBCYDN6rqemAJ0NfdPQBYBHwEHC4iBV6Zqm4FWohI\nKxH5Jc6UXwTKfEtxikbRODCfKCMbKS4upqysrGZJCFUNZAEuBs5w1+dH2K9QqpdeWqqlpaVaXl6u\n2cBee6m2aKF65pmqEL0eqHbunD65GgKorlkTed8pp9QeZ9eusccdiQsuqP8xsejb12nvjjucbVC9\n6abEj7/33pA8oPrgg8HJ5gGqBx1U/2P+/e/Q+i9/GbxcXtvLl6tecknt8/Dww8H28dhj8euVl5dr\naWlpzeLcYoK5x8RbgHOB9UC5uxwH3AzMx1GuCt16Q4EFwEygtVt2MrAQeA3YL0Lb6qiqqVi2aWFh\nM9+5xjtvhmFkkETuX0FO5x0CHC0ilwPdROQqVf177SplXHYZHHNMgL02kE2bHGtBItGod989SDZj\n3AAAIABJREFU9fI0FM/SF83i9+OPtbeTmaIKb6OheP66mzaFyuqTGD68rhsqJ3CaNq3/MX6rWNDn\nzU+kazhoi1wi5zWTcaJU9SngqbDi14ExYfUm4yhV/rLXcBQowzCMhAkyYvmt3rqIzKurQDlkm1+J\nJ48kEMkmkTqZxhtPtPMcPoZkvo+gp2QjyZCN/mfJfP/+c5XK6ycXrk3DMIx8IyVePqraJ/q+VPSY\nHnLBJ8rzwUn0dfxsfW2/IUpUqq6xbFai0kEu/+8a2YX5RBn5QpBpX7oBj+C82bJcVa+IVC/bbsSe\nPGaJSpygv8NI7RUGHsGs4WSzEpWOazPb/neN3MXiRBn5QpC2lZXqRCvvAzQTke6RKmXbdJ5HIg+h\nfLBEBaFEpQObzss+TIkyDMOoTZBpX/zpWVvgxF+JUC+oHoOlsVqikpnOS4clKhun8xo7dl4NwzBq\nE6htRUROF5H3gO2qujpSHS9Wjiq8/TasXOk8yJcuhW++qV9/778P27bBzJm139D68MP4b0Jt3Qrv\nvuuX3fncvh3Gj4cZM+o+NAoKasdYioW/3pIltd88C2flyugPqA0bnPF4rFkDs2fXVpLWr4fFi516\n4ZaoH35wzu3mzfDii7BwoVP+2WfO51dumtX//hfWro09ph9+cGJpeWN7553k3gD7+GNH/oULHTm9\nsa9bFxpXkyYwa5YjV3jMKC8u0gcf1I5XFekcfvVV/Gvh66+dNwTffjs0Tu+8fPxxKD5SJCVaNfY1\nsWaN0z44ckybFr2uv50NG5xxr1jhrHt8841T/umnzrZftq9qpcx1jkvkel2+PPSGZLT9ifLSS44c\nkyY5MdgMIxLmE2XkDfFiICSzAPcDvworUyhVcOLHPPhgeU2clIceCsVMqV8MB9Wrr3Y+f/vb2uW3\n3x77WC+2EKgWFan+z//UleWTT2q3edRRicm4eXPteqA6alTscSxaFHnf0KF12wLVjz4KlbVoESqf\nPt35XLrU2XfGGc52nz5149N8+23dsljcfHPd+lOnxj4m2ngnTdKa+Ebdujnrv/mN6ooVzvrYsaE+\nbrstdOyWLU7Z55+rtm7tLHfe6ZTNm+d8/vWvtfsaPDi+PCef7Hxu2xa6Frx9t9zifJ5wQt1j33gj\n+nnz5O/dO/45fuut2vv23tuJSwXONRDeplfX6/+TT2qXg+qBByZ2vYLqyJGx94Pqffcl0lZ5zf95\n69alCcVZyYXFuX/Vvf6DWSxOlGFkI4ncv4J0LG+qqp5dohKIEFWnzPlbBvPmhUqTiZrt8e23zue6\ndZHLo+G3bvz857Dvvs7699+HysOnujTB6YxIU2TbtsU+Jtr+aNahKt/kqf9YL1aQZ9HxLH+eNcRP\nfSNQR5Jl69b6teHhfedVVaHzuttuIZmaNQvV9Y/Ps3zt3Fk3PlS0c5hIpHBvbNXVdet710pRUd3j\nEhn/ypW1t1XrWrXCZf/225D1MpaFNpaVrD4+fImco8Su/2K8aN7O92PWhkSoqtpB376n1yoL324I\nRUUwZcp42rdvH1ibhmEEmztvoIhcDwiwGngpVmX/Tb8hzs3eseE3+Hj+S34lBEIPHL8CFN5mJpyd\no52baOXRHMsjPQDre96DdEL35Kuuri2bvzy8DEJKQyxfrkSVXT/+6yj82vGulUjtJtJXJGf+oK6l\nSOfLI/waj0UidZM5r0YiFAHP+X5YzgRg3rzhgfXQvPlwtsX7JWcYRr0JMtjmDGBGMscGoUSFE+9X\neDQlyt9eeNvewzDSg9aP97Dx10vWKT2eshStfiJBROvrVJ4KJcrvEwWh78VvJfP365VHeug3xPHf\nk6G6uu614/UVafzJKBa7diWmRCXSdiwFrz7fbyJ1TYlKFU2ASFan4CxRTZq0DKytIPD8oSzUgZHr\nBDmddywwFqgGFqvq9bHrh9YbcnOOdmy8B2r4VJZX3/8wiWUFivUQjKREJUu08SVqiYrVf32VoiAf\notEUE09uv5IUzRIlEpxMfuUzkiWqqCh5JSqVYSW8c5MOJcowgsKUJyNfCPLtvDVAP1U9CdhHRA6P\nVTkXp/O8NuPJGy/MQCTqqyzFKw+3REWqn8npPL+ckabz/EpuLCUqEskoVrEU3507nbx5ySpsQYSV\niEYsJcqm8wzDMFJLkHGi1vkcy3cCMW/LQVmiglCiRBKbzvOI9xCM5JeU6em8SA/J+j7MU2GJ2rWr\n9ncYyRLlPwf+48LPaUOsfrEsUbt2OUpUUJaodClRNp1nGIaRWgJPriEiRwJ7q+qKaHVWrqz9Rp7/\n4fTVV9CxoxO3ZuNGOPDAusevXx96K8qLofP5586xXrvffuvU27HDmXpr3tx5CGzdCvvtVzsuztat\nofb8MXFUnTg/nTqF+gAn/k2TJk4fxxwTSlGyaxe89VZo++OP4aCDQu1t2+bERqquhj59nDfQvIfX\nypVw4olOf4cc4sj+/fexLVSrVtWNP+W9ybV9e+3ySA/JRCxLq1c7cnTuHLn+8uVO+YYNsM8+zjnZ\nvBkOPrj2uL/5xhlLq1a15Xn1Vec8efJ4bxH+9FPo+I0bnXhJbduG3rr89NPoD/61a2H6dNh/f2d7\n5UonLpYqtG/vXBO77+6c4332cer4fYu8GExffOF8/vCDo2SrOvUqKhzFqHv30PezebMTq+uEE6Bl\ny9pvMkaybH34oXNdtWjhxL3yYjxt2xbq15Pp008dWcPjLq1aBQsWhM6dx5o1IbnBiee1fbtz/rxr\ny3tJy7PsedfNJ5841+z770O7dtChQ6jdxYtDMbW6dHHOyTvvONfxjh1wxBERvgzDiID5RBl5Q7wY\nCPVZgD2BucA+EfbVxI9xlvKaOCl/+EPtuCmqqm3aOOsbN0aK3RBamjRJLBaLFwfIa7+kJLS9556q\nZ51V95iFC53PlSujt/vkkyG5/LGnvOX880NjHD++tjyqqtu3h8qeeiok3377Oevt2oXK/GNfsCCy\nPIWFzufTTzv1vRhS++5bt+7y5XXLYp3rQYMi9/n3vzufP/4Y6t/PyJF1j7n99rplXlyjWH21bl23\nzIsT9eqr8a+DAw90rpk1a0Jyxjsnhx2mus8+qj17huKSecsrr9Te/sUv6rbZoUPtbS8W2WmnqX78\ncWLXb7zl/fcTq/fcc7W/n+uuq/3dQyiGF6i+/nrkdt55R/Wrr2qXOddvudb+P0eDvMdkanHuX8F8\nV/EXNOj+WrU6UFevXl33H9wwjKgkcv8K0rG8EJgM3KiqUaLOlEVR5OqWeZaieL4aTZvGj8EEtaOT\nQ+0Et7vt5rTj57DDQtac8HhEfvzRpCPFYlrhs8f5rUNeuWdN2W232tYXz+oQbWzRrEi77eZYpzzH\nd+/4SOcxKMdyz4qxY0fkfiLFOYpUz2+djPa9x/ouIr2R2a1bbeuiF6ndi6cVTrgFD5xr5dBDnWP8\nEdKh7jkJ3w91LVGelerjjx0LVhBE+27CCY+f5p2PVq1C14Pfuum/Jv389FPdfc7/QjFQzE03wV//\nCqoWJ8owjPwlSMfys4CewBgRKReR4xI9sCEOy8n6l8Trs7Aw9JBINLVJPJ+cSA7Sfl+ceMmDo7Xl\nJ5pTexA+UdHOmfcAj6b4RFJuIvXtL6uPU7RHfQJORlM6IgUgra52rgfV5AKwxvKJSmackUhUiYpW\nzz82fwDRWC8wxAsjkqhMhmEYuUqQcaKeAp5K7tjo++IpJskqYOHHhctQWFg7Onay+B1/Iz08vQd0\ndXWozP9gjXZuEn07L1b9oEMcRFPKIoWDiGcZS7USFY1oSpQX4iDedZOIXNECiTaERL/LRJQov/Uz\n2vcQyQE/FxJ0G9mB+UQZ+UKQ03kdgBeArkArVU34ER3rARDv4RCUJSqWEpVMkl0Pv8Up2qv6RUXO\nw8orS0Rpi3Ze/G+v+UnWsTxeG/52wsNDeA/VSIpMPKUuGSUqUj+xlIZIRDr3u3aFLFHJKO2xLFFB\nKVFBWqL8SlS06bzwIKlQ943bION4GfmFKU9GvhDkdN73QH/g9foe2BAlKtmbtL/dSL+gmzSp/3Re\nJFm8Y3ftqq0Y+JUrz8oRSYmK9us+2sPX6y8V03nR6keK7eTvL5PTefWNsxVNifJCHCSbTzG8vUjr\nDaGhShSEzrl/Oi+aEuW3nHqEB6qtrxXQMAwj1wgyTtRPqropfs1Ix0bfl6pIyuF9hm8XFNR/Oi/S\ngzlRS9SuXZGVqGSn81JhiYo1tQO15favp2s6L1FlLRbR5Mr26byGWnyi+UTFskSFy+7/sRFpus8w\nDCPfCDxOVDJ48Zc8/G9ObdgArVs7b+uJOLFuksH/MNi6Nb4CUVUVeltsRdSIVw7btzsPEP/bZR7e\n21Bff137Ib9rlxMb6JtvQuWrVzufXpwgT1Zw6u21V6g8PD6Un4ICJ1aQ/02zeG/DeVRWOnGOPv+8\n7oN5fZR3Lj25V66sXda1a21lNF7f/u8k0puO0fDedvP37xHtbT7ve/HeTosl13ffOdN533xTV6GO\n9OZheDyn8DfwPHkrK+te+8mS6Ft+69Y5n99955xv71r76afQ2P3n0YvhFc769bD33rXL/OM2S5QR\nC/OJMvIF0YCdFkSkHDg53CdKRFSk1PdgLnaXzHDccU6QQ3CCHh53HDz9dP3bGTsWro+ZJTD3OOec\n5M5FOM88A0OGpNYise++kRWZoLn6anjggdT3k/tUABUMHgxz5sD3349CVdNik4rklykim4GlOLGX\nzlTVTSJyPnAljgvCear6g4j0B/4EbAeGqepXYW2r00RaRuJ+Btdfq1adeP/9Cjp5kYMNw4iLiMS9\nf6Xqt2LETmfOLMOJFVVGJhUoqBsPyFPuBg9ObGqkSxfnMxNTFo88ktr2Fy1KrF6kac4DDgit+6eF\n4hHtnL/6at2y665zPr/7DiZNctbffDPxvpKhXbvUth+Lk09O7jj/d5Es/oj7iVEMlPHss2V8911Z\nwwWoH5H8Mt9V1X6q2t9VoIqAy4CTgEnuOsDtwK+AW4GRaZTZMIwcJjAlSkQKReRV4CjgFRH5ZXid\nSL4xmSJ8est7iCc6BdG8ee3j0onXd6pI1JE+3lt3QZybWG/ciTi+ShD6TBWZfMusMMlJ9/AAssmQ\nTf+z8Yjil9lVROaJyF/c7S7Ae66l/FXgeBFpAWxT1S2q+ibQLY1iG4aRwwQZJ6oKGBCrTjb5SERL\nDpyojC1aBCtPfQji4RiLaM7E4USywvmVjYbE1/KIpUQVFDQOJSpZRSaIc5JLSlQUDnYtUA+LSAmw\nAfAyZ1YCbd3Fl02T3B91lmM+UUa+EKhjuYj8DegBLFXVEeH7s+mGHG6J8iwoiSlRFTRvXhywRIkT\nnMJQQaRp1WxSoiJdM9535bdELV1aQSqniBsSVb/+VOAfS7IKXLIWLD+Z/uEjIk8CT6nqS8kc77NM\nPQd0B6YDbdyyNsAmYLOvDCDKO5NlvvViMu2SkMuY8mRkIxUVFVRUVNTrmCCDbR6D48zZR0QeFJGe\nqrrEXyeblKhEQgBEx5SoREiVJcqv0HjnYsmSCjKlRAUfVLKCbFGisuB/9hLgbBF5BlgIPKqqUTIf\n1kJEpCXwk6ruAk4E3gE+Ag4XkQIcy/kiVd0qIi1EpBXOVN7yyE2WNXQshmFkMcXFxRQXF9dsexbT\nWAT5O/NYYJa7/ipwfJ3Osmg6L1qgwEQfWJ5fUiYcy1M9ddWQfG7psET5FV7vXKT6YR9LiUr1dZ2s\nFSyI6yQL/mf3AjrjWIvWAY9Hqxjml/kycDjwpojMBToC/3LdDsYD84FhwD/cw/8MzAb+AtydmqEY\nhpFvBDmd1xb41F3fTATnzCz4VVuD33laNXqk72g0a+Z8BmW1qQ+pVqIagl+J2rq1fm/oRSJWAE3V\n0LnIpCJTUJC6oLCQvCUqTxzLbwAeVNVVACLyRbSKUfwye0SoNxmYHFb2GvBag6U1EsJ8oox8IbA4\nUSJyJfCtqj4rImcCHVV1nG+/ZdEyjEZIQ+JEiUiJqs50109T1ReCk6xeclicKMNoZCQSJypIS9Qi\nnJgrzwInAxP8O9MVcM8wjLyiLzDTXT8JJ5imYRhGVhBkiINlIrJdROYBy8Kdyg3DMJJgbxE5Gccs\n0z7TwhiGYfgJNMRBpLAGhmEYDeAa4DycOS67v+QJ5hNl5AuB584zDMMIChE5AjgNaAaoqv4xQ3KY\nT5RhNDIymTsvXJC/uakX7k1Hf8kiIh1EZKmIbHPjyCAiN4nIfBGZLCKFbtn5IrJARGaKSGu3rL+I\nLBSROSLSMZPjcOU51pVxvoiMdctybiwi0s2Vb56IPJSr4/AjIteJyHx3PSfHIiKdRGSdiJSLyMtu\nWSrGcj3wPPA08Ewqx2QYhlFfUq5E+YNwAk1FpGeq+2wAtRKYisg+QLGqngS8CwzKoQSma4B+ruz7\niEgfcnMsK1W1t3v9NBORXuTmOAAQkWY4cYxURPYmh8cCzHKT+w5M4f/K+6r6vqquVNWVqRmGYRhG\ncqTDEhU3CGe2EJbAVICeOOGjIST7weRAAlNVXaeqXjSsnTgyVbjbOTMWN/aPRwugFzk4Dh//C0wk\nx68vl36uhXAETjymCrc8yLH0c61Yz4rIs6kZhpFuRo0alVA0aMPIdgJ1LI9C3CCcWczuxE5WmvUJ\nTEXkSGBvnBxhXsjInBqLiJyOE1H6LWAjodxmuTaOIqCvqj4oTqj7eHJn7ViAtUAXYAdOPrrWwHp3\nX5BjOQfoqqqLRWS/YEQ3Mo05lBv5QjosUf7knrvjPMxzAaW27JGSldYzgWl6EZE9gXHAxeTwWFR1\nhqoegfPw3UKOjgMnzcg/fdu5/J3sUNVtbl6654FVpGYsfwMudNf/0HDJDcMwgiMdStQinOCbuJ+L\n0tBnEAiwBCfYH7jJSomSwBRoISKtROSXRE1gmj5cx97JwI2qup4cHYuI+JOXeNaMnBuHyyHAFSLy\nEo5Ftic5OhYR2c232Rv4hNSM5UecnHkA24KS3zAMIwhSPp2XS0E4XcXjZUIJTG8D5rlvUn0GjFXV\nKhHxEph+jxPDBkIJTLcBF6Rb9gichfOQHuNOHY0kN8cyUESux1FqVwOlwL45OA5U9VZvXUTmqeof\nReTmXBwLcJKI3An8BMxT1Tdd/6igx7LB7eseQtPRRo5jcaKMfMHiRBmGkdWIyGFAgap+kEEZLE6U\nYTQyJM258wzDMAJFRJ5yV1u4N7RBGRXIMAzDhylRhmFkLap6LoA4c9LXZVgcwzCMWqRNiXLM4YZh\nNDbimcNjISLdcOa1isit8ChGDMwnysgX4r6dJyKPu+kd3otR534R+VhE3hGR7tHqqWpeLKWlpRmX\nwcZhY8mFJQAG47wkcQpwfxANGpmntLTUFCgjL0gkxMEEYGC0nSJyKnCwqnYBLgUeCkg2wzCMJe7y\nHrCfiJyWYXkMwzBqiKtEqep8nCjR0TgdJ40FqvoG0FZE2gcjnmEYjZzhQFfgMHe9XWbFMQzDCBGE\nT1RH4Avf9pfAfoQC5OUdxcXFmRYhEPJlHGBjyWNWqOpfAURkb1WdmGmBjIZjPlFGvhCUY3m442he\nO5Hny0MuX8YBNpZ8RkQew7mn5O0Ps8aGKU9GvhCEEvUVsL9vez+3rA5lZWU168XFxfawMIw8o6Ki\ngoqKiiCbvA3nnrIJJzq6YRhG1pBQxHIR6QTMVCcJbPi+U4GrVfVUETkOuFdVj4tQTwN6W8cwjBwh\nkYi/cY6/H2ilqv8rIo+o6qUBilcfOSxiuWE0MhK5fyUS4uApYCFwqIh8ISIXi8hlInIZgKq+CHwq\nIp8A/wCuDEB2wzAMcPLlfeaub4pVUUQ6iMhSEdnmJj1GRG4SkfkiMtnNjYmInC8iC0Rkpoi0dsv6\ni8hCEZkjIh1TOSDD8Yny/KIMI5dJW+48s0QZRuMjAEvUaOBAYAFwpKpeEqNuM6AFMA04GedNvgmq\nepqI3Ax8CkwHXgOKcWJQHaCqfxWROUAJTkDP36vq1WFtmyXKMBoZgViiDMMwMoGb6uVfOCFUVgGX\nx6qvqj+pqmetEqAnUOFuvwocDxwMvKeq1V6ZiLQAtqnqFlV9E4uMbhhGgljuPMMwshJVVRHpp6pj\nkmxid6DSXa8E2rpLrDKAJkn2ZxhGI8OUKMMwshIROQM4Q0R+A3wPoKpnJXi4Aptx3uwDaIPjU7XZ\nXY9WBrArcpNlvvVidzGSweJEGdlIMm8Xx/WJEpGBwL04v84eVdXRYfvbAZOBfXGUsr+q6hMR2jGf\nKMNoZDTEJ0pEHlLVK7zPehxXDgwA9gIeV9Xf+nyinsPxieqH+UQZhhGDRO5fMS1RItIEeADnhvQV\nsFhEZqjqh75qVwPLVHWkq1CtFJHJqlrVQPkNw2jcHODmyjvADaXivQ0cEfftu5eBo9zP24B5IjIf\n5w2/sapaJSLjgfk41q3z3MP/DMwGtgEXpGg8hmHkGfGm834JfKKqawBE5GngDMCvRH0NHOmutwG+\nMwXKMIwAeBbnDbupwN7xKrv3nQFhxW8CY8LqTcaxnvvLXsOxUBmGYSRMPCUqUl68Y8PqjAfmiMha\noDUwJDjxDMNorERyCzDyA/OJMvKFeCEOEpmU/wPwtqr+DDga+LsXwC5Znn/++Zp/sssvj/lWc1wm\nTpzIzp07G9RGOP3792ePPfbghRdeCLRdwzCMxkBpaakpUEZeEM8SFZ4Xb38ca5SfE3D8CVDVVSKy\nGjgUWBLeWFlZGRUVFTV58xLJnffwww/HrROLJ554gsGDB1NUVBS3rqrihKaJzZQpU3jkkUcaJFd9\nZKmurqagwEJ6GdlPCnLnGYZhZC3xlKglQBc3d95a4Gzg3LA6K3D8EBaISHscBerTSI2VlZUhIhFv\nsps3b+bss89GRGjbti1du3YFoGfPnixZsoQ77riDOXPm0KxZM+6++246derEOeecQ1VVFe3bt+eZ\nZ55h9erVDBs2jObNm3PooYdywQUX8Pbbb3PKKadw5plnMnToUC655BIqKyvp0KEDTz75JPPmzeOe\ne+6hqKiIkpIS5s2bx6pVqygsLGTChAkceOCBdWTt0KFD1BOmqvz6179m586dNG3alH//+9+0bt2a\nCRMm8Mgjj9C8eXNuv/12evXqxdChQ2vJsmDBglqyjBs3jj59+rBhwwYmT54ctU/DyBbCfxxZag/D\nMPKZmEqU+ybL1cArOCEOHlPVD3158/4B3AVMEJF3cKYHb1bV7+sryPjx4xk8eDDDhw9n5MiRNeWe\nNWb27NksXLiQgoICVJWqqipmz55NkyZNGDFiBHPmzOHzzz9n2LBhXHHFFTWWnKOPPpoXXniBli1b\ncuONN3LNNdfQr18/xowZw7Rp02jXrh2VlZXMnTuXqqoqHn30URYsWOCNv77DQESYMWMGLVq04N57\n7+WZZ57hjDPOYPz48cyfP5/CwkJUlXvuuYff/va3XHrppfzpT3/i6aef5oADDqiRBeDOO+/kmmuu\noXPnzvWWwzAMI1sxnygjX4g7R6SqL6nqoap6sKr+xS37h6tAoaobVLVEVY9S1SNU9Z/JCLJq1Sp6\n9OgBQK9eveooMKNGjeKiiy7i8ssvZ/369WzYsIHf/e53FBcX8+KLL/L1118zZMgQVq9ezdChQyNa\nbj788ENKS0vp168f06ZNY926dYBj7QIoLCzkqquuYtiwYYwYMYKtW7fWexw//vgjw4cPp7i4mMcf\nf5y1a9eyevVqevToQWGho7OKCKtWraJXr1414/34449ryQKwxx57mAJlGEbeYT5RRr6QNY42Bx98\nMEuXLgVg8eLFdfb36dOHiRMn0rdvXx555BGeeuopSkpKqKioYODAgVRXV1NYWMiYMWOYPHkyo0eP\nRlUpKiqiqsqJuHDYYYdx1113UV5ezqJFi7j00ksBavyNqqurGTJkCJMmTaJ9+/b85z//iSpvNCvV\nrFmz6Ny5MxUVFVx44YWoKj//+c9ZunRpjRzV1dUcfPDBvPHGGwC8+eabHHLIIbVkCV83DMMwDCO7\nyJq0L8OHD2fIkCFMnTqVDh061FhgvOm8QYMGsWPHDnbt2sVDDz1EVVUVw4YNY+bMmbRs2bJmGu2B\nBx4AYODAgYgIp59+OkOGDGHw4MHcdtttXHLJJTW/gMaMGVOrj8rKSgYNGoSIUFBQwJQpUyLKevHF\nFzN37lymT5/O8uXLufnmm2v2HXfccdx1110sW7aM9u3bc+CBB7LXXnsxfPhwevfuTatWrWrkOP/8\n83n66afZd999GTlyJAsWLKjl2J6Ik7thGIZhGJkhbtqXwDpy0764YdTT0qdhGJmlIWlfsglL+xIs\n5hNl5AKJ3L9MiYrBRx99xGWXXVarbMqUKfzsZz/LkESGkVuYEpVUb+5ncP01bdoJke8RSY2LQEEB\nTJ/+LwYMCA8Ybxi5S4Nz57mNxExA7NYpBv4GFAEbVLU4GYGzjUMOOYTy8vJMi2EYhtEgdux4F6hO\nWftt2vyuxufTMBoTDU5ALCJtgb8Dv1HVL90kxAlRVlZGWVlZUoIbhmEYidImpa2LxA9mbBj5SDzb\nbk0CYlXdCXgJiP2cB/xbVb8EJ+RBop1bID7DMIzGx6hRo+z+b+QFQSQg7gIUiUg5TgLi+1R1UnAi\nGoZhGPmEOZQb+UI8JSoRz8Yi4BjgZKAlsEhEXlfVj8MrelN3ZWVlCeXNMwwjt7DceYZhNCZivp0n\nIscBZao60N0eCVT7nctF5BaghaqWuduPAi+r6r/C2qrzdl4uvalnGEb9sbfzkurN/cyde+Puuw/k\n6adHMHDgwEyLYhiBkcj9K55PVE0CYhFpipOAeEZYnenAiSLSRERa4kz3fZCs0IZhGEZ+Yz5RRr7Q\n4ATEqrpCRF4GvHdox6uqKVGGYRhGRMwnysgX4saJUtWXgJfCyv4Rtv1X4K/BimYYhmEYhpG9ZE2G\nW4sXZRiGYRhGLpE1SpTNjxuGYTQOzCfKyBfiTucZhmEYRpCYT5SRL8S1RInIQBFZISL9Jk9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"text": [ "" ] } ], "prompt_number": 41 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fine-tuning the MCMC algorithm\n", "\n", "MCMC objects handle individual variables via *step methods*, which\n", "determine how parameters are updated at each step of the MCMC algorithm.\n", "By default, step methods are automatically assigned to variables by\n", "PyMC. To see which step methods $M$ is using, look at its\n", "step_method_dict attribute with respect to each parameter:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "M.step_method_dict" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 42, "text": [ "{: [],\n", " : [],\n", " : []}" ] } ], "prompt_number": 42 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The value of step_method_dict corresponding to a particular variable\n", "is a list of the step methods $M$ is using to handle that variable.\n", "\n", "You can force $M$ to use a particular step method by calling M.use_step_method before telling it to sample. The following call will cause $M$ to handle late_mean with a Slicer (slice sampling) step method, and assigns an initial slice width w=0.5:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from pymc import Slicer\n", "M.use_step_method(Slicer, disaster_model.late_mean, w=0.5)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 43 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another step method class, AdaptiveMetropolis, is better at handling\n", "highly-correlated variables. If your model mixes poorly, using\n", "AdaptiveMetropolis is a sensible first thing to try." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "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()\n" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n" ], "metadata": {}, "output_type": "pyout", "prompt_number": 44, "text": [ "" ] } ], "prompt_number": 44 } ], "metadata": {} } ] }