{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 3\n", "\n", "\n", "_______\n", "\n", "## Opening the black box of MCMC" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The previous two chapters hid the inner-mechanics of PyMC, and more generally Markov Chain Monte Carlo (MCMC), from the reader. The reason for including this chapter is three-fold. The first is that any book on Bayesian inference must discuss MCMC. I cannot fight this. Blame the statisticians. Secondly, knowing the process of MCMC gives you insight into whether your algorithm has converged. (Converged to what? We will get to that) Thirdly, we'll understand *why* we are returned thousands of samples from the posterior as a solution, which at first thought can be odd. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Bayesian landscape\n", "\n", "When we setup a Bayesian inference problem with $N$ unknowns, we are implicitly creating an $N$ dimensional space for the prior distributions to exist in. Associated with the space is an additional dimension, which we can describe as the *surface*, or *curve*, that sits on top of the space, that reflects the *prior probability* of a particular point. The surface on the space is defined by our prior distributions. For example, if we have two unknowns $p_1$ and $p_2$, and priors for both are $\\text{Uniform}(0,5)$, the space created is a square of length 5 and the surface is a flat plane that sits on top of the square (representing that every point is equally likely). " ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import scipy.stats as stats\n", "from IPython.core.pylabtools import figsize\n", "import numpy as np\n", "figsize(12.5, 4)\n", "\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "jet = plt.cm.jet\n", "fig = plt.figure()\n", "x = y = np.linspace(0, 5, 100)\n", "X, Y = np.meshgrid(x, y)\n", "\n", "plt.subplot(121)\n", "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n", "uni_y = stats.uniform.pdf(y, loc=0, scale=5)\n", "M = np.dot(uni_x[:, None], uni_y[None, :])\n", "im = plt.imshow(M, interpolation='none', origin='lower',\n", " cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n", "\n", "plt.xlim(0, 5)\n", "plt.ylim(0, 5)\n", "plt.title(\"Landscape formed by Uniform priors.\")\n", "\n", "ax = fig.add_subplot(122, projection='3d')\n", "ax.plot_surface(X, Y, M, cmap=plt.cm.jet, vmax=1, vmin=-.15)\n", "ax.view_init(azim=390)\n", "plt.title(\"Uniform prior landscape; alternate view\");" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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fpG3btgwfPhzQSki9//77rF27lkGDBtGvXz+efvrpgM00wn3nijvXunVr5s+f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+0kJcAjE6O5kFey4LM59A18n7csQEqiys0tPbw6zEHVKvp86q/HRJZ8b+SR3k5OnZPoO+Lq+NtW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\nW4Au0KOrpjfNetML+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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alternatively, if the two priors are $\\text{Exp}(3)$ and $\\text{Exp}(10)$, then the space is all positive numbers on the 2-D plane, and the surface induced by the priors looks like a water fall that starts at the point (0,0) and flows over the positive numbers. \n", "\n", "The plots below visualize this. The more dark red the color, the more prior probability is assigned to that location. Conversely, areas with darker blue represent that our priors assign very low probability to that location. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(12.5, 5)\n", "fig = plt.figure()\n", "plt.subplot(121)\n", "\n", "exp_x = stats.expon.pdf(x, scale=3)\n", "exp_y = stats.expon.pdf(x, scale=10)\n", "M = np.dot(exp_x[:, None], exp_y[None, :])\n", "CS = plt.contour(X, Y, M)\n", "im = plt.imshow(M, interpolation='none', origin='lower',\n", " cmap=jet, extent=(0, 5, 0, 5))\n", "#plt.xlabel(\"prior on $p_1$\")\n", "#plt.ylabel(\"prior on $p_2$\")\n", "plt.title(\"$Exp(3), Exp(10)$ prior landscape\")\n", "\n", "ax = fig.add_subplot(122, projection='3d')\n", "ax.plot_surface(X, Y, M, cmap=jet)\n", "ax.view_init(azim=390)\n", "plt.title(\"$Exp(3), Exp(10)$ prior landscape; \\nalternate view\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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iZux8GzfZsc3OEat9pJQII4mmRJhVMjBz//kx37RpR9KrV6/Mqd83YXbu3Nm4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\nWbdQKCqNri2H5ieCkRvmEmm1HLlhrilbLTcH4hJfTdPcwO8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urpznaRN3/JjK7vyvMoeP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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "These are simple examples in 2D space, where our brains can understand surfaces well. In practice, spaces and surfaces generated by our priors can be much higher dimensional. \n", "\n", "If these surfaces describe our *prior distributions* on the unknowns, what happens to our space after we incorporate our observed data $X$? The data $X$ does not change the space, but it changes the surface of the space by *pulling and stretching the fabric of the prior surface* to reflect where the true parameters likely live. More data means more pulling and stretching, and our original shape becomes mangled or insignificant compared to the newly formed shape. Less data, and our original shape is more present. Regardless, the resulting surface describes the *posterior distribution*. \n", "\n", "Again I must stress that it is, unfortunately, impossible to visualize this in large dimensions. For two dimensions, the data essentially *pushes up* the original surface to make *tall mountains*. The tendency of the observed data to *push up* the posterior probability in certain areas is checked by the prior probability distribution, so that less prior probability means more resistance. Thus in the double-exponential prior case above, a mountain (or multiple mountains) that might erupt near the (0,0) corner would be much higher than mountains that erupt closer to (5,5), since there is more resistance (low prior probability) near (5,5). The peak reflects the posterior probability of where the true parameters are likely to be found. Importantly, if the prior has assigned a probability of 0, then no posterior probability will be assigned there. \n", "\n", "Suppose the priors mentioned above represent different parameters $\\lambda$ of two Poisson distributions. We observe a few data points and visualize the new landscape: " ] }, { "cell_type": "code", "collapsed": false, "input": [ "# create the observed data\n", "\n", "# sample size of data we observe, trying varying this (keep it less than 100 ;)\n", "N = 1\n", "\n", "# the true parameters, but of course we do not see these values...\n", "lambda_1_true = 1\n", "lambda_2_true = 3\n", "\n", "#...we see the data generated, dependent on the above two values.\n", "data = np.concatenate([\n", " stats.poisson.rvs(lambda_1_true, size=(N, 1)),\n", " stats.poisson.rvs(lambda_2_true, size=(N, 1))\n", "], axis=1)\n", "print \"observed (2-dimensional,sample size = %d):\" % N, data\n", "\n", "# plotting details.\n", "x = y = np.linspace(.01, 5, 100)\n", "likelihood_x = np.array([stats.poisson.pmf(data[:, 0], _x)\n", " for _x in x]).prod(axis=1)\n", "likelihood_y = np.array([stats.poisson.pmf(data[:, 1], _y)\n", " for _y in y]).prod(axis=1)\n", "L = np.dot(likelihood_x[:, None], likelihood_y[None, :])\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "observed (2-dimensional,sample size = 1): [[2 2]]\n" ] } ], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(12.5, 12)\n", "# matplotlib heavy lifting below, beware!\n", "plt.subplot(221)\n", "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n", "uni_y = stats.uniform.pdf(x, loc=0, scale=5)\n", "M = np.dot(uni_x[:, None], uni_y[None, :])\n", "im = plt.imshow(M, interpolation='none', origin='lower',\n", " cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n", "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", "plt.xlim(0, 5)\n", "plt.ylim(0, 5)\n", "plt.title(\"Landscape formed by Uniform priors on $p_1, p_2$.\")\n", "\n", "plt.subplot(223)\n", "plt.contour(x, y, M * L)\n", "im = plt.imshow(M * L, interpolation='none', origin='lower',\n", " cmap=jet, extent=(0, 5, 0, 5))\n", "plt.title(\"Landscape warped by %d data observation;\\n Uniform priors on $p_1, p_2$.\" % N)\n", "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", "plt.xlim(0, 5)\n", "plt.ylim(0, 5)\n", "\n", "plt.subplot(222)\n", "exp_x = stats.expon.pdf(x, loc=0, scale=3)\n", "exp_y = stats.expon.pdf(x, loc=0, scale=10)\n", "M = np.dot(exp_x[:, None], exp_y[None, :])\n", "\n", "plt.contour(x, y, M)\n", "im = plt.imshow(M, interpolation='none', origin='lower',\n", " cmap=jet, extent=(0, 5, 0, 5))\n", "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", "plt.xlim(0, 5)\n", "plt.ylim(0, 5)\n", "plt.title(\"Landscape formed by Exponential priors on $p_1, p_2$.\")\n", "\n", "plt.subplot(224)\n", "# This is the likelihood times prior, that results in the posterior.\n", "plt.contour(x, y, M * L)\n", "im = plt.imshow(M * L, interpolation='none', origin='lower',\n", " cmap=jet, extent=(0, 5, 0, 5))\n", "\n", "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", "plt.title(\"Landscape warped by %d data observation;\\n Exponential priors on \\\n", "$p_1, p_2$.\" % N)\n", "plt.xlim(0, 5)\n", "plt.ylim(0, 5)\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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EEuLQv6gpHu6Ee2VIlW/HkD7LgYw+E/f4fRfxS9bipzym5JyK8HbDo5BxZQ2A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QQZsL2CJFMECRt8DLlZIyYheNC4w+goFhgPgnoX1A8ZSiUFxIaPs5f9JRLvOYQmUGyI540m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\na4cMe9UKTJQP4VqHgIm85DkOJhjzU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"text": [ "" ] } ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot on the left is the deformed landscape with the $\\text{Uniform}(0,5)$ priors, and the plot on the right is the deformed landscape with the exponential priors. Notice that the posterior landscapes look different from one another, though the data observed is identical in both cases. The reason is as follows. Notice the exponential-prior landscape, bottom right figure, puts very little *posterior* weight on values in the upper right corner of the figure: this is because *the prior does not put much weight there*. On the other hand, the uniform-prior landscape is happy to put posterior weight in the upper-right corner, as the prior puts more weight there. \n", "\n", "Notice also the highest-point, corresponding the the darkest red, is biased towards (0,0) in the exponential case, which is the result from the exponential prior putting more prior weight in the (0,0) corner.\n", "\n", "The black dot represents the true parameters. Even with 1 sample point, the mountains attempts to contain the true parameter. Of course, inference with a sample size of 1 is incredibly naive, and choosing such a small sample size was only illustrative. \n", "\n", "It's a great exercise to try changing the sample size to other values (try 2,5,10,100?...) and observing how our \"mountain\" posterior changes. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exploring the landscape using the MCMC\n", "\n", "We should explore the deformed posterior space generated by our prior surface and observed data to find the posterior mountain. However, we cannot naively search the space: any computer scientist will tell you that traversing $N$-dimensional space is exponentially difficult in $N$: the size of the space quickly blows-up as we increase $N$ (see [the curse of dimensionality](http://en.wikipedia.org/wiki/Curse_of_dimensionality)). What hope do we have to find these hidden mountains? The idea behind MCMC is to perform an intelligent search of the space. To say \"search\" implies we are looking for a particular point, which is perhaps not an accurate as we are really looking for a broad mountain. \n", "\n", "Recall that MCMC returns *samples* from the posterior distribution, not the distribution itself. Stretching our mountainous analogy to its limit, MCMC performs a task similar to repeatedly asking \"How likely is this pebble I found to be from the mountain I am searching for?\", and completes its task by returning thousands of accepted pebbles in hopes of reconstructing the original mountain. In MCMC and PyMC lingo, the returned sequence of \"pebbles\" are the samples, cumulatively called the *traces*. \n", "\n", "When I say MCMC intelligently searches, I really am saying MCMC will *hopefully* converge towards the areas of high posterior probability. MCMC does this by exploring nearby positions and moving into areas with higher probability. Again, perhaps \"converge\" is not an accurate term to describe MCMC's progression. Converging usually implies moving towards a point in space, but MCMC moves towards a *broader area* in the space and randomly walks in that area, picking up samples from that area.\n", "\n", "####Why Thousands of Samples?\n", "\n", "At first, returning thousands of samples to the user might sound like being an inefficient way to describe the posterior distributions. I would argue that this is extremely efficient. Consider the alternative possibilities:\n", "\n", "1. Returning a mathematical formula for the \"mountain ranges\" would involve describing a N-dimensional surface with arbitrary peaks and valleys.\n", "2. Returning the \"peak\" of the landscape, while mathematically possible and a sensible thing to do as the highest point corresponds to most probable estimate of the unknowns, ignores the shape of the landscape, which we have previously argued is very important in determining posterior confidence in unknowns. \n", "\n", "Besides computational reasons, likely the strongest reason for returning samples is that we can easily use *The Law of Large Numbers* to solve otherwise intractable problems. I postpone this discussion for the next chapter. With the thousands of samples, we can reconstruct the posterior surface by organizing them in a histogram. \n", "\n", "\n", "### Algorithms to perform MCMC\n", "\n", "There is a large family of algorithms that perform MCMC. Most of these algorithms can be expressed at a high level as follows: (Mathematical details can be found in the appendix.)\n", "\n", "1. Start at current position.\n", "2. Propose moving to a new position (investigate a pebble near you).\n", "3. Accept/Reject the new position based on the position's adherence to the data and prior distributions (ask if the pebble likely came from the mountain).\n", "4. 1. If you accept: Move to the new position. Return to Step 1.\n", " 2. Else: Do not move to new position. Return to Step 1. \n", "5. After a large number of iterations, return all accepted positions.\n", "\n", "This way we move in the general direction towards the regions where the posterior distributions exist, and collect samples sparingly on the journey. Once we reach the posterior distribution, we can easily collect samples as they likely all belong to the posterior distribution. \n", "\n", "If the current position of the MCMC algorithm is in an area of extremely low probability, which is often the case when the algorithm begins (typically at a random location in the space), the algorithm will move in positions *that are likely not from the posterior* but better than everything else nearby. Thus the first moves of the algorithm are not reflective of the posterior.\n", "\n", "In the above algorithm's pseudocode, notice that only the current position matters (new positions are investigated only near the current position). We can describe this property as *memorylessness*, i.e. the algorithm does not care *how* it arrived at its current position, only that it is there. \n", "\n", "### Other approximation solutions to the posterior\n", "Besides MCMC, there are other procedures available for determining the posterior distributions. A Laplace approximation is an approximation of the posterior using simple functions. A more advanced method is [Variational Bayes](http://en.wikipedia.org/wiki/Variational_Bayesian_methods). All three methods, Laplace Approximations, Variational Bayes, and classical MCMC have their pros and cons. We will only focus on MCMC in this book. That being said, my friend Imri Sofar likes to classify MCMC algorithms as either \"they suck\", or \"they really suck\". He classifies the particular flavour of MCMC used by PyMC as just *sucks* ;)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Example: Unsupervised Clustering using a Mixture Model\n", "\n", "\n", "Suppose we are given the following dataset:\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(12.5, 4)\n", "data = np.loadtxt(\"data/mixture_data.csv\", delimiter=\",\")\n", "\n", "plt.hist(data, bins=20, color=\"k\", histtype=\"stepfilled\", alpha=0.8)\n", "plt.title(\"Histogram of the dataset\")\n", "plt.ylim([0, None])\n", "print data[:10], \"...\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "[ 115.85679142 152.26153716 178.87449059 162.93500815 107.02820697\n", " 105.19141146 118.38288501 125.3769803 102.88054011 206.71326136] ...\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 37 }, { "cell_type": "markdown", "metadata": {}, "source": [ "What does the data suggest? It appears the data has a bimodal form, that is, it appears to have two peaks, one near 120 and the other near 200. Perhaps there are *two clusters* within this dataset. \n", "\n", "This dataset is a good example of the data-generation modeling technique from last chapter. We can propose *how* the data might have been created. I suggest the following data generation algorithm: \n", "\n", "1. For each data point, choose cluster 1 with probability $p$, else choose cluster 2. \n", "2. Draw a random variate from a Normal distribution with parameters $\\mu_i$ and $\\sigma_i$ where $i$ was chosen in step 1.\n", "3. Repeat.\n", "\n", "This algorithm would create a similar effect as the observed dataset, so we choose this as our model. Of course, we do not know $p$ or the parameters of the Normal distributions. Hence we must infer, or *learn*, these unknowns.\n", "\n", "Denote the Normal distributions $\\text{Nor}_0$ and $\\text{Nor}_1$ (having variables' index start at 0 is just Pythonic). Both currently have unknown mean and standard deviation, denoted $\\mu_i$ and $\\sigma_i, \\; i =0,1$ respectively. A specific data point can be from either $\\text{Nor}_0$ or $\\text{Nor}_1$, and we assume that the data point is assigned to $\\text{Nor}_0$ with probability $p$.\n", "\n", "\n", "An appropriate way to assign data points to clusters is to use a PyMC `Categorical` stochastic variable. Its parameter is a $k$-length array of probabilities that must sum to one and its `value` attribute is a integer between 0 and $k-1$ randomly chosen according to the crafted array of probabilities. (In our case $k=2$) *A priori*, we do not know what the probability of assignment to cluster 1 is, so we create a uniform variable over 0,1 to model this. Call this `p`. Thus the probability array we enter into the `Categorical` variable is `[p, 1-p]`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pymc as pm\n", "\n", "p = pm.Uniform(\"p\", 0, 1)\n", "\n", "assignment = pm.Categorical(\"assignment\", [p, 1 - p], size=data.shape[0])\n", "print \"prior assignment, with p = %.2f:\" % p.value\n", "print assignment.value[:10], \"...\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "prior assignment, with p = 0.31:\n", "[1 1 0 0 0 0 1 1 1 1] ...\n" ] } ], "prompt_number": 38 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the above dataset, I would guess that the standard deviations of the two Normals are different. To maintain ignorance of what the standard deviations might be, we will initially model them as uniform on 0 to 100. Really we are talking about $\\tau$, the *precision* of the Normal distribution, but it is easier to think in terms of standard deviation. Our PyMC code will need to transform our standard deviation into precision by the relation:\n", "\n", "$$ \\tau = \\frac{1}{\\sigma^2} $$\n", "\n", "In PyMC, we can do this in one step by writing:\n", "\n", " taus = 1.0/pm.Uniform( \"stds\", 0, 100, size= 2)**2 \n", "\n", "Notice that we specified `size=2`: we are modeling both $\\tau$s as a single PyMC variable. Note that this does not induce a necessary relationship between the two $\\tau$s, it is simply for succinctness.\n", "\n", "We also need to specify priors on the centers of the clusters. The centers are really the $\\mu$ parameters in this Normal distributions. Their priors can be modeled by a Normal distribution. Looking at the data, I have an idea where the two centers might be — I would guess somewhere around 120 and 190 respectively, though I am not very confident in these eyeballed estimates. Hence I will set $\\mu_0 = 120, \\mu_1 = 190$ and $\\sigma_{0,1} = 10$ (recall we enter the $\\tau$ parameter, so enter $1/\\sigma^2 = 0.01$ in the PyMC variable.)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "taus = 1.0 / pm.Uniform(\"stds\", 0, 100, size=2) ** 2\n", "centers = pm.Normal(\"centers\", [120, 190], [0.01, 0.01], size=2)\n", "\n", "\"\"\"\n", "The below deterministic functions map an assignment, in this case 0 or 1,\n", "to a set of parameters, located in the (1,2) arrays `taus` and `centers`.\n", "\"\"\"\n", "\n", "@pm.deterministic\n", "def center_i(assignment=assignment, centers=centers):\n", " return centers[assignment]\n", "\n", "@pm.deterministic\n", "def tau_i(assignment=assignment, taus=taus):\n", " return taus[assignment]\n", "\n", "print \"Random assignments: \", assignment.value[:4], \"...\"\n", "print \"Assigned center: \", center_i.value[:4], \"...\"\n", "print \"Assigned precision: \", tau_i.value[:4], \"...\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Random assignments: [1 1 0 0] ...\n", "Assigned center: [ 174.74278858 174.74278858 126.25164007 126.25164007] ...\n", "Assigned precision: [ 0.00034557 0.00034557 0.00012237 0.00012237] ...\n" ] } ], "prompt_number": 40 }, { "cell_type": "code", "collapsed": false, "input": [ "# and to combine it with the observations:\n", "observations = pm.Normal(\"obs\", center_i, tau_i, value=data, observed=True)\n", "\n", "# below we create a model class\n", "model = pm.Model([p, assignment, taus, centers])\n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 41 }, { "cell_type": "markdown", "metadata": {}, "source": [ "PyMC has an MCMC class, `MCMC` in the main namespace of PyMC, that implements the MCMC exploring algorithm. We initialize it by passing in a `Model` instance:\n", "\n", " mcmc = pm.MCMC( model )\n", "\n", "The method for asking the `MCMC` to explore the space is `sample( iterations )`, where `iterations` is the number of steps you wish the algorithm to perform. We try 50000 steps below:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "mcmc = pm.MCMC(model)\n", "mcmc.sample(50000)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 50000 of 50000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 42 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below I plot the paths, or \"traces\", the unknown parameters (centers, precisions, and $p$) have taken thus far. The traces can be retrieved using the `trace` method in the `MCMC` object created, which accepts the assigned PyMC variable `name`. For example, `mcmc.trace(\"centers\")` will retrieve a `Trace` object that can be indexed (using `[:]` or `.gettrace()` to retrieve all traces, or fancy-indexing like `[1000:]`)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(12.5, 9)\n", "plt.subplot(311)\n", "lw = 1\n", "center_trace = mcmc.trace(\"centers\")[:]\n", "\n", "# for pretty colors later in the book.\n", "colors = [\"#348ABD\", \"#A60628\"]\n", "if center_trace[-1, 0] > center_trace[-1, 1] \\\n", " else [\"#A60628\", \"#348ABD\"]\n", "\n", "plt.plot(center_trace[:, 0], label=\"trace of center 0\", c=colors[0], lw=lw)\n", "plt.plot(center_trace[:, 1], label=\"trace of center 1\", c=colors[1], lw=lw)\n", "plt.title(\"Traces of unknown parameters\")\n", "leg = plt.legend(loc=\"upper right\")\n", "leg.get_frame().set_alpha(0.7)\n", "\n", "plt.subplot(312)\n", "std_trace = mcmc.trace(\"stds\")[:]\n", "plt.plot(std_trace[:, 0], label=\"trace of standard deviation of cluster 0\",\n", " c=colors[0], lw=lw)\n", "plt.plot(std_trace[:, 1], label=\"trace of standard deviation of cluster 1\",\n", " c=colors[1], lw=lw)\n", "plt.legend(loc=\"upper left\")\n", "\n", "plt.subplot(313)\n", "p_trace = mcmc.trace(\"p\")[:]\n", "plt.plot(p_trace, label=\"$p$: frequency of assignment to cluster 0\",\n", " color=\"#467821\", lw=lw)\n", "plt.xlabel(\"Steps\")\n", "plt.ylim(0, 1)\n", "plt.legend()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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L9npkcgJjE1M0NOh+RrXNEly43Tr60pWTuWmmUwrlESW5tBEDHc3a3UZOCCQy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\neX1Wr16N4OBgjBkzBgEBAfjoo4+gVCrh6emJn3/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okvP159dtXeDp14X1hDuV3lVdTreH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Sz/2RwJJvnnswBavDs+hyehnJRacUeCoaWmnu++XsKq2O9V10vtI2ytinQBAEWiRSVDe2olUi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"text": [ "" ] } ], "prompt_number": 47 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice the following characteristics:\n", "\n", "1. The traces converges, not to a single point, but to a *distribution* of possible points. This is *convergence* in an MCMC algorithm.\n", "2. Inference using the first few thousand points is a bad idea, as they are unrelated to the final distribution we are interested in. Thus is it a good idea to discard those samples before using the samples for inference. We call this period before converge the *burn-in period*.\n", "3. The traces appear as a random \"walk\" around the space, that is, the paths exhibit correlation with previous positions. This is both good and bad. We will always have correlation between current positions and the previous positions, but too much of it means we are not exploring the space well. This will be detailed in the Diagnostics section later in this chapter.\n", "\n", "\n", "To achieve further convergence, we will perform more MCMC steps. Starting the MCMC again after it has already been called does not mean starting the entire algorithm over. In the pseudo-code algorithm of MCMC above, the only position that matters is the current position (new positions are investigated near the current position), implicitly stored in PyMC variables' `value` attribute. Thus it is fine to halt an MCMC algorithm and inspect its progress, with the intention of starting it up again later. The `value` attributes are not overwritten. \n", "\n", "We will sample the MCMC one hundred thousand more times and visualize the progress below:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "mcmc.sample(100000)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 100000 of 100000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 48 }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(12.5, 4)\n", "center_trace = mcmc.trace(\"centers\", chain=1)[:]\n", "prev_center_trace = mcmc.trace(\"centers\", chain=0)[:]\n", "\n", "x = np.arange(50000)\n", "plt.plot(x, prev_center_trace[:, 0], label=\"previous trace of center 0\",\n", " lw=lw, alpha=0.4, c=colors[1])\n", "plt.plot(x, prev_center_trace[:, 1], label=\"previous trace of center 1\",\n", " lw=lw, alpha=0.4, c=colors[0])\n", "\n", "x = np.arange(50000, 150000)\n", "plt.plot(x, center_trace[:, 0], label=\"new trace of center 0\", lw=lw, c=\"#348ABD\")\n", "plt.plot(x, center_trace[:, 1], label=\"new trace of center 1\", lw=lw, c=\"#A60628\")\n", "\n", "plt.title(\"Traces of unknown center parameters\")\n", "leg = plt.legend(loc=\"upper right\")\n", "leg.get_frame().set_alpha(0.8)\n", "plt.xlabel(\"Steps\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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G5sEgR5uRkfmP0q5dO5KTk/nxxx+5c+cO27dvZ/PmzXp5FixYQGhoKJMmTcLf35+wsDB+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FeXbmDx1gKs+Vdf9ryssQsnpZp1Aw0yBVbsLMLlOs1n85FdV/DxqRr8pbdLXkuvlWbupxfQ0qXA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\nZvAJQ+h+5t7cvmtGBEEQGjxlp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"text": [ "" ] } ], "prompt_number": 50 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `trace` method in the `MCMC` instance has a keyword argument `chain`, that indexes which call to `sample` you would like to be returned. (Often we need to call `sample` multiple times, and the ability to retrieve past samples is a useful procedure). The default for `chain` is -1, which will return the samples from the lastest call to `sample`.\n", "\n", "#### Cluster Investigation\n", "\n", "We have not forgotten our main challenge: identify the clusters. We have determined posterior distributions for our unknowns. We plot the posterior distributions of the center and standard deviation variables below:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(11.0, 4)\n", "std_trace = mcmc.trace(\"stds\")[:]\n", "\n", "_i = [1, 2, 3, 0]\n", "for i in range(2):\n", " plt.subplot(2, 2, _i[2 * i])\n", " plt.title(\"Posterior of center of cluster %d\" % i)\n", " plt.hist(center_trace[:, i], color=colors[i], bins=30,\n", " histtype=\"stepfilled\")\n", "\n", " plt.subplot(2, 2, _i[2 * i + 1])\n", " plt.title(\"Posterior of standard deviation of cluster %d\" % i)\n", " plt.hist(std_trace[:, i], color=colors[i], bins=30,\n", " histtype=\"stepfilled\")\n", " # plt.autoscale(tight=True)\n", "\n", "plt.tight_layout()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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cRzscuyCgLPMy7uVc1UxA7STl3AMcvy5JOXZ18OCAac1vf/4n0Mo86L2iXobP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"text": [ "" ] } ], "prompt_number": 51 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The MCMC algorithm has proposed that the most likely centers of the two clusters are near 120 and 200 respectively. Similar inference can be applied to the standard deviation. \n", "\n", "We are also given the posterior distributions for the labels of the data point, which is present in `mcmc.trace(\"assignment\")`. Below is a visualization of this. The y-axis represents a subsample of the posterior labels for each data point. The x-axis are the sorted values of the data points. A red square is an assignment to cluster 1, and a blue square is an assignment to cluster 0. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "import matplotlib as mpl\n", "figsize(12.5, 4.5)\n", "plt.cmap = mpl.colors.ListedColormap(colors)\n", "plt.imshow(mcmc.trace(\"assignment\")[::400, np.argsort(data)],\n", " cmap=plt.cmap, aspect=.4, alpha=.9)\n", "plt.xticks(np.arange(0, data.shape[0], 40),\n", " [\"%.2f\" % s for s in np.sort(data)[::40]])\n", "plt.ylabel(\"posterior sample\")\n", "plt.xlabel(\"value of $i$th data point\")\n", "plt.title(\"Posterior labels of data points\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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+sZtpGUudn6W0u43c0UEGquvpr64nrE1EFbvSM2m58z4cjScIGE23neN9M1BG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"text": [ "" ] } ], "prompt_number": 58 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the above plot, it appears that the most uncertainty is between 150 and 170. The above plot slightly misrepresents things, as the x-axis is not a true scale (it displays the value of the $i$th sorted data point.) A more clear diagram is below, where we have estimated the *frequency* of each data point belonging to the labels 0 and 1. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "cmap = mpl.colors.LinearSegmentedColormap.from_list(\"BMH\", colors)\n", "assign_trace = mcmc.trace(\"assignment\")[:]\n", "plt.scatter(data, 1 - assign_trace.mean(axis=0), cmap=cmap,\n", " c=assign_trace.mean(axis=0), s=50)\n", "plt.ylim(-0.05, 1.05)\n", "plt.xlim(35, 300)\n", "plt.title(\"Probability of data point belonging to cluster 0\")\n", "plt.ylabel(\"probability\")\n", "plt.xlabel(\"value of data point\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 60, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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qiipceHExyv+6AJ+pTyD3hwOovZxuWK/Kyoe+QQ3bsADwJWJcWfUNMr7YgcJ9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"text": [ "" ] } ], "prompt_number": 60 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Even though we modeled the clusters using Normal distributions, we didn't get just a single Normal distribution that *best* fits the data (whatever our definition of best is), but a distribution of values for the Normal's parameters. How can we choose just a single pair of values for the mean and variance and determine a *sorta-best-fit* gaussian? \n", "\n", "One quick and dirty way (which has nice theoretical properties we will see in Chapter 5), is to use the *mean* of the posterior distributions. Below we overlay the Normal density functions, using the mean of the posterior distributions as the chosen parameters, with our observed data:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "norm = stats.norm\n", "x = np.linspace(20, 300, 500)\n", "posterior_center_means = center_trace.mean(axis=0)\n", "posterior_std_means = std_trace.mean(axis=0)\n", "posterior_p_mean = mcmc.trace(\"p\")[:].mean()\n", "\n", "plt.hist(data, bins=20, histtype=\"step\", normed=True, color=\"k\",\n", " lw=2, label=\"histogram of data\")\n", "y = posterior_p_mean * norm.pdf(x, loc=posterior_center_means[0],\n", " scale=posterior_std_means[0])\n", "plt.plot(x, y, label=\"Cluster 0 (using posterior-mean parameters)\", lw=3)\n", "plt.fill_between(x, y, color=colors[1], alpha=0.3)\n", "\n", "y = (1 - posterior_p_mean) * norm.pdf(x, loc=posterior_center_means[1],\n", " scale=posterior_std_means[1])\n", "plt.plot(x, y, label=\"Cluster 1 (using posterior-mean parameters)\", lw=3)\n", "plt.fill_between(x, y, color=colors[0], alpha=0.3)\n", "\n", "plt.legend(loc=\"upper left\")\n", "plt.title(\"Visualizing Clusters using posterior-mean parameters\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 61, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Eh4d/cDmUD4OOUYo0dBvJT4y/vz+mT5/e3GI0CefOncPEiRM/uByBQPCfOqAi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\nykGtbdJB7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"text": [ "" ] } ], "prompt_number": 61 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Important: Don't mix posterior samples\n", "\n", "In the above example, a possible (though less likely) scenario is that cluster 0 has a very large standard deviation, and cluster 1 has a small standard deviation. This would still satisfy the evidence, albeit less so than our original inference. Alternatively, it would be incredibly unlikely for *both* distributions to have a small standard deviation, as the data does not support this hypothesis at all. Thus the two standard deviations are *dependent* on each other: if one is small, the other must be large. In fact, *all* the unknowns are related in a similar manner. For example, if a standard deviation is large, the mean has a wider possible space of realizations. Conversely, a small standard deviation restricts the mean to a small area. \n", "\n", "During MCMC, we are returned vectors representing samples from the unknown posteriors. Elements of different vectors cannot be used together, as this would break the above logic: perhaps a sample has returned that cluster 1 has a small standard deviation, hence all the other variables in that sample would incorporate that and be adjusted accordingly. It is easy to avoid this problem though, just make sure you are indexing traces correctly. \n", "\n", "Another small example to illustrate the point. Suppose two variables, $x$ and $y$, are related by $x+y=10$. We model $x$ as a Normal random variable with mean 4 and explore 500 samples. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pymc as pm\n", "\n", "x = pm.Normal(\"x\", 4, 10)\n", "y = pm.Lambda(\"y\", lambda x=x: 10 - x, trace=True)\n", "\n", "ex_mcmc = pm.MCMC(pm.Model([x, y]))\n", "ex_mcmc.sample(500)\n", "\n", "plt.plot(ex_mcmc.trace(\"x\")[:])\n", "plt.plot(ex_mcmc.trace(\"y\")[:])\n", "plt.title(\"Displaying (extreme) case of dependence between unknowns\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 500 of 500 complete" ] }, { "metadata": {}, "output_type": "pyout", "prompt_number": 62, "text": [ "" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Pf8h0vnv27MGMGTNkZezSpQt0Op1MGtW5c2fExMSwz/S4x44dC+ha+WcOSHW/oKCgVsrc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TRBggfJbqN97sTfXwUATY08EC/DSBZkC0ZDnFxAq92wwTxx5hgsWBJDkCTYFSvP9rfeB6JROCaN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\nyC7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"text": [ "" ] } ], "prompt_number": 62 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the two variables are not unrelated, and it would be wrong to add the $i$th sample of $x$ to the $j$th sample of $y$, unless $i = j$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Returning to Clustering: Prediction\n", "The above clustering can be generalized to $k$ clusters. Choosing $k=2$ allowed us to visualize the MCMC better, and examine some very interesting plots. \n", "\n", "What about prediction? Suppose we observe a new data point, say $x = 175$, and we wish to label it to a cluster. It is foolish to simply assign it to the *closer* cluster center, as this ignores the standard deviation of the clusters, and we have seen from the plots above that this consideration is very important. More formally: we are interested in the *probability* (as we cannot be certain about labels) of assigning $x=175$ to cluster 1. Denote the assignment of $x$ as $L_x$, which is equal to 0 or 1, and we are interested in $P(L_x = 1 \\;|\\; x = 175 )$. \n", "\n", "A naive method to compute this is to re-run the above MCMC with the additional data point appended. The disadvantage with this method is that it will be slow to infer for each novel data point. Alternatively, we can try a *less precise*, but much quicker method. \n", "\n", "We will use Bayes Theorem for this. If you recall, Bayes Theorem looks like:\n", "\n", "$$ P( A | X ) = \\frac{ P( X | A )P(A) }{P(X) }$$\n", "\n", "In our case, $A$ represents $L_x = 1$ and $X$ is the evidence we have: we observe that $x = 175$. For a particular sample set of parameters for our posterior distribution, $( \\mu_0, \\sigma_0, \\mu_1, \\sigma_1, p)$, we are interested in asking \"Is the probability that $x$ is in cluster 1 *greater* than the probability it is in cluster 0?\", where the probability is dependent on the chosen parameters.\n", "\n", "\\begin{align}\n", "& P(L_x = 1| x = 175 ) \\gt P(L_x = 0| x = 175 ) \\\\\\\\[5pt]\n", "& \\frac{ P( x=175 | L_x = 1 )P( L_x = 1 ) }{P(x = 175) } \\gt \\frac{ P( x=175 | L_x = 0 )P( L_x = 0 )}{P(x = 175) }\n", "\\end{align}\n", "\n", "As the denominators are equal, they can be ignored (and good riddance, because computing the quantity $P(x = 175)$ can be difficult). \n", "\n", "$$ P( x=175 | L_x = 1 )P( L_x = 1 ) \\gt P( x=175 | L_x = 0 )P( L_x = 0 ) $$\n", "\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "norm_pdf = stats.norm.pdf\n", "p_trace = mcmc.trace(\"p\")[:]\n", "x = 175\n", "\n", "v = p_trace * norm_pdf(x, loc=center_trace[:, 0], scale=std_trace[:, 0]) > \\\n", " (1 - p_trace) * norm_pdf(x, loc=center_trace[:, 1], scale=std_trace[:, 1])\n", "\n", "print \"Probability of belonging to cluster 1:\", v.mean()\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Probability of belonging to cluster 1: 0.025\n" ] } ], "prompt_number": 63 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Giving us a probability instead of a label is a very useful thing. Instead of the naive \n", "\n", " L = 1 if prob > 0.5 else 0\n", "\n", "we can optimize our guesses using a *loss function*, which the entire fifth chapter is devoted to. \n", "\n", "\n", "### Using `MAP` to improve convergence\n", "\n", "If you ran the above example yourself, you may have noticed that our results were not consistent: perhaps your cluster division was more scattered, or perhaps less scattered. The problem is that our traces are a function of the *starting values* of the MCMC algorithm. \n", "\n", "It can be mathematically shown that letting the MCMC run long enough, by performing many steps, the algorithm *should forget its initial position*. In fact, this is what it means to say the MCMC converged (in practice though we can never achieve total convergence). Hence if we observe different posterior analysis, it is likely because our MCMC has not fully converged yet, and we should not use samples from it yet (we should use a larger burn-in period ).\n", "\n", "In fact, poor starting values can prevent any convergence, or significantly slow it down. Ideally, we would like to have the chain start at the *peak* of our landscape, as this is exactly where the posterior distributions exist. Hence, if we started at the \"peak\", we could avoid a lengthy burn-in period and incorrect inference. Generally, we call this \"peak\" the *maximum a posterior* or, more simply, the *MAP*.\n", "\n", "Of course, we do not know where the MAP is. PyMC provides an object that will approximate, if not find, the MAP location. In the PyMC main namespace is the `MAP` object that accepts a PyMC `Model` instance. Calling `.fit()` from the `MAP` instance sets the variables in the model to their MAP values.\n", "\n", " map_ = pm.MAP( model )\n", " map_.fit()\n", "\n", "The `MAP.fit()` methods has the flexibility of allowing the user to choose which optimization algorithm to use (after all, this is a optimization problem: we are looking for the values that maximize our landscape), as not all optimization algorithms are created equal. The default optimization algorithm in the call to `fit` is scipy's `fmin` algorithm (which attempts to minimize the *negative of the landscape*). An alternative algorithm that is available is Powell's Method, a favourite of PyMC blogger [Abraham Flaxman](http://healthyalgorithms.com/) [1], by calling `fit(method='fmin_powell')`. From my experience, I use the default, but if my convergence is slow or not guaranteed, I experiment with Powell's method. \n", "\n", "The MAP can also be used as a solution to the inference problem, as mathematically it is the *most likely* value for the unknowns. But as mentioned earlier in this chapter, this location ignores the uncertainty and doesn't return a distribution.\n", "\n", "Typically, it is always a good idea, and rarely a bad idea, to prepend your call to `mcmc` with a call to `MAP(model).fit()`. The intermediate call to `fit` is hardly computationally intensive, and will save you time later due to a shorter burn-in period. \n", "\n", "#### Speaking of the burn-in period\n", "\n", "It is still a good idea to provide a burn-in period, even if we are using `MAP` prior to calling `MCMC.sample`, just to be safe. We can have PyMC automatically discard the first $n$ samples by specifying the `burn` parameter in the call to `sample`. As one does not know when the chain has fully converged, I like to assign the first *half* of my samples to be discarded, sometimes up to 90% of my samples for longer runs. To continue the clustering example from above, my new code would look something like:\n", "\n", " model = pm.Model( [p, assignment, taus, centers ] )\n", "\n", " map_ = pm.MAP( model )\n", " map_.fit() #stores the fitted variables' values in foo.value\n", "\n", " mcmc = pm.MCMC( model )\n", " mcmc.sample( 100000, 50000 )\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Diagnosing Convergence\n", "\n", "### Autocorrelation\n", "\n", "Autocorrelation is a measure of how related a series of numbers is with itself. A measurement of 1.0 is perfect positive autocorrelation, 0 no autocorrelation, and -1 is perfect negative correlation. If you are familiar with standard *correlation*, then autocorrelation is just how correlated a series, $x_\\tau$, at time $t$ is with the series at time $t-k$:\n", "\n", "$$R(k) = Corr( x_t, x_{t-k} ) $$\n", "\n", "For example, consider the two series:\n", "\n", "$$x_t \\sim \\text{Normal}(0,1), \\;\\; x_0 = 0$$\n", "$$y_t \\sim \\text{Normal}(y_{t-1}, 1 ), \\;\\; y_0 = 0$$\n", "\n", "which have example paths like:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "figsize(12.5, 4)\n", "\n", "import pymc as pm\n", "x_t = pm.rnormal(0, 1, 200)\n", "x_t[0] = 0\n", "y_t = np.zeros(200)\n", "for i in range(1, 200):\n", " y_t[i] = pm.rnormal(y_t[i - 1], 1)\n", "\n", "plt.plot(y_t, label=\"$y_t$\", lw=3)\n", "plt.plot(x_t, label=\"$x_t$\", lw=3)\n", "plt.xlabel(\"time, $t$\")\n", "plt.legend()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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p5KEeHgmSNsFy9eL1Bx+Pv3x946AOFpsdMiktiEwIIeGMztKE+OCadDJdLMviO+9dwdPH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\nZk8ftxzHKSZSgilHsTFuDAJKY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"text": [ "" ] } ], "prompt_number": 65 }, { "cell_type": "markdown", "metadata": {}, "source": [ "One way to think of autocorrelation is \"If I know the position of the series at time $s$, can it help me know where I am at time $t$?\" In the series $x_t$, the answer is No. By construction, $x_t$ are random variables. If I told you that $x_2 = 0.5$, could you give me a better guess about $x_3$? No.\n", "\n", "On the other hand, $y_t$ is autocorrelated. By construction, if I knew that $y_2 = 10$, I can be very confident that $y_3$ will not be very far from 10. Similarly, I can even make a (less confident guess) about $y_4$: it will probably not be near 0 or 20, but a value of 5 is not too unlikely. I can make a similar argument about $y_5$, but again, I am less confident. Taking this to it's logical conclusion, we must concede that as $k$, the lag between time points, increases the autocorrelation decreases. We can visualize this:\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def autocorr(x):\n", " # from http://tinyurl.com/afz57c4\n", " result = np.correlate(x, x, mode='full')\n", " result = result / np.max(result)\n", " return result[result.size / 2:]\n", "\n", "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n", "\n", "x = np.arange(1, 200)\n", "plt.bar(x, autocorr(y_t)[1:], width=1, label=\"$y_t$\",\n", " edgecolor=colors[0], color=colors[0])\n", "plt.bar(x, autocorr(x_t)[1:], width=1, label=\"$x_t$\",\n", " color=colors[1], edgecolor=colors[1])\n", "\n", "plt.legend(title=\"Autocorrelation\")\n", "plt.ylabel(\"measured correlation \\nbetween $y_t$ and $y_{t-k}$.\")\n", "plt.xlabel(\"k (lag)\")\n", "plt.title(\"Autocorrelation plot of $y_t$ and $x_t$ for differing $k$ lags.\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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jsXXr1lLjKcrLV+p3Q0XlqlWrFi5fvoygoCDcvn0b9erVw/Dhw/Hf//5XnUZWVhbHPZBN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\naWruK5afblT6KDkVBZl3S6WvT7mlniPdz4nlJ7a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"text": [ "" ] } ], "prompt_number": 66 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that as $k$ increases, the autocorrelation of $y_t$ decreases from a very high point. Compare with the autocorrelation of $x_t$ which looks like noise (which it really is), hence we can conclude no autocorrelation exists in this series. \n", "\n", "\n", "####How does this relate to MCMC convergence?\n", "\n", "By the nature of the MCMC algorithm, we will always be returned samples that exhibit autocorrelation (this is because of the step `from your current position, move to a position near you`).\n", "\n", "A chain that is [Isn't meandering exploring?] exploring the space well will exhibit very high autocorrelation. Visually, if the trace seems to meander like a river, and not settle down, the chain will have high autocorrelation.\n", "\n", "This does not imply that a converged MCMC has low autocorrelation. Hence low autocorrelation is not necessary for convergence, but it is sufficient. PyMC has a built-in autocorrelation plotting function in the `Matplot` module. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Thinning\n", "\n", "Another issue can arise if there is high-autocorrelation between posterior samples. Many post-processing algorithms require samples to be *independent* of each other. This can be solved, or at least reduced, by only returning to the user every $n$th sample, thus removing some autocorrelation. Below we perform an autocorrelation plot for $y_t$ with differing levels of thinning:" ] }, { "cell_type": "code", "collapsed": false, "input": [ "max_x = 200 / 3 + 1\n", "x = np.arange(1, max_x)\n", "\n", "plt.bar(x, autocorr(y_t)[1:max_x], edgecolor=colors[0],\n", " label=\"no thinning\", color=colors[0], width=1)\n", "plt.bar(x, autocorr(y_t[::2])[1:max_x], edgecolor=colors[1],\n", " label=\"keeping every 2nd sample\", color=colors[1], width=1)\n", "plt.bar(x, autocorr(y_t[::3])[1:max_x], width=1, edgecolor=colors[2],\n", " label=\"keeping every 3rd sample\", color=colors[2])\n", "\n", "plt.autoscale(tight=True)\n", "plt.legend(title=\"Autocorrelation plot for $y_t$\", loc=\"lower left\")\n", "plt.ylabel(\"measured correlation \\nbetween $y_t$ and $y_{t-k}$.\")\n", "plt.xlabel(\"k (lag)\")\n", "plt.title(\"Autocorrelation of $y_t$ (no thinning vs. thinning) \\\n", "at differing $k$ lags.\")\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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v3+aN9Swd612lgXmyfMyRNDBPhtM48S8ru1EqjXdTqISEBJw4cQIJCQkYMmQI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\niuosqm1L7SJld4j3+j5Ls2f6VFvOXM6TPnUqPaf6nE9DlE21LqGTRlm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"text": [ "" ] } ], "prompt_number": 67 }, { "cell_type": "markdown", "metadata": {}, "source": [ "With more thinning, the autocorrelation drops quicker. There is a tradeoff though: higher thinning requires more MCMC iterations to achieve the same number of returned samples. For example, 10 000 samples unthinned is 100 000 with a thinning of 10 (though the latter has less autocorrelation). \n", "\n", "What is a good amount of thinning? The returned samples will always exhibit some autocorrelation, regardless of how much thinning is done. So long as the autocorrelation tends to zero, you are probably ok. Typically thinning of more than 10 is not necessary.\n", "\n", "PyMC exposes a `thinning` parameter in the call to `sample`, for example: `sample( 10000, burn = 5000, thinning = 5)`. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `pymc.Matplot.plot()`\n", "\n", "It seems silly to have to manually create histograms, autocorrelation plots and trace plots each time we perform MCMC. The authors of PyMC have included a visualization tool for just this purpose. \n", "\n", "As the title suggests, the `pymc.Matplot` module contains a poorly named function `plot`, which I prefer to import as `mcplot` so there is no conflict with other namespaces. `plot`, or `mcplot` as I suggest, accepts an `MCMC` object and will return posterior distributions, traces and auto-correlations for each variable (up to 10 variables). \n", "\n", "Below we use the tool to plot the centers of the clusters, after sampling 25 000 more times and `thinning = 10`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from pymc.Matplot import plot as mcplot\n", "\n", "mcmc.sample(25000, 0, 10)\n", "mcplot(mcmc.trace(\"centers\", 2), common_scale=False)\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 25000 of 25000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "Plotting centers_0\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " centers_1\n", "\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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CUSalZwt3/e+tkdfgWhWioMYEVfXFy1tSAWjv40InP8MPu1sa7ZBiVp5k+cRg/m/vJQpL\n5SzYkyYCKxtn/vz56v8jIiJ4++23+eSTTwgPDycgIIDZs2cjk8mYNm0a4eHh6lIGS7Ny5UqCg4Nr\nFFiVl5djZ1d1CYRmjZWPjw/r1q1j3759ZGRkEB0dzaFDh7TkdEAp4Kzvt3dUVBRRUVFVnuvEiRMc\nP368zgMrWxl2shY/RI2VebCawOrGgS24tOxIUMQE1t3JfFzetpQ2j72HzNmNlO/fonGPYUgkEhyb\ntCBwSAyXt35HXsrfNOk7juKbGbR59B0UCgUX13xBhxlfgAQOL3uZVk/2BomEjp1DmD7nXfZvW8uD\nDz7IE088ofXQ0BxOKy+6Ra7cAYVCQUaxjKVbk7Br14/oLr4cPnyYSZMmsea6B57B95B39hj5+fls\n3rwZUAZezz77LDdu3OCJJ55g0KBBvPvuu7z//vuEhoaiUCjIyspi3bp1bNmyhYKCAiZNmqQTWGkO\nTlZ+uF3JLVb/n1VYxhvbzlaZMSorl+uVptBMhevjZkEpCWezqnzdkmQVaetsVfVhttNIHubc0Sir\nPGxqbYgHU92we/duAObMmcOcOXO0XjNHKQPAuXPneOmll7h58yZ2dnasWLGCgIAAFi5cyMaNGyku\nLmbUqFG89tprpKWlMXHiRPr27cvBgwdp1qwZcXFx/P777xw7dowZM2bg7OzMtm3bOH36NHPnzqWg\noABvb2+++eYb/Pz8GDNmDCEhIRw4cID77ruP5s2b8+mnn2JnZ4e7u7v6mQQVX5aJiYn89ttv3H//\n/djb29OqVSsCAwM5fPgwvXr10vFpyZIl/P7775SWlvL999/Trl07fv75Z44fP87HH3/M+vXr1ef0\n8PBg7dq1zJs3j+LiYvbv38+LL77I+PHja/3eCuoeoWFlHqwmsLp94xI+vUZorSvKOMfZH94GoOx2\nASU5yuJtF/+2ADh4NqGs6JbWPmUFOdy+cZl/v3sFAGnxLcoKlLpaa26488v6M3w4eBibf1jEjBkz\nGDx4MBMmPkBBSbmWXpadkxvzfj/F1RIZG49ewNG7GYv3XyG6i6/G2e601EFCt24VAcqqVatYvXo1\nRWUKzl1KJy3nNunp6YSGhiq3l0jYd+I0p5JPM3bsWABu3ryp512piIY0M1Yl5XKm/O9UdW+nFjm3\nywxvpIc5W1O4pBHA1TUFJeVcyy8hqLEz5XIF/1y9RUdfV5yMqLs7lp5P/ulMnTqvykHUqhPXzWpz\nQ0GhUPDL8WuENHWjS1M3S5tjs0yfPp3Zs2czcuRISkpKKC8vZ8eOHZw/f574+HjkcjmPPPII+/bt\no3nz5pw/f57ly5fz5Zdf8sQTT7Bp0yYmTpzIsmXL+OCDD+jatSulpaW8+uqrrFy5Em9vb9auXct/\n/vMf/u///g+JREJZWZm62H7AgAGsWbOGpk2bquvGKjNgwAA2bdpEz5491ev8/f3JyMjQu72Pjw8J\nCQksX76cr7/+mq+++gqoaEf22WefaZ3T3t6eN954g+PHj2tlDOsCW/kBYit+gG35YipWE1g5+bYi\n/9wJXFu0Ry6XI5VKcWnWhjaPvoOdkysKuRyJVEpu8n7tHRUKJFI7FArlgJfMxQMn35a0m/YJUjsZ\n7b0d+DdLOcSVd1uOM5B04zbvvfceAP369eOAS3eSrhVwX5eKuh231p3ISzlCnKcvealHaT2hov5g\nwIABHDx4EOTKcypQaKXQv/vuOxITExn85Q5uL36Bj3ZcwN/fnxMnThAaGkpBcRmfHy+h0L0FGzdu\nBFALFRaWlPPL8WsMaeuFZpLptzMVgVdRadWDe2dvFmJXSRysrFz/OGJ12SrA7EGVQqEg6VoBAZ5O\nuDvp3npP/O8U2UVlLBzbnsNX8vnhcAb3tHTng3vbGDz2xrymkHiJiCAvXB3sSL5egLujDGkD7NNt\nyoOpXK7Que6afP3XZTYla9fomQu5QsGb287S3MORZ/q1NOuxGxL5+flcvXqVkSNHAuDg4ABAQkIC\nCQkJDBw4EIDCwkLOnTtH8+bNCQgIoHPnzgB069ZNXTQLFVnqlJQUTp8+TXR0NKAc8tMcIlStB7jn\nnnuYNWsW48ePZ8yYMTWyv6ra0NGjRwMQGhrKpk2bdOzTd06FQmFU31WBwBaxmsCqSe9RnP/1Y05/\nO5uode788MuvNB8xldT/vgsKORKZPW0fe//O1hoPAIkEe/fGyEuLOfvjezQfMZVmQ2L49zulJMSN\nxj40mfC61m7/7N3BqPdXAzBkyBAO3JnxdiCt4heeT++RnF85j8xDv+HRqS8OHspMSEFJOc72Ulp1\n6cXVuLnknT2KV2ftL8I+ffoQFRXFVadW2Dm6kFdcxotz3uKtN5QFse06hSBrOwHvbpGMHj0aOzs7\nmge2593/fMiaf66z7uQNfjl+jTHB+mfZyasouLqUc5uZ63S1Wcot9JBTKBTsuZBD28Yu+Ls7cuhy\nHm/9fg5vFxm/PByis332HfG+/x7J4O/LSvXrmrbLKSmTc7tMzvMblb0Op/byr6UX1k9qZiGz1p/h\nsR7NiOmuvyZHFVTVBZdzijl8JZ/DV/Lv6sCqOl544QUef/xxrXVpaWnq4AuU7cLKyytqAjUDnY4d\nO/L777/rPbaLS4XG0ueff87hw4f5448/iIyMJCEhQV14rllj1axZM65cqZCWSU9P15qco4mjoyMA\ndnZ2WvZVd876wlaGza3FD1FjZR6sJrCS2jvQ5pG56uWXN6fg2qI9HaZ/qrWd/7DH1P/79qsYt2//\nZEXK2cmnOR7tlWnuYF8Xkq8XEvhARU1Ft4FRfDF7inpZNYPuSl5FhsbOwZm2k9+nMtH/PYFfzhlu\nN+1Mx5kL1Ovfn/q4+v/PP/+cvNtlTPjpHwAyC0p5c38pXaZ/xrtDgygoKWfyr6doHDaMzYvmkF1Y\nyoM/JxHzy0l6NG9U+ZQ6VFXI/uTqZL3rk68XMlSP9IShGqva8vflfP6z/QKgzJIcvaIMlrIKqx+a\nVAVVNUHly85z2QT7VhS1G6PsXx3/t/cSmQWlvDsssN7kGWr6YFKp4P/3cEaVgZWg7mnUqBH+/v5s\n3bqVkSNHUlxcjFwuZ/DgwXz00UdMnDgRV1dX0tPTtQIqTVQ/gNzc3NStddq2bcvNmzc5dOgQvXr1\norS0lLNnz9KxY0ed/c+fP0+PHj3o0aMH27dvJz09XR1YadZYRUVFMX36dGbNmkVGRgbnzp2jR48e\nJvmt75yNGjXi1q1bhncWWBWixso8GAysMjIyGDVqFMnJyRQUFHDx4kUmT56MRCKhRYsW/Pjjj0il\nUjp06IC/vzI7sGjRIoKDg2tlmDFNgI1BXzscuUb2pkyu4FriWnKSKnQsnJsF0WrcM1UeM+VmEY0b\nV93mYHNyJgv36kobJF0tIOaXk8Tep/1A3PZvxTCf5nd3VVkGfTpShqhu+LCuOJel3R6nusDkdpl5\n7EvPK9aaLSitZWSlugaZhaU0cdX/ZWhxLF2Lb+nzWxHffvsts2fPZt68edjb27NixQoiIyP5999/\nuffeewFl0BQbG4tEItH5TKiWJ02axEsvvaQuXl+xYgWvvfYaeXl5lJWVMXPmTL2B1TvvvMO5c+dQ\nKBQMHDhQPcyoiSpoHz9+PH379kUmk/Hpp5/q/XxqrtO0V/N/feds3rw5X331FQMHDqzT4nVbyYzY\nih9gW76YisHAytvbmx07dqjH8b28vNiyZQuNGjXirbfeYuvWrYwePRpfX996TQEbS2WFcICNpzJ5\nvKc/u85l8+GOC/gNuA+/AfcZfUz3Nt0orVS39M1fl3igqx9ztqRqZb4qc7tMrvP6939XFI0aM2Pt\n1d9SjbZVxdJD6TrrzJ2t+utiDttTs7m3vTe9W3rovF7Zs5JyOQUl5aCAB39O0tm+Jqh8UQC3iiuC\nXnPNADR0lBMZ+fxztYCHu/nVOLNVuT6qugfT35fzyL1dxhCNDGRdlpGlZd/mo4QLPNnLn14t9ct5\n1DYraEsEBQWxfv16nfUzZsxgxowZOus1hQmfeabix9yYMWO0aqS6dOmiNcNPhapGU8V///tfo22d\nPXs2s2fPrnabo0cr9PC6devGhg0bAGXgN2nSpCrP6enpqSMsbQ5uFJRQYsKPMDuphLLqNGsEAjNi\nMLBydHRUj7EDWqrEMpkMmUx5iKysLAYOHEhwcDBfffWV1j7Wxq07s88+3HHBbMfccCqTDaeMq2N5\nY9vZKl9LryYos3be/fM8oFSEX/lwF5ZVCuYqxxvT1ySTnlfCYz3013ZocinntjIIu8OW5EwGtNZV\nyJYr4M3fK95fc33pV9UIXIVKXyvQ24l+AcY1IQf4ZNdFdqRmsfLhLng52+u8vi7pOmdvFtHU3ZGJ\nIb7qe6eLnxsnr90irHkjnffVVBQKBf/75zodm7gQ2qyR2r5zWUW8+XvVch4irmoY2EKvwKSrBcxL\nuKBerutyhvrCWuqSRI2VeTC5xio9PZ34+Hjeflsph7B37148PT2ZN28eS5Ys4dlnnzWbkXXBo6tO\nIpVUL7xZFXX5Yb5cj/IGdenHJD0ZqMpfwOl5ytmaJ69WX4vx25mbOu12Dl+pqMN6P/6c2heFQqF1\nTQ1JNdwuk/PRjvMMCvKqtgWSscFLZg2HsOPvtBTacz6HsZ2aUC5XMPmLVURGhPNoWDN1JwCA3eey\n1f/PWJtMYamcAE8nvf0sVZTLFVwv0C/8quJ/J67hKJPSwsORpQeVwbAqiCoqrXrIG5SzWBPOZle7\njcBybN++nfff164V/f3339myZYuFLBJYM6LGyjyYFFgVFxfz+OOPs3TpUrXMgCqTFR0dzYIFC/Tu\nd27Vxzh6KYtr7ZxdcfFva3SvJltdTssOttj5C9NT6+18iYmJnD2dCQSol/POpuDephsSSfX7L9iT\npvf1xMQC/IN7kHghl8J0ZcaovP0Qrf2v38mGVXX8zcnN2Z+Wxx8Ju/lsVDut3lHKWjyl5tP+v/bi\n7iSrsteU6njyvi30vp6YmEhxmZwM93ZEBHmRlvQ3SpT1YMlHDuCd5Yl3u+6k3iwidd0fHNrvBi5t\n1cc/oWH/1dNHALjYphutvJzU5z94KYgufm4cObgPgB23/Um8kKvl/7yECwyQXUIikeAa2JXvDqaT\nd/YYk7r6Ac207FfgrfV+V/Z/V3Fzdp3PUR8/MbHALL22BOZhyJAhFm0pVNfUR7bq7M0ick3QAnR1\nsKOzn3GacbaU4bElX0zF6F6BkZGRxMfHY2dnx+TJk7nvvvsYN24coOwgL5fLcXR0ZOnSpWRnZ/PK\nK69o7W9sr8C7jQAvJy5m17wYvaGx/rFQfjp6ldX/KAU6Xwxvpc5C9W7pzsEayioAPNOvBXFHr6pl\nGkwhpntTfjqqnFVXeairqLSccT+cAGDlpC40dtUdqlOhmlk6s09ztYhsamYhW0/f5PGezXB3khG7\n/zJrkm4glcC2J7X7PT7TrwVjOzXh38xCnlmvK5lRHQMDPdl1Pkdr3ZC2XqRmFnGxiokOi8Z3oLBU\nzstbUtTrZvVtwaJ9ygbFqvdiyq+n1DWB+oYC7116VEtv7edJnbmQfRtHmZSQpm4W7xV48uRJpk+f\njp2dHZ07d2bx4sV4eHgQFhaGRCJh7dq1eHp6EhcXx6JFi9QtbRo10p6dW9+9AgX6STibrTUUaAo1\n7RVoKv0C3Hl3mGENPoH1Ume9AsvKyoiKiuL48eNERUUxd+5c1q1bR1paGl9++SUvvPACffv2ZcSI\nEbi5ueHt7c1PP/1kkhN3I3kmqqI3NMb/94TWsubQnqnh9td/Xa6FRUo0ewlWRjPAkWPcmLFcAUeu\n5LH+5A3239FFKymX80J4K9Yk3VBvUxnVz5uL2UW6LxpCzxu4PbX64blyhYJfjl/VWrfkQMWw4+bk\nTJKvF2jNoNWHVAKa8zgeXnlS/X99NOU2RIcOHdi7dy8ATzzxBEePHiU0NFRrok1paSmxsbHs2bOH\n1atXExsbq9OE2RawhRqryogaK/MiaqzMg8HASiaT6czu0Ncq4fDhw+azysox54e5NtmW2mLJh5KP\nq726Hskcxdem+rL+5A2ddeVyBb+duamlPG+svqpCoeC137QnJ1zNLzE4KUF1+HVJN2rsy65zOYY3\nqsSzG/7V7PIuAAAgAElEQVTVWac5a0qfXIgmCoWCc1lFVCHqbzWoJteAsoenh4cHycnJRERE0L9/\nf+bNm0dKSgohISFIpVKGDh3KtGnTLGhx3aGpYyUQ6EPUWJmHBtjwQ2AL3NbQ1aov4U1jmfvHWZ3A\nwlDmRoW+rSQSZbCmSUZ+MddvVRSVKxQK4lOySL1pQsbKAvxy/JpelX9rZOPGjYSEhODk5ERQUBCp\nqans3r2b7OxsNm3aRG5uLu7uSikJd3d3cnJqHqg2JGwpm2AL2SqwrWtiS76YitUorzckbOXDbEk/\nNIfgzBFWmdMXfcrv5Xqkc8rlCvZdzCVYQ5BU3zCfRAKllV6YvEq3ifYnuy4C1n9/Xb9VoqW9VhXG\nBqN1zdixYxk7dizPPfccf/75J8OGDQOUAplHjx5l3Lhx6ix8Xl6elqSMJrNmzaJVq1YAeHh4EBIS\nUuVkBrFcN8s0Uwqe1nYyjWpdXU7euXzLFe7UWFnL+yeWDdxfd/6v7eQbo4vXa4soXhdYO6qaIFVB\nuSYeTjL+F1PR31ChULApOVOnzsveTqIjHtvN341j6Q2/vUeAlxPTevuTmlnEisOGA6stU7ryz/Fj\nFi1eLykpUbePeeutt+jduzejR49GKpXy1ltv0bVrV6KjoxkyZAgJCQmsXr2atLQ0nRorWyhet4Ua\nq8rF66aUAFhj8bq11CWJGitt6qx4XaCLrRRM2oofUPe+qKZbl8sVTPzpH26VlNNZI1OlonJQBTXP\nyFnrdbmYfZu3fj/Ho2HG9SO0RBulymzbto0vvvgChUJBYGAg0dHR9OrVCzc3N4KCgvjggw+QSCRM\nmzaN8PBw9axAW8RaaqxKyuQUGtBHqwpryYLaKqLGyjzYRGD1wwOdWHoonT3nbbs2QmB51iVdVw9j\nnrym2y5JH9ZWQ1ZbjBXV/TMli8C6NcUgqmFATfRNtImJiSEmJqa+zLIols4mZBWV8vKWFKMnhGiS\nX6wdkFnjDxBTsPQ1MSe25IupNPjAyt5OQjN3R+YOCdQ7hFMX2MqH2Vb8APP4Ui5XVNsC50RGPksO\n6vZcNEROUc3U2K39usQdvWp4IyD2wBXmN+zRM0EdceNWqZECJgJBw8PgrMCMjAzCwsJwdnZGLpdz\n/vx5IiIiGDhwII888ghyuTLdHxcXR//+/RkzZgz5+brFv3VFFyOVbQUCQ9z/4wler6aPo6ofYE05\nl2X7ArAC62fhwoUsXLjQ4kOB5kRVNN7QsZZrorpHaoO1+GJJDAZW3t7e7Nixgz59+gDg5eXFli1b\n2LVrF4GBgWzdulVLYO/RRx8lNja2To32c3NQ//9wN786PZc+bOXDrOnHzD7NLWhJ7THHNSkslXPk\nSv39KKgKW7m/BNbFc889J2poBNUi7hHzYHAo0NHREUdHR/Wy5lRke3t7ZDIZqampJgnsdWziQu7t\nMjLyq28SW5mn+jSnf2tPCkvKcXGwq9G+toydhgp2SFM3/jHQ3FiT6C6+Wg1/BQKBbWJLNTDWPmxu\nLLZ0TWzJF1MxWSA0PT2dP//8k+HDh5OdnV0jgb3PRrVjRIfGzB/RlhUPdGJUx8ZVbntPS3eddY0c\nlcFUXQVVH97bBrdqjt0QPsxvDW7N9xODq91G5Ud4oDJYjpvUuc7tqisawjUxFlvyRSAQCO42TAqs\niouLefzxx1m6dClSqRRPT0+jBPZUhDZz48XwVrg42CGRSJjZpwVvDm5NRKDufiM7+uisc7GvPqDq\n2qx2dVetPJ2YP7JtrY5hCTRnn9lJJTT3cDJqP9VN4ONSdZNhgUDQsBE1VtaLtVwTUWNlHmo0K1Cl\nJTp9+nSefvppOnbsCEC7du1ISkpCLpcTHx9P37599e5/btXHjL2nE/Pn/66lXOwgk2KXfpI2RbfZ\njTJ7pfrASIcHEejlxPG/9wPKX/P2dhK9yqmP+d1G1qoLD4T68fPm7Xz91yWTlHMlEkg+coC8sxf0\nvq75YW4W3IOCkvI6Ue6t6bKdRIJrUFcADu77Cyd7KeCqd3uX66c4d+YUTcMnIJFofhj0b2/ty1f3\nrMbFv63V2FObZc37yxrsqckyQP7Z4xRn35k5GDYHgXVgLTpWAutF1FeZB4PK62VlZURFRXHkyBF6\n9OjB3LlzGT16ND169ADghRdeYNy4cfz0008sXrxYLbDXqFEjreMYq1z82KqTXNWouVoc3YFAb2e2\nnbnJl4nK/m0/PNCJZu6OVR0CUAaB9y4z7dfMz5M6U1Ku4PFfdduOgLaAYyNHOx1tFUsxuqMPm09n\nArBhcijO9nZVSlD8MbU7fV7/Hvc23Yhs48Xrka0B/arjDQFrFdU0hcq+TOnZjAkhvjy74UyDm2E4\nP0xhUeV1c2ELyuvWwtX8YiavOmUxuQVrVF4XWCd1prwuk8mIj4/XWqca9tPEXAJ7Hk4yrcCqTWMX\nQFmMrcLezrDgokQi4ZvxHXh6fc0bxUokEuSKqlWjrfUL/NEeTdWBlZ0RopQqP9wdTZMz83aWkVVU\nZtK+5sZar4kpVPYlqn1j7O2kvDqoNTPWnraQVQ2TkydPMn36dOzs7OjcuTOLFy/m008/ZePGjQQE\nBLBixQpkMhlxcXEsWrSoyh+GAoFAYCwmF6/XFVUJNEo1AgV7O+PMbufjwrvDaq79LMV4dWlr0tSW\nSbVrrAzx3rAgerVw12pR8t6wIKPP9/nodjUzUGASqlvfiEsqqESHDh3Yu3cvu3fvpri4mEOHDrFz\n50727NlDaGgo69evr3e5GEshaqysF2u5JqLGyjxYXWAV3dlX73rNWMq+Bt8wfVp5cH+XJjWyQSKp\nqCfTh+aH2ZralWhaUt1b9Fz/lgCUX/qHD6Pa4O5UkbHqG+Bh1Lm8nWU093BiYFDVExUmdTWvxpi3\nc9WZteoesMZkOK2Jyr6oflRIrCqMbxjIZBX3TFFREYcOHWLQoEEADB06lH379unIxezbt89C1tYt\nQqNIYAhxj5gHqwusBrXx4pWBrXTWa2esjP+CkUokzOjTQu9rbg52rH00hD+mdtfZp3JY9dmodnT3\nt16V97eGtNbKslUO+Nr5OKv/d3c0Xabiwa5+rHigE8sndgKott+Xay3OY04Wjm1vaRNqhepSNveo\nvq5QoJ+NGzcSEhKCo6MjXl5eOtIwOTk5NZKLaejYks6QrZQA2NI1sSVfTMXqAisw3KZGZqYxkdWP\nhuB2p77o4xEV8grKjJX2tq29nPh4ZDtl0Xff/jU6T3VZHQAf19rLHEQEeunt/P7xyLZ09nNVF6cD\n6tRWTT8AAZ5OPNnLH393R7WG2ANmykp9M75Dta/P7NO82uHN6h6wbRq70Laxc5WvWxuVfVH9qDBm\neFegy9ixY/nnn39wd3fH1dVVRxrGw8OjRnIxAoFAUB3W2YRZz/eHr5sDk7r60dTd0WzDb5pZsPZN\nXLTWVy7oNvWUcZM609jFnl3n9A9VTe7RDGd7Kd/eUT13tpfSrVkj9qXlmnbCSnT3b0R3/9oX4j7V\npzkDg7x01rf3cWHVw1148OekWh2/umB5zaMhNHKU0dnPjbl/nCXbyIL5Fh6ORHdWDgNHtvEi9WZR\nrWy0FDW99Wb2aV4jFX1HmZQpPZup78Ha0LSRg9bkE0tTUlKCg4OyBZYqG7Vr1y5eeeUVtTRM+/bt\njZKLmTVrFq1aKbPpmnIxgF75F2tbXrNmDYGBgVqzGy1lT97ZYygwj7yHpkSJsfur1tWl/MjlW65w\nZ1agofdj8eLFVnE/HTlyBEB9j5hyPM0aK0v7U9Nl1f9paWkATJ06FVMwKLdgLmoyXVmuUPDshjP4\nuTnw9lDji6mrY17CBRLOZmut0xwCLCgpJ/q/JwDY/HhXHGRSdp/P5j/bLwCw7rFQXO9kaR78eCXZ\njZUaXh5OMnJvK7/og7ydmNq7OW/caeQb1b4xsyOUD+Lpa5K5kK09VX51TAjuTjI2nLzBN/suA9Ch\niQs+LvbsvVh9YNXd341Ab2fWJt3Q8uWzXRdxd5Ix/R7d3n8qKYW5QwIJD/QkMTFRb9ZKtd2cgQFs\nT81iSk9/rcCzMoUl5Yy/895pMrW3P0sPplfrh4rY+zpWOeOt8lDtdweu8L9/rmut0ye3oLlf8vUC\nnt/4r1G2WJrKvqikMwB2n8vm2wNXyCworXL/1wYFMH/nRaPP18jRjjWPhppFauPr8R14aXMKxWXK\nWbWWllvYuHEjX3zxBQqFgsDAQJYtW8bnn3/Opk2btGYFmksupiFQ1ee+vjCn3IIpMivWKLdg6Wti\nTmzJlzqTW7AEUomEr8d1MGth+FP3NKdMrmDPef31E5p1Ww4y5Qhp/4CKIQFNS6p6IHx7n3YLmerM\n/2J0O3XReGsvbYV0zeNPv6c5Sw7oZhLspBKaNdKtuXl5YEDVJ1XZZXALJV2aujK0nbfB7aT1PEQ1\nuUczncBKxdRe/iw9pBvMBfu68p97g3jr93MA9G3lYbasYF2jmVmNCPLinlYejFlxvMrtI4K8ahRY\nmfPqtfdx4YcHOvFQLTOY5mLs2LGMHTtWa92cOXOYM0dbuNRccjENAVv50gNRY2WN2JIvpmKwxioj\nI4OwsDCcnZ2Ry+WUlpbSt29fGjVqxNmzZ9XbdejQgcjISCIjI0lOTq61YeaebeflYs/cIYFV1js5\n2En574OdWPlwF/U6zXhB0xy/jsZn3qqii4YuV9dqhuruq2JGo1QiMXl4UkVVH4DPRrXj9cgAmuoJ\n3PTbUvVrkW10hw+N5e2hgax7LFT3BT3nUz1gBwR6smFyKBsf76qzTccmrur/3xzS2mS76prKXxaV\nr7OhOLamNYjm/qyJUjCBQHA3YzCw8vb2ZseOHfTp0wcAe3t7NmzYwIQJE7S28/X1JSEhgYSEBIKD\nq2/+a0mqe+Y3beRIY41+eZpfOFV9+TjJqn4LNWfpGVs8rVBoZ6ykEglfjW1PeKAnczSyUV7OMtMz\nDQZ2DG3mRmQbw5kqFVV9kdek96Dm2zu1tz8vRbRiQGtP9fCrMefzdpHh7+6Is72d3uuiWfxtjICq\ntSCtZGvl5ZrSyddV6xYw9ztRW/sEdYPQsbJerOWaCB0r82AwsHJ0dNSZJePrq6s1lZWVxcCBA3nq\nqacoLi42n4VmpvOdGYfVaSLpQ7MUTXJZOczhaCdh7tBAWno4Mn9ExVj6Y2FNkUqU0gQqZvVtQT8j\nNKIUegYag31dmTskkKHtvBl8JwP0ZC9/hrT1pqWHIzHdm+rsYwzm+gBofpEuGN2Oab39eaR7UwYG\neeltrK0PzeRexyYu3Nu+cbXnW/lwF1ZpZBfzzh4jWCMjpQ/NwMrcWRVj9b8McW97b50vi8qmGmN7\ndUKvz/VvSez9HSuOb+b3QmSsrBOhUSQwhLhHzIPZ5Bb27t3Lrl27CAgIYMmSJeY6rNkZHezDq4MC\n+GZ8R8Mba6Cp9j6mkw8PhvqyKLoj7X1cWDaxE2HN3dWvx4Q1Y8uUbrTyrKidcnOU8VhYM+NOVk1V\n52uRrfljanc8ne1xcbBj2cROPNbDyOPWIe8OC+TZfi3o3NSNiaF+TO7RDDuphH4BHnwb3ZFNeobm\nNPF1c6jR+Rq72ONVKSNmKEDQvNklEolaKFUfnXyrD9Iq80RP81yDUR19mB2ureNW2S+JRMKi8R20\nJCpc7LU/yn0DPFj7aEiV2mutvZzV/lf3PpiCNYnmCnSxpRoYUWNlfdiSL6ZSq+J1zQeoKqsVHR3N\nggUL9G5vLdOVh7T1Nnr72Pt6UC5XsP+vverXh0UOJDExkYtJ52lZxf77NLZXva6cKdUIDyeZ3unH\nAIrGfVGg0MhadDeb/3lnU3Bv0w0Jutmq2h5ffikJZS6tic7rQY2dtc7ftZkbEfaX+TDhAu5tuvHD\ng504enCf+nWFoibTYysCoEsnD8OdWaT6tlfWvLmplz2B1yM709rLiUmf/gJUPKgz/z1C3s0io6dX\nnzp8gLyz52s9XVuuaM8DI4ew5YtVnLlRSKvOPZFKJDr+XD19RMv/3NRjFJXJ1cdTbX9flxCOpt/S\nOZ/K/81T+uFgJ9W6PrWxPzGxgIRdezi3805xfZh2kbhAIBDYOkbLLURGRhIfH4+dnbLmZcqUKbz1\n1lu0adOG0tJS5HI5jo6OLF26lOzsbF555RWt/W1punJtKCgpx95OgkOlfodzfz/LgUt5PNWnOcfS\n89mfphQsrCw1UBtU0+nfGRpI/9b1L4KoOn83fzfeGRqklrdQ+ah6/ZORbelmpPaWpkTAgNaevD20\n+t6Q2UWlSCUSPJy0f1NUlhro7u/G0fRbVR6nZ4tGPN23BX+kZNGmsTMRgV565Qqi2jdm2783jXEF\nUA6ldm7qRnGZnNSbhQT7ulZbs6Q6Z4cmLpy5UQho3zPH0/N5ZWuq1j6Lozuom5vrO1ZN+HhkW17V\nOP4fU7tryW9YWm7BXNjC80tVOxMWFibkFhByC/pQ3SO1GQ60Fl/MgalyCwaHAsvKyhg6dCjHjx8n\nKiqKgwcP8uCDD/LHH38wefJkNm3aRHZ2Nv369WPgwIFs2bKFWbNmmeREQ6E2tUmuDnY6QRUotaW+\nHNOe8Z2bVNsmxpxYqsjQWVZ9qxtT3M87e0xHtkIfXs72OkGVfiqCmeUTdSdjDGvXmOYeTkzp6U9E\nYNUzH8d3rlmfyvI72TpHmZTOfm4GC8EXR3fgoa5+vH+npqryEGZIMzeGtfPmmX762zrVlgCN4W7V\nhAFzdUaoiscee4zffvutTs9hi4j6GYEhxD1iHgx+w8hkMuLj47XWrVq1Sme7w4cPm8+quxAHmZRO\nfjWr6zEVS5XAPNWnOXFHrzLtHv/qN6xBZOXn5sC1WyV0a+amNVmgpnwb3ZElB69w5Eo+oJSJOJqu\n/L+Fh27Apu8tjJvUmUdWntRaF9TYmS/HtOeFTcaJk9ZUr7dNYxd19mnz412R2enOIHzlzmzSr/+6\nXKNjG8tz/Vty+noBL96pDXOQSZkzMAAHOwnknDf7+b777jtWrVrFgw8+SL9+/Zg6dSqurvXz2bEF\nbCWbAKLGyhqxJV9MxSoFQq0dW7lx6tuP+7r4Et25ibo2L7KNl1bR9T0t3fnn6i06+lat8l6Z7yYE\nk1VYir977YZMgxo7My+qDRtPZdK+iYvOzDZ/d0fS8ypmu+oLTpu4OvBwNz9+PnYNH1d7xndSZqs6\n+bkS2tSNE1d1hxY7+7ly8lqBelmB6dfFoRrpD1No5GiHvZ2EZ/q2pHdLdwpKyrVaF43u6IO3iz2j\ng30YHeyjta9KWPbIEfMHVjdv3uTcuXN4eHjg5+fHE088offHnkBgSRQKZVeKchOGIOylEpzsraOJ\nvaDmiMDKCqnrkUB9iu31heaEB63G0MD7w4OQK2rWbNhJJsXf3Tz+SCQSxmkM3b04oCWt7gwvPhDq\ny5eJlyq2reIYj/dUSk3YVxrulWosdvJ15dR1ZTD11uBA1p28TmZBKddvlRDStPoG5PVJsK8rHwwP\nUl8zB5mUDZNDSTibzYDWnurOAfXN559/zqxZs2jTRlm/0rJl1bMaDxw4wOzZs5FKpfTq1YsvvvgC\nDw8PwsLCkEgkrF27Fk9PT+Li4li0aFGVLW1sAWupsTInptRY1RcHL+XxzIYzRm1748wRmnSoqOGb\nHd5KS0S6vhA1VuZBBFYmUNc3TrCvKwcv5dHI0by/WL67vyPpeSUEeivFSq3tAyCRSLAzcZiyLnwZ\n0bEiCzOiQ2Pyi8tZpmqXU42dlYMqgGf6tWTu72d5vGczdp2raKvU2NWeqb21+zrW1XUZ3dGHizm3\n1dffEHYSiY50grO9HSM7+lSxR/0waNAgdVC1ZcsWRo0aVeW2rVu3JiEhAQcHB2JiYkhKSiI0NJSE\nhAT1NqWlpcTGxrJnzx5Wr15NbGwsL7/8cp37Ud+oviyFgGP9UK6Ay7nGaTrmFZRSrLFtmbyeCm0r\nIeqrzIN5xw4EZuGBUF+eH9CSxdE109oyRICXs9mELO82JBJJrWq4Wnk68cODnYls4212pXNjeW5A\nSz4f3c5oZfRBbep/5qgx7Nq1S/3/nj17qt3Wz88PBwelRpq9vT12dnYkJycTERHB66+/DkBKSgoh\nISFIpVKGDh3Kvn376s54K8CafkzVFmvNVtUUW/EDbOv+MhWRsTKBur5x7O2kjKqHrIAtfQDq2xd9\nMzuNxVBcY6nr8v7wIJYdSueVCGWxezsf4zJb9c2NGzfYvn07EomEa9euGbXPiRMnuHHjBsHBwaSm\npuLp6clTTz3Fpk2b8PHxwd1dKfDr7u5OTo7+Ru0CgUBgDCJjJRCYgLtjbX6TWKcyeZ9WHnx3fzDt\nm7jQvomL1SqoL1y4kH///ZfTp0/z5ZdfGtw+KyuLZ599luXLlwMVYsbjx48nKSkJDw8P8vKUunF5\neXk6LbxsBdEr0HqxFj9Er0DzYPDbISMjg1GjRpGcnExBQQHl5eVERESQlJTE8ePHCQpS6ufcDcWf\nKqytNslUbMUPqD9fZvVtwfmsIoJrMHOxMobiFVu6LnVBWloaubm5FBcX89VXX/H2229XuW1ZWRkx\nMTF89tln+Pr6UlhYiKOjI3Z2diQmJtK1a1fat29PUlIScrmc+Ph4+vbtq/dY1tI5wtRlVdF6YmKi\nxe3JO3sMBTVX9q+8rKKm+6vW1fb85louTE/VWj52cB+3fFzq/fpUrsOzpvu3PpZV/6elpQEwdepU\nTMGg8npxcTFFRUVER0ezfft2pFIp169f59VXX9VSXh8yZAg7d+5k9erVpKWl6RR/2oJysYrFixcz\nc+ZMS5tRa2zFD2hYvsTuv8yapBuAfmX9huSLIUxVLq6OKVOm8NJLL2Fvr+wV2aFDhyq3XblyJc8/\n/zydO3cGYN68eTz99NO4ubkRFBTE8uXLkUgk/PTTTyxevLjKH4a29PyyNOZUXjeF+lJerw016T4h\nqDtMfX4ZzFg5Ojri6Kg9nd3X11druXLx57Rp02psSEMiNzfX0iaYBVvxAxqWLzFhzSgslTO8vbfe\n1xuSL5agS5cudOnSxahtJ02axKRJk7TW6RMzjomJISYmxiz2CQSCuxuzFK/n5uaK4k+BwEhcHezU\nKuWCmpOQkMDOnTtxclJqjP3vf/+zsEUNA6FjZb1Yix9Cx8o81CqwUhW33i3FnypU468NHVvxA4Qv\ndxO//PILycnJ9OrVi8uX66ZNjy0idKwEhhA6VuahRoFV5XIs1XK7du0MFn/eunWLI0eO1MJU62Hq\n1Kk24Yut+AHCF2vl1i3dNj615cUXX8TBwYFevXrx0UcfsWjRIrOfw5axpWyCNWR5zIGt+AG2dX+Z\nisHAqqysjKioKI4fP05UVBQffvghn3/+OYmJiaSkpPDqq68yZswYpk2bRnh4uLr4szLjxo2rEwcE\nAsHdhZubG15eXgA4O1un1pZAILh7MRhYyWQy4uPjtdbpa3gqij8FAkF94OPjw549e3jppZeQSoUU\nn7GIGivrxVr8EDVW5kEorwsEggbFm2++yenTp5HL5XTq1MnS5jQYRI2VwBCixso81MvPvRdffJGI\niAheeOGF+jidWbhw4QJ+fn5ERkYSFRUFwKeffkp4eDgxMTGUlZUBSmHU/v37M2bMGPLz8y1pshYZ\nGRmEhYXh7OyMXC4HjLd/x44d9OvXj8GDB3PlyhWL+aBCny8eHh5ERkYyePBg9SxUa/flwIED9O/f\nn/DwcGbPng003Guiz5f6uiaTJk3ivffe44033mD8+PHmc+ouwVzZhAtZRfx9Oa/Gf2k5t82mYWUN\nWR5zYCt+gKixgnrIWB05coSCggJ2797NrFmz+Pvvv+nZs2ddn9YsDB8+nB9//BGA69evs3PnTvbs\n2cMnn3zC+vXrGTduHLGxsezZs4fVq1cTGxurI4xqKby9vdmxYwfR0dFAzez/z3/+w59//snJkyeZ\nN28eX3/9tVX5AhAaGkpCQoJ6ubS01Op9ad26NQkJCTg4OBATE8Pu3bsb7DWp7EtSUlK9XZOVK1cC\nyskzCxYsMKtfAuM5mp7P4v2WD/IFAmujzjNWBw4cYPjw4QANrnN8QkICERERfPnllxw+fJhBgwYB\nFX6kpqZqCaNak2+Ojo5q2QuFQsHff/9tlP1FRUU4Ozvj6upK7969OXnypAW9UKLpi4rk5GQiIiJ4\n/fXXAV2RWmv0xc/PDwcHBwDs7e05efJkg70mlX2xs7Ort2ty8uRJTp06xYkTJ6zivWgoiF6B1ou1\n+CF6BZqHOs9Y5eTkqPsJenh4NJgHob+/PykpKTg4ODBu3Djy8/PVivMqEdScnJwGI4yqT8RVn/2a\n6wDKy8stYq8hUlNT8fT05KmnnmLTpk34+Pg0GF9OnDjBjRs38PT0VBdfN9RrovIlODi43q7J6tWr\nAWXAbagm5MCBA8yePRupVEqvXr344osv+PTTT9m4cSMBAQGsWLECmUx2V/Q6FTVWAkOIGivzUOcZ\nK03x0Nzc3AYjHurg4ICzszN2dnaMHj2aNm3a6IigNhRhVIlEotdWQ+sA7OzsLGKzIVTv9fjx40lK\nSmowvmRlZfHss8+yfPnyBn9NNH2B+rsmPXv2pGfPnoSEhHD58mW2bNlS5baqIcs9e/Zw/fp1reHX\n0NBQ1q9frzVk+eijjxIbG1tjmxoStlQDYyu1SbbiB9jW/WUqdR5Y9e3bl+3blc0ut2/fXmXneGtD\nU9hw7969tG3bll27dgGoRVDbt29vUBjVGlAoFPTs2dMo+11cXCgqKqKgoICDBw+qm9daCwqFgsLC\nQnWmIzExkbZt2zYIX8rKyoiJieGzzz7D19e3QV+Tyr7U5zVZunQpycnJnD59mqVLl5KZmVnltqYO\nvwoEAoGp1PlQYPfu3XFyciIiIoLu3bs3mML1PXv2MHfuXBwdHYmIiKB3795EREQQHh5OQEAAs2fP\nRiaTGRRGtRT6hF2Ntf/NN99k2LBhODs788MPP1jYE/2+zJw5Ezc3N4KCgvjggw+QSCRW78v//vc/\n/rKQHksAACAASURBVP77b+bMmQPAvHnzGuw10efL008/XS/XpGPHjupJIjdu3GDy5MkG96np8Kst\nInSsrBdr8UPoWJkHiaJynxqBQCCwYl5//XWuX7+ORCLBz8+PDz/8sNrts7KyiI6OVgeDJ0+e5JVX\nXuHIkSPExcXx5JNP8s033/DNN9+QlZXFtGnTWLNmjdYxtm/fTlhYWF26VW+Y64tvXdJ1i88KNCUg\n+XvOEAB6frK9Lkwyicp+fDKyLd38G2adny0FVkeOHGHIkCE13k8IhAoEggbFhx9+yOXLl/H09MTR\n0bHabfUNvy5atIhXXnmlxkP6s2bNolWrVoCydjQkJET9BaIqCG8IywMGDDDL8U6fzwZaABWz2lTB\ngbUvq9ZZqz3HDu7jlo+LVdwvNV021/1liWXV/2lpaYCyb6spiIyVQCBoUDz33HMUFBSwbNkypk+f\nzpIlS6rcduXKlTz//PPqWq558+axe/duNm3apDUr8KeffmLx4sVVzgq0pYyVubCGjJUpWGPGqjIN\nOWNlS1h9xmrdunVa06wFAsHdgSkPpuqQSqUEBAQAGJyJO2nSJCZNmqS1rk+fPuraMBV3Q69TUWNl\nvViLH6LGyjzUW2Dl7u5+1/7imzVrFosWLbK0GRbjbvb/bvYdlL/4zI2joyOnTp3i//7v/8jOzjb7\n8W0VoWMlMITQsTIPBuUWnnjiCfz8/AgJCalym+eee4527drRtWtXjh49alYDbQFVXcbdyt3s/93s\ne12gUCiYMGECkydPpk2bNnz77beWNqnBYUvZBGvI8pgDW/EDbOv+MhWDgdWUKVPYtm1bla9v3bqV\n1NRUUlJSWLJkCTNnzjSrgQKBQKBCIpGQkJDAiBEjGDlypNWIpQoEAoEKg4FVeHg4Xl5eVb6+ceNG\ntY7MPffcQ05ODteuXTOfhTaAh4eHpU2wKHez/3ez73XBhg0b2LBhA0OGDGHixIlMnDjR0iY1GESv\nQOvFWvwQvQLNQ61rrK5cuULLli3Vyy1atODy5cv4+fnV9tA2Q3XDqHcDd7P/d7PvdcG2bdvYu3cv\nM2fOZPHixZY2p0EhaqwEhhA1VubBLMXrlRUbJBKJ3u1sRQempssNWdejNsvp6ens37+f1q1bo8Ka\n7BPL1qsDUxVpaWls2bKFtLQ0tm7dCsDIkSPNeg5bx5ZqYGylNslW/ADbur9MxSgdqwsXLjBmzBj+\n+ecfndeeeuopBg0axEMPPQQo203s2rVLJ2MldGDuPvbv38/IkSPp3bt3tXV6AtvFVB2YqlixYoXO\nDzdjWtrUFvH80kXoWNUdQsfKOrCYjtXYsWP5+uuveeihh9i/fz+enp5iGLASd7uuR15enqVNsBh3\n+7U3N48//rilTWiwCB0r68Va/BA6VubBYGA1adIkdu3aRWZmJi1btuS9996jtLQUgBkzZjBy5Ei2\nbt1K27ZtcXV15fvvv69zowUCgUBQM0SNlcAQosbKPBgMrFauXGnwIF9//bVZjLFV7vbo/W5W3L/b\nr72lycjIYNSoUSQnJ1NQUIBUKsXDw4OwsDAkEglr167F09OTuLg4Fi1aVGVLG1vClu5Ja8jymANb\n8QNs6/4yFYNyCwKBQNBQ8fb2ZseOHfTp00e9LjQ0lISEBHbs2IGnpyelpaXExsayZ88eHn30UWJj\nYy1osUAgaOiIwKoeuNtT73d7jZXAcjg6Our0E0xOTiYiIoLXX38dgJSUFEJCQpBKpQwdOpR9+/ZZ\nwtQ6R+hYWS/W4ofQsTIP9dYrUCAQCKyB1NRUPD09eeqpp9i0aRM+Pj7q4Wp3d3dycnIsbGHdIGqs\nBIYQNVbmwWBgtW3bNl544QXKy8uZOnUqr776qtbrmZmZxMTEcPXqVcrKynj55ZfFzJ1K3O1jzqLG\nSmBNqDJY48eP5+jRo4wbN06dVc3Ly9PJcKmwFR0+c+nqnT6fDbRQvm93Mi6qWiFrX1ats1Z7jh3c\nxy0fF6u4X2q63JB1G1X/11aHr1odq/Lycjp06EB8fDzNmzenV69erFy5kuDgYPU27777LsXFxcyb\nN4/MzEw6dOjAtWvXkMm0YzahA3P3IXSsBObWsTKVyMhI4uPjKS4uxtHRETs7O9566y26du1KdHQ0\nQ4YMISEhgdWrV5OWlsbLL7+stb94fukidKzqjs9GtSW0me1OoGgo1ImO1cGDB2nbtq1aOfuhhx5i\nw4YNWoFVs2bNOHHiBKD8tde4cWOdoOpu527X9bjba6zu5mtvacrKyoiKiuL48eNERUXx4YcfMnPm\nTNzc3AgKCuKDDz5AIpEwbdo0wsPD1bMCbRGhY2W9VPZjbdINDl/Jr/FxGrvYM7ydN072pjUnFzpW\n5qHaCEhfH8ADBw5obTNt2jQGDx6Mv78/+fn5/Prrr3VjaTXk5eWxY8cOxo8fb7ZjFhQUMHPmTDIz\nM4mKihJjzwJBA0QmkxEfH6+17vDhwzrbxcTEEBMTU19mWQRRY9Vw+OtiLn9dzK3xfkHezgxr523y\necX3nHmodlZgVT3/NPnoo4/o1q0b6enpHDt2jKeffpr8/JpH2rUhJyeH9evXG7WtER18APjxxx8Z\nPnw4W7duZc+ePWRkZJhsX1XRe2VbjLWtoSFqrAQC60HzniwqLSe7sLTmf0WllMkt/7yyhWwV2I4f\nIJ55YCBj1bx5cy5duqRevnTpEi1atNDa5q+//uLNN98EoE2bNgQGBnLmzBl69uypc7zqij+3b9/O\nwoULkcvlyGQyXnrpJVJSUli/fj1lZWV07NiR6OhoEhMTuXjxImfPnuX27dv88ccfLF++nF27djFw\n4ECWLFnCpUuXePfdd5HL5bz00kvcf//9TJgwAScnJwoLC3nzzTd59tlnsbe3p2fPnnz++ec6xWy/\n/fYbU6ZMAWDQoEH8+OOP9OvXT/36119/za+//oqDgwNjxoyhR48eFBcXs3LlSq5du8atW7f44IMP\nUCgUfPDBB+Tn5zNy5Ejmzp3L008/TW5uLunp6Tz//PP88ssv5Obm0rt3b959913Aeor5arN86tQp\n9bW3BnvEcsMp/hTUD9fyS3htW6pJ++bfLjezNQKBbVBt8XpZWRkdOnRg+/bt+Pv707t3b53i9dmz\nZ+Ph4cE777zDtWvX6NGjBydOnMDbWzsdaaj4MzY2lvLycmbNmqVeFx0dzQ8//IC7uzsPP/wwX331\nFcuXL8fOzo6XX36Z9957j3vuuYfOnTszd+5cVqxYgUKhYOTIkWzatAmJRMLo0aPZsmULzz77LP36\n9eORRx7hp59+oqSkhCeeeAKFQqE3M3f//ffz/fff4+7uzo8//ohcLtdq9lpUVISzszNyuZzhw4ez\nefNmfvjhBx0fhg8fzosvvsiwYcO499572bJlCy+99JLalsTERObPn8/mzZsNXKqGh6p4vWPHjvz1\n11+WNsci3O31BtZSvF5bbKF4XV+N1fmsImasPW1Js2qFKTVW1li8bq5asSBvZxaMaYezqLEyC3VS\nvC6Tyfj666+59957KS8v58knnyQ4OFitTDxjxgzeeOMNpkyZQteuXZHL5XzyySc6QZUxpKSk6NQ4\nnDp1Sr0uNzeXK1eUM1BCQ0MBZUatsuZMZmYmZ8+e5b777gOU9VeZmZkAdO/eHVBOs/7000+ZMWMG\ngwcP5sEHH9Sxx8PDg7y8PNzd3cnNzSUgIEDr9WPHjvHJJ59QVlbGpUuXyMzM1OuDXC6nUaNGyGQy\nAgMDuXr1qpYtEomEbt1sJw0sEAisE1FjJTCEqLEyDwan740YMYIRI0ZorZsxY4b6fx8fHzZt2lRr\nQ9q3b89ff/1Ft27dkMvlSKVSOnfuzIoVK3B3d1ev+/3337X2UygUyGQy5HI5AI0bN6Zdu3asWbMG\ne3t7ysrK1LMUVZkpmUzGe++9B//P3pnHRVX9///JsKMsIoqCiooLuYCau4KiaGju2sf8pKWmmaVW\ntti3zer3qUxL08rcMsst08otVzYBNRRz3wLBHURUdoEZuL8/xhkZGGAYBmYYzvPx6BH33HvPeb/v\nuc6855z3eR2gd+/eWgOr7t27c+jQIZ577jkiIyNZunSpxvlvv/2WJUuW0KxZMwIDA5EkScMH1UiY\nhYUF7dq1Qy6Xk5CQQKNGjTRskSQJmcy8BfBFjpVAYDqY0ztpLrlJ5uIHmNf7pS8mo4vw/PPP8+qr\nrzJ8+HCsrKz4888/mT9/Pi+88AKFhYXY2Niwfv16QDOp3sLCgkaNGvHw4UMmT57MRx99xJtvvsmY\nMWOQyWS4ubnx448/aty3d+9e1qxZA1DqMN+kSZN4+eWX2bhxI8HBwTRu3Fjj/PDhw5k4cSLt2rXD\n0dERCwsLrT58+OGHjB8/Xr2k287OTsMWVfAlEAgEAoGg5lNmjpUhMYccBX0xpznniiByrGpv36sQ\nOVamg8ixUiJyrEpH5FhpUiU5VrWFlStX8tdff6mP27Vrx4IFC4xokUAgEBgWkWMlKA+RY2UYKr1X\nIEBERARvvPEGcrkcNzc3IiIiqsLWKmPGjBkaeWOGxlyid30ROVYCgelgTu+kueQmmYsfYF7vl76U\nmTVdUFDArFmz2LdvHxcuXGDz5s1cvHhR45q0tDReffVVdu3axblz59i2bVuVGiwQCAS6kpSURJcu\nXdTSKACLFi3C39+fiRMnolAoANi4cSN9+vRh+PDh1S5wLBAIzIsyA6uiewVaW1ur9wosyqZNmxg7\ndqxaONTNza3qrK2h1Pah99q+V6DAeLi6uhIWFkbPnj0BSElJISIigqioKHx9fdm+fTtyuZyVK1cS\nFRXFpEmT1HIy5sayZctYtmyZWb2TGVdOGdsEg2AqfqjekcpgTu+XvpQZWGnbK1ClJaUiLi6O+/fv\nExgYSNeuXdUr9wQCgcDY2Nra4uLiAiilTWJjY+nfvz8AQUFBHD16lPj4eDp27IhMJlOXmSNz5swR\nOTSCMhHviGEoM8dKFxkAuVzOP//8Q2hoKDk5OfTq1YuePXvSunVrgxlZ06ntc84ix0pgKqSnp6vf\nRycnJ9LS0khLSytRZs6Y0ztpLrlJ5uIHmNf7pS+V3iuwadOmuLm5YW9vj729PQEBAZw+fVprYFXW\nXoGmsteZOBZ7BYpj89wr0MLCAmdnZ27evAkop6hdXFzUuywULdOGOX5+ebZ7Uun3o6ko1Re8uR+r\nykzFHkMd49oLMJ33q6Ydq/6u7OdXpfcKvHTpErNmzWL//v3k5eXRo0cPtmzZQrt27TTqMgcdGH0x\nJ12PiiB0rGpv36swFR2rwMBAQkJCuHfvHlOnTmX37t0sXLiQli1bMmrUKAYOHEh4eDjbtm3j+vXr\nvPXWWxr3m8Pnl9CxUiJ0rEpH6FhpYrS9An18fAgODsbX1xeZTMb06dNLBFUCgUBgDBQKBcHBwZw+\nfZrg4GA+++wzAgIC8Pf3x8vLi7lz52JlZcX06dPx9/fH1dWVTZs2GdvsKkHoWAnKQ+RXGQahvC6o\nMlQjVt27d2ffvn3GNkdgBExlxKqymOvnV00fsdIHUxyxMhT17K14K6AZBXp8q3s42dDMxd7wRtVg\nhPK6QCAQCAS1mAcPFby/P0Gvez8e1EIEVgaiTLkFgWGojUPvBw8eZMWKFYBSkuPdd98lPz/fyFZV\nP7Wx7wWmidCxMl1MxQ+hY2UYxIiVoEo4ceIEO3fuBODBgwesWrWK+fPnG9kqgaD2InKsBOUhcqwM\nQ7kjVvv27cPHx4fWrVvz5Zdflnrd8ePHsbKy4o8//jCogeaAuayQ0Bdd9NDMldre9wLTw5zeSXPR\nfzIXP8C83i99qfRegarr5s2bR3BwMNWUCy8QCAQCgUBgclR6r0CAb7/9lnHjxtGgQYMqM7QmU9uH\n3mtzsF3b+15gOogcK9PFVPwQOVaGocwcK217BcbExJS4ZseOHYSFhXH8+PFaPe0jEAgEporIsRKU\nh8ixMgxljljpEiS9/vrrLFiwAAsLCyRJqtWjE6VR2+eca3OwXdv7XmB6mNM7aS65SebiB5jX+6Uv\nld4r8MSJEzz77LMApKamsnfvXqytrRkxYkSJ+sxxry1xXPI4NDSUyMhIirNgwQKmT59OkyZNTMpe\ncWx6e20JBAJBTaXSewUWZcqUKQwfPpwxY8aUOGeuysW6YE57J5VFQUEBhw8f5t133+XSJe1qzu+9\n9x6jRo2iVatW1WydcagtfV8apqi8fvXqVXr06EG7du2wtbVl3759LFq0iJ07d+Ll5cW6deuwstL8\nzWkOn19ir0Alpqi8bqi9AivDx4NaELvjF0DsFajCaHsFCmofhYWFFBQUYGFhwZo1awgLC0MulzN5\n8mSmTJlS5tTf559/zt27d8nIyODixYv07duXcePG0b59ewCsra2ryw1BLWbw4MGsX78egJSUFCIi\nIoiKimLhwoVs376dcePGGdnCipGVr4BysjCmzngFgKNHDpOVpwDAWlZ7p+kFJRE5VoahXIHQIUOG\nMGTIEI2y0gKqn376yTBWmRmmHL3n5OTw9ttvExsbS1ZWFikpKbz++uvMmjWLNWvWcPbsWebOnYuv\nr6/6ns2bNzN79mzq1q2LQqEgNzcXgLS0NK1tqPLvVISHh5OUlER2djZnzpzh119/5f79+7i5ufHv\nv/9q3LtgwQIuXbrE3Llz8fDwoEePHqSnp+Pt7U3Tpk0ZO3YsEyZMqIInYxhMue9rM+Hh4QQEBDBm\nzBjatm1L//79AQgKCmLjxo01LrDafu4u4Vce6Hh1A37dqfx3lqsorDqjqgFjj/IYClPwQ2ZhQXZ+\ngV732lnJsHwUpIvPPKG8bhRSUlK4fPkyly5donXr1ty5c4fbt2/zzDPPlMhhK45CoSAvLw9LS0vs\n7OyQy+Xk5OSQkZHB6NGjycrK4r///S+TJk2iRYsW6vsePnxIQkICH330ER4eHnz77bfs27eP2bNn\nc+/ePWQyGYWFyg/Zr7/+mp9++gmZTEZqaio5OTk899xzjBw5ksuXLxMfHw9AVlYWlpaW6jZOnz6t\nk//x8fEaUy33798HQC6Xc/jwYfz8/HBwcOCtt95i3759JCcnEx8fz4ULF9R2xsXFERcXx5EjR/jx\nxx8JCQnh6NGjLFmyBF9fX15++WXc3Nw02t2wYQO7du3i8uXLjBs3jilTplC/fn1sbW2RJImHDx9i\nYWGBg4NDuT5s376dxMREAgMDOX/+PA8fPqRfv35qaRKB6eLh4UFcXBw2NjaMHDmSzMxMGjZsCICT\nk1OpPxBMmQcP5dxIzzO2GYIazNeR16lnX/GQwNHWivcGeFHfwaYKrKqZiMCqGoiOjqZz585s3bqV\nHTt2cPXqVa5duwaAo6MjhYWFZGdnc/ToUfr27UtQUBDt2rUjIyODe/fu4ejoiJubG7/99hu//vor\nERERtG/fngkTJpCUlMT333+v0d4333yDjY0NlpaWNGnShJCQEPbu3aseWXJ0dOT48eMkJSWRmZmp\n1WZVsAMQEhLC4cOHmTFjBgqFQh2A6YquK0WzsrIYPnw4lpaW2NrakpOToz534cIFrffk5uZy7tw5\nvLy8aNWqFSdPniQkJISlS5fi4ODAsmXLuHPnDunp6ezdu5dTp5R6MYsXL2bp0qUUFBSwfft2QkND\n+fbbb3F0dGT8+PG8+eabNGjQgGvXrmFhYUHz5s3JyMjg0qVLrFy5kuPHj3Pz5k3WrFlDUlISlpaW\nFBQU0KNHD7p06cJTTz1FQECAWeUbmAs2No+/AIYNG4aTkxO3bt0CICMjAxcXF633mfLim8Szx8m4\nlqEe+VDpIhU97pV7hhYtWrApyVHtU1nX14RjVVlF71eVGdt+1XFy1DYcPFoZ1Z4MwL+x8vtA9Y7o\ncr+LnRUxRw7jZGdN3759NRaymMq/j+pefFNm8rohqYnJnzk5OURFRWFnZ0e/fv0qfP+FCxdISUkh\nNjaW7Oxsli5dipWVFQqFQuO64lNl3bp1Y//+/axevZp58+bRtWtXOnfuzKVLl4iKilJfZ2dnh7u7\nuzpI00bRkSgV2mzQdl1xVMFDeWXF/dGGNhu01VWcqvCnbdu2XL58WaOuuXPnkpWVxapVq7C3t+fW\nrVscPXqUp59+Wqt/xW338/Nj2LBh1KlTh27dutGsWbMKC+gmJSVx5swZ3N3d6dTJ+FMF+mCKyetZ\nWVnUrVsXgEmTJjF79mw+/fRTdu/ezcKFC2nZsmWJqUBT//z69vB1dl28p9O1ppAobShE8rrxcbGz\n4ocxbdUjVub0Y7JKktdV7Nu3j9dff52CggKmTZvGvHnzNM5v3LiRhQsXIkkSjo6O/PDDDxo5OTWN\nVatWERERgaenJz/++CNNmjTh0KFDHD58mFdeeYUhQ4aoE/jPnTvHhx9+SGpqKt7e3kyfPh0bGxsm\nTpxIWloacrm8wu0nJyfz0ksvqackYmNjOXXqVIngQS6XlxlUmQq6BFrGRBVUFWXx4sXqvxUKBXPm\nzCE/P1/nOk+fPs25c+fUwVadOnV46qmnmDt3LqGhocTExHDt2jV69erFwoULAUhMTFRPJ+7du5fQ\n0FDmzJlDp06daNy4MXXr1uW9997Dy8urkh7XbqKiovjwww+xtbUlICCA7t27ExAQgL+/P15eXsyd\nO9fYJlYpNfULXBvm4ou5+AEixwp0GLFS/aIPCQnB09OTbt26lZBcOHr0KO3atcPZ2Zl9+/bx8ccf\n8/fff2vUY+hffAkJCZw8eZKUlBTatWtX5oiSJEnqoKS8/JevvvqKbdu2aSRRq0YxVKMSMpkMW1tb\nBg8ejI+PD19++aVG8PDaa6+xdOlSrSMwuoxY6ToqY6wRnvLKivujLbAyVX90qUuXESttZd26dSM/\nP18jF61t27YEBQVx7NgxTp48iUKhwNramoKCAo02VTY899xzTJgwgd69e5fqV9FVm8VlA4qSmppK\nVFQU165do3379gwcOBCZrNx92SuEKY5Y6YM5jVjVdkxxxKomU3zEypyoshGrovsFAur9AosGVr16\n9VL/3aNHD27evKm1rtzcXG7fvk1sbCyNGjWiadOmZGVl4eXlhZOTk8a1hYWF5OTkYGFhQZ06dQDl\nCM28efM4ePAgd+/eVY8gdO3aFVdXVw4ePMiRI0fIzc3l7NmzZGZm8umnn9K4cWOmT5+Oo6Mj3377\nLf369cPZ2RmAPXv2EB0dTXZ2Nm3atGHZsmVkZWVptV/1JVlYWEheXh47duzQunfi0qVLy3ustQpT\nHq2qTo4fP16iLC4ursSImSRJpQaFGzduxNbWll9//ZX09HT8/f0JDg5WL3qIjY1l8+bN/PTTTwwd\nOpSgoCB2795NWFiYOrBr0KABM2fORC6X8+KLL6oDRTs7O/r27cuECRMYPXo0oPw3l5eXh5WVFXZ2\ndiXsuXLlCjk5OTg7OxMbG6uuw9HRsVYr7psiw3KUaQSbkhzNZoSkJk+hFcVU/FC9I7sd/PWuw5ym\nAvWl3MBKl/0Ci/Ljjz8ydOhQrecmT57MgQMHAGUOip2dHTExMTRs2JDGjRvTpUsXXFxciIiI4MyZ\nMxQUFNCwYUOOHDlCnTp1yMnJYd26dSVGDFJTU5k1axZnz5597NijX+offfSRuiwnJ4fJkyfz5ptv\nsmzZMjp16lRiBKHoKjeBwBRZu3at+u9du3Zx7do1Vq9ejbe3Nx4eHoSGKn+J79mzh/3796t/EKgC\nO5lMRkhICM8884xGvbm5uYSEhNCsWTOCg4NRKBT89ttvvP3228hkMhwcHOjTpw/BwcFERUURGRlJ\ndnY2Dx8+5PXXX+ebb75Rj6zNnj0bKysrnn766Wp6KoLyePxlaRob/gpMj8oEVILHlBtYVeRXZ3h4\nOGvXruXw4cNaz6uCKoAzZ86og6OUlBRSUlI0clJU3L9/n1atWjFkyBD27t2rtd7r169XaKXa119/\nDWgfQRAYHlPPsarpqFaF/vvvv1y8eFHn+7Zu3aq1fO3atezevZtGjRpx5swZQDlK+/DhQ/bv38/+\n/fvV16o+H7755huNOr799lsAEViZIKYwMmIozMUXc/EDRI4V6BBY6bJfICgDpenTp7Nv3z7q1atX\nbsPavmjL+vItLagqDW2BliG/3IvXVVF/Kkp1+6PvNbpibv5Udf9Xtz+pqamkpKQY1QaBQCCoiZQb\nWHXt2pW4uDiuXr2Kh4cHW7ZsYfPmzRrXXL9+nTFjxrBhwwad94DTNophyJwMbcnLhqxflwTtmuxP\nadfog7Z6a7I/utZVG/0Ro5P68+ChnIfyiiuhW8osyNHhPpFjZbqYih8ix8owlBtY6bJf4KeffsqD\nBw+YOXMmoFx5d+zYsaq1XCAQCMyIpIw8Xt8VV2X1ixwrQXmIHCvDoJOOVXn7Ba5Zs4Y1a9YY1jKB\n2SBGMQQC08EURkYMhbn4Yi5+gMixAjCsaI1AIBAIBAJBLUbsFSiocsRolUBgfESOleliKn7ok2NV\nIEkUFkJKllJXMuboYXr06qPTvVYyC1wdzG/TehFYCQQCAfDGG29w4sQJunTpUkI+whxQfVnm3N5m\nEl/ihiDndrxZ+GIqfuiTY5WZV8DkrRdQLW25fSgUj5vlKwMAvBnQjEBv1wq3aeqUG1iVt08gwJw5\nc9i7dy8ODg6sW7eOzp07V4mxgpqJyLESmDr//PMP2dnZREZG8sorrxAbG0vXrl2NbVaVUPAw29gm\nGAxz8aWm+yEvePz5npeTRX6Bbp/3F1OycbHTb8TKq54tria6jU6ZgVVBQQGzZs3S2CdwxIgRGtvZ\n7Nmzh/j4eOLi4oiJiWHmzJkl9gkUCAQCUyYmJobBgwcDEBQUxNGjR/UOrFKzdd+suygysQWQoJax\n/Xwq28+n6nXvuv+0M7A1hqPMwEqXfQJ37tzJCy+8ACj3CUxLS+POnTu4u7tXndWCGoUYrRKYOmlp\nabRs2RIAZ2dnzp8/r3ddPx6/zcWUnArfJy8opK5N1W2p1T8tAoAf0u9UaTvVSWElfDGlZ1AZBlaY\n2wAAIABJREFUPwyJ6h2JcOmvdx2m4osxKTOw0mWfQG3X3Lx5UwRWAoGgxuDs7ExGRgYA6enpuLi4\naJzPysrin3/+0amuQU7K/0wP5TJ45XJ4hXFNMRRfvE1FffkgJOTRXyb0DPTwo2p49I5UxpZq8iU5\n/jzJVdxGVlaWXveVGVjpquSsu+L44+u0DWIU2yYQAIWW/il+r7ZtArXdp61+fW0o3qap+qNrXbps\ntaitPW1lugxQmao/huxrU/BHW5kh/Sn/3Q0teZMJ0qtXL1auXMkzzzxDaGgoU6ZM0Tg/cuRII1km\nEAhqGmUGVrrsE1j8mps3b+Lp6VlKjZOB5o/+dgE6Af0fHUc8+r84FsfiuOYeq/6++ujvSdQEOnfu\njJ2dHQEBAXTu3NlsE9cFAkHVYyGVkQCjUCho27YtoaGheHh40L17dzZv3lwief27775jz549/P33\n37z++utak9dDQ0Pp0qVL1Xhh4tT2vZNqs/+12XdQrrYbOHCgsc0QCASCaqNM5fWi+wS2a9eO8ePH\nq/cJVO0VOHToUFq2bEmrVq2YMWMGy5cvrxbDaxJnz541tglGpTb7X5t9r2kkJSXRpUsX7O3tKSws\nRC6X06tXLxwdHUlISFBft3HjRvr06cPw4cPJzMw0osWlU5YvV65cUV/Xtm1bAgMDCQwM5OLFi0a0\nuHSK+5KYmEhAQAD9+vXjueeeU2/mXhP7pTRfTL1fivuRmppKnz596N+/P+PGjUMulwM1s09K86Ui\nfVLuljZDhgzh8uXLxMfH83//93+Acp/AonsFfvfdd8THx3P69OlaOypVFunp6cY2wajUZv9rs+81\nDVdXV8LCwujZsyeg3Ex+x44djBs3Tp1HKpfLWblyJVFRUUyaNEn9A9PUKMuXojRs2JDw8HDCw8M1\nZiJMieK+1KtXj7/++otDhw7RokUL9uzZU2P7RZsvYPr9UtwPV1dXDh8+TEREBL6+vuzevbvG9ok2\nX6BifSL2ChQIBALA1ta2xGrAhg0bahzHxcXRsWNHZDKZWu/KFNHFF4D79+/Tr18/Xn75ZfLy8qrL\nvApR3BcXFxccHR0BZcBoZWVFfHx8jeyXor5YWVlhZaVMezb1finuh0z2OJTIysqifv36NbZPtPkC\nFesTEVhVA9evXze2CUalNvtfm303R9LT03FyUmopODk5kZaWZmSLKsfhw4c5dOgQXl5erFq1ytjm\nVIjbt29z8OBBBg8ezIMHD2p0v9y+fZuQkBC1SG1N7Jdjx47RrVs3Tp48SZ8+fWp0nxT3BSrWJ9W6\nV6CuOjDmxrRp02qt71C7/a/NvpsTKgmZonpXGRkZJUaFagJF5XBU9o8ePZolS5YYy6QKk5eXx+TJ\nk1mzZg0ymQwXF5ca2y/FfYGa2S/du3fn+PHjLF68mLVr19KnT58a2yfFfZk+fXqF+qTaAiuxMkgg\nENQUii+WVh23bt2ac+fOUVhYSEhICL169TKGeRWiNF/kcjmFhYXY2toSHR1Nq1atjGFehVDZ/tJL\nL/Hqq6/i4+MD1Ox+Ke5LTesXSZKQy+VYWyv3/HN0dCQ/P582bdrUyD7R5kuF+0QSCAQCgSSXy6WB\nAwdK9erVk4KCgqSYmBjpP//5j+Th4SH16dNH2rlzpyRJkrR+/Xqpd+/e0rBhw6SMjAwjW60dXXy5\nc+eO1KVLFykgIEAaNWqUlJWVZWyztVLcl0OHDkmOjo5S//79pf79+0vbt2+XJKlm9os2X2pCv2h7\nv/r16yf1799fGjlypNrmmtgn2nxJTk6uUJ+UqWMlEAgEAoFAINAdgyevb926lfbt22NpaVkit+SL\nL76gdevW+Pj4cODAAXX5iRMn6NixI61bt+a1114ztElG4+OPP6ZJkyZ07tyZzp07s3fvXvW50p6F\nObFv3z58fHxo3bo1X375pbHNqRaaN2+Or68vnTt3pnv37oByNcmgQYNo06YNgwcPrlFJnGUxdepU\n3N3d6dixo7qsLF9rwzsvEAgEBp8KvHjxonT58mWpf//+0okTJ9Tl58+fl/z8/KT8/HwpMTFR8vb2\nlgoLCyVJkqRu3bpJMTExkiRJ0pAhQ6S9e/ca2iyj8PHHH0tff/11iXJtz6KgoMAIFlYdCoVC8vb2\nlhITE6X8/HzJz89PunDhgrHNqnKaN28u3bt3T6Ps7bfflr788ktJkiRpwYIF0rx584xhmsGJjIyU\n/vnnH6lDhw7qstJ8rQ3vvEAgEEiSJBl8xMrHx4c2bdqUKN+xYwcTJkzA2tqa5s2b06pVK2JiYkhK\nSiIzM1P96/75559n+/bthjbLaEhaZlq1PYtjx44Zwbqq49ixY7Rq1YrmzZtjbW3Ns88+y44dO4xt\nVrVQvM937tzJCy+8AMALL7xgNu+3v78/9erV0ygrzdfa8M4LBAIBVKOO1e3btzU2cG7SpAm3bt0q\nUe7p6cmtW7eqy6wq59tvv8XPz48XX3xRPS1S2rMwJ27dukXTpk3Vx+boozYsLCwICgqia9eurF69\nGoA7d+7g7u4OgLu7O3fu3DGmiVVKab7WhndeIBAIQE+5hUGDBpGcnFyi/PPPP2f48OGVNqomUdqz\n+Oyzz5g5cyYfffQRAB9++CFvvvkmP/74o9Z6imrLmAPm5o+uHD58mMaNG3P37l0GDRqkXkKtwsLC\notY8m/J8rS3PQSAQ1C70CqwOHjxY4Xs8PT25ceOG+vjmzZs0adIET09Pbt68qVHu6empj1lGQddn\nMW3aNHXQqe1Z1CSfdaG4jzdu3NAYsTBXGjduDECDBg0YPXo0x44dw93dneTkZBo1akRSUpLWrUXM\nhdJ8rQ3vvEAgEIAOU4ExMTH06dMHf39/5s6di0Kh0HnH96K5JiNGjODXX38lPz+fxMRE4uLi6N69\nO40aNcLJyYmYmBgkSWL9+vWMGjWqClytfpKSktR///nnn+rVU6U9C3Oia9euxMXFcfXqVfLz89my\nZQsjRowwtllVSk5Ojvrdz87O5sCBA3Ts2JERI0bw888/A/Dzzz+bzfutjdJ8rQ3vvEAgEADlrwpM\nTk6W8vLyJEmSpOeee046e/asdOfOHWny5MlSfHy8JEmSlJ+fL/n7+0sFBQXSm2++KTk7O0t2dnaS\nu7u7FBwcrK7rs88+k7y9vaW2bdtK+/btU5fHxsZKHTp0kLy9vaXZs2cbMjnfqEyaNEnq2LGj5Ovr\nK40cOVJKTk5WnyvtWZgTe/bskdq0aSN5e3tLn3/+ubHNqXISEhIkPz8/yc/PT2rfvr3a53v37kkD\nBw6UWrduLQ0aNEh68OCBkS01DM8++6zUuHFjydraWmrSpIm0du3aMn2tDe+8QCAQVEggdMqUKcyb\nNw8fHx+mTJnCBx98gLe3NxcuXOD777/n+++/5/79+0yfPp3ff/+9KuNBgUAgEAgEApND51WBZ86c\n4e7duyWSccH8dnwXCAQCgUAg0Aedktfv37/P7Nmz2bp1q0a5Oe34LhAIBAKBQFBZyg2sFAoFEydO\n5KuvviqxmkmqwI7vmzZtUuvbCASC2kFWVhYjR440thkCgUBQbZQbWG3dupXY2FjeeecdQLnf15Il\nS4iOjiYuLo558+YxfPhwpk+fjr+/P66urmzatKlEPe7u7nTp0sXwHhiBBQsW8O677xrbjEpjLn6A\n8MVUKb5fqEAgEJg75QZWEyZMYMKECRplW7ZsKXHdxIkTmThxouEsEwgEAoFAIKhhVFjHCmDRokX4\n+/szceJEFAoFAB988AF9+/YlICCA+Pj4qrXayFy/ft3YJhgEc/EDhC+C0vnll18ICgpiwIAB3L59\nW+vnlzYdPoFAINCHcgOr5s2bEx4eTlRUFCkpKURGRhIREUFUVBS+vr5s376d9PR0/v77b6Kjo1mw\nYAHLly+vDtuNhkros6ZjLn6A8EWgnVu3bhEZGUlISAhhYWFYWVmV+PySy+WsXLmSqKgoJk2axMqV\nK41ttkAgqMGUG1i5u7tjY2MDgLW1NefPn6d///4ABAUFcfToUWxtbQEoLCzkwYMHuLm5GdxQSZKo\ngORWlTJz5kxjm2AQzMUPEL4ItLN//34KCgoICgpizpw5xMbGlvj8io+Pp2PHjshkMnWZQCAQ6IvO\newWqdKxcXFyQyZTxmEqzys7Ojt69e9O2bVsKCws5fPiwQY2UJInZO/5FZgHLRrY1aN0CgcB8uXPn\nDnK5nJCQEN59912tmntpaWlCh08gEBgMnQRCVTpWa9eu1apZdfXqVc6cOUNcXBy//fYb77//vkGN\nLJTg39QcLt3NMWi9+hIdHW1sEwyCufgBwheBdlxcXAgICABgwIABJCYmlvj8Ejp8AoHAkFRYx6pr\n164sX76ct99+W61ZlZmZqf7FV79+fdLT07XW9corr9CsWTNAKSrasWNH+vbtCzz+MintOOPKKQAk\nqRMWFhblXi+Oyz8+e/asSdlTmeOzZ8+alD219Vj1tyoBf9q0aRiT3r17s3r1agBOnjxJ06ZN2bJl\ni8bnV5s2bYQOn0AgKIG+Onzl7hW4efNmXnvtNdq3bw8odawiIyPZtWsXXl5erFu3DisrK2bMmMHF\nixdRKBQsW7aMrl27atQTGhqqt45VQaHEkLXKwGrfi52QPVJ8FwgEps0///zDwIEDjWrD22+/TWxs\nLA0aNGDjxo0sWbKkxOfXhg0b+OGHH9Q6fI6Ojhp1VObzSx+MoWVW3W0auz1XV1dAOSNTHe1VNeKd\nMTz6fn7ppWPVs2dPtWCoiupaSSNJgIirBAKBjixatEjj+J133inx+SV0+AQCgaHQeRNmY2IaawEf\nYy45MObiBwhfBOaFMbTMSmtz2bJlLFu2rNraqypqU3tV1WdltVkd1BSNv3JHrGJiYpg7dy4ymYxu\n3bqxePFiFi1axM6dOzWG0k+ePMm8efNQKBS89dZbDB06tEoMNrUgSyAQCAyNMbTMSmtzzpw51dpe\nVVGb2quqPiurTXNsT1/KzbG6c+cO9erVw8bGhokTJ/LSSy/x5Zdf8tdff7Fw4UJatmzJuHHjGDt2\nLBs2bMDe3l5rPaGhoRzLb8jtjDw+GdQSiwrkSckLCnn6p9MA/DXFD2vLGjHQJtCRM0lZfBV5jTf9\nm+Hn4Vj+DYIagynkWBmC6s6xElQ9VZ1jJaj56Pv5ZRCB0MTERHJzcxk3bhyjR48mJSVFa11/nLvL\n39czuJGWVyEjpWJ/Z+cXkJxZsToEpsv/7Y0nOTOfd/aY91ZIAoFAIDB/dB76KSoQWlxM786dO/z7\n77/8/vvvzJgxg88++6zMugoqo6Auwdj1Z3h+ywXuZcv1r6cSmEsOjKn4IS9Uvg+VmeY1FV8MgTn5\nItAPY7wDpbVZVfk61e1jbWqvunKszP2Z6otOyusqgdCtW7cSGxvLzZs3AU2BvW7dumFnZ0dgYCCL\nFy/WWk/Cli+xrdeIFTfcaN6ofrk6VlcfPOQfvHi5V5PHOlb4USgpda3+3J/CtDFPAbB48x4irtxn\n7Rv/wa2Ojdb6MnIV2Db3pX/Lehw9crjEeV2OfTp3p7BQ0jhfUCgRFR2FlUxW6v17QiJwsJHR/5FY\nYXXpCvXu04f/2xtP7tUzPOPrrj7/0/YDrNwdxffNfXmyiZPRdZBU/Qud9bpf6FiZxrHqb1PRsRJU\nnurK1xEYDtFnxqXcHCuFQsGIESP45JNP6NatGykpKUydOpXdu3erc6xGjRpFcHAwBw4c4Pjx4/z0\n00+sWLFCo57Q0FDe/UeZV/XD6LY0cbZj48lkfBo60NvrsdJxoSSx/OhNfBvV5X9hVwFwr2vDnax8\nAHZO9mPEOmW+1dv9mmEls8CvviWDP/oJV99+PNXGlTcDvLT68t9N50jNkfNSD0/GdWxY5oM5evQo\nc+fOJS0tjYsXLwLwz60M3t17hd5ezgxySKJRo0Z4e3vzwpbzpObI2fGCH1aykrlj19NymbbtIi1d\n7Vgx5oky2zU0t9JzmbJVaf+BaZ3V5YPXnFT/XbTcGJRlS/TVNO5k5jO2nP4SmCYix0pgqogcK0F5\nVJmOlWqUSqX78sUXXxAQEIC/vz9eXl7MnTsXKysrpk+fTv/+/bG0tGTdunVl1jn/YAIpWY+n8dY+\n8wTr/0lmgHc9CiXYeSGVnRdS1ecz8xTqv4vGgYsOKX8Vd3PO5cHpCFx9+6EoLD1OTM2RI0kSp25n\nlhtYtW/fnrCwMIYNG6Yu23f5HgBHrqVjlxpFly5d8Pb2JilTGfSlPZRT38G6RGL+8RvK7TIS7ueS\nnV9AHRvLMts2LGUvEtASB5oUn4YkAtCzmROeznZGtkYgEAgEgrIxmEDo+PHjGT9+vE6NFg2qAKZu\nvUihPI8fP32TRpbZ3MhU0Hb6IrJvXObmnlVQWIBzu9406vcfvl60kMSwUyhyMijIz6XNiwv4c/Mv\nZCac4fLKN3k4ag5PKuJZsmQJBQUFTJ8+nbFjx/Lqq69y7VoOeXdv0mzSLJ5a/Ap2dna0atWK6fM+\npY6NJU1dHn9xq/LItJF2+Ti/HvyV3bt3s337djKdu5Mc+Ruvhrky4ukh3L9/n4MHD5KZmcn8+fOh\nfjtyU29x7Y8ldPvJgnEDezP/40949fPlXDq0CztLeP/99/H399fp+VWEsgKnjCuncG1t3NGq4txK\nz8PT2bZEeba8sMz7oqOj1dNSNR1z8kWgH8Z4B0prU5WrY+jpper2sTa1V1V9Vlab1UFN+Ww0mI4V\nKIfNunbtikKhQCarmCTC3Zi/cGjqw/wP56pHom7uW4P3859gZV+XuJ8+oP6TgwALbBs0ocXAidzc\ns5qMuFga9BpJ3r0kvCfNR5Ikvv76fXbt2oWFhQXDhg1j9OjRANTxbIPXqDmk/hvG+PHjmTp1Khm5\ncsZtOAeUPyWmGomSWVkzYcIEunTpwkPPTvyzfjcFuTksX7OD+g7WPHz4kNmzZ3P37l2mTp3K5M9/\n5OaeVTR9egYOnq355MVObD0Wz76/dtLmxQX8PqENEyZMqJLAqjyVeksLSMnK58q9h/Rs5lQhGYyq\nYMrWC2pJjcLKLHLQQqEkkZotp2FdG4PWKxCYMyJfp+Yh+sy4lBv9NG/enPDwcKKiokhJSSEyMpKI\niAiioqLw9fVl+/bt6muXL1/Ok08+qZchuXdv4NjSl6v3c9VlD5MSuPLzR1xeMZf89Lvkp90FwMGj\nFQA2Lg1QPMzSqEeRncbZS/8yZswYRo8eTUZGBqmpymnFOk3bAtCs+0CuXbvGjBkz2LxlS4VtdfLu\nBMDV+zl8d+QmFlhQp0kbdQyzZcsWhg0bxosvvsiN28msjLlFfvpdHDxbA8oA7XJ8Arl3rnF5xVwm\nTJjAvXv3dG4/I1fBnkup5OQXlHutrEhkFRKnmUvg5N0JmcyCib+eZ/7BBI7fzNDZhqpEXqAMqA5f\n1b6ZtzZ0+RXz1aFrTPz1PJGJD/S2rTqoCb/IBFWLMd6B6m5TtFez2zNGmzXls7HcEauiO7pr07Ha\nuHEj48aN4/z58zRt2pQrV65QTj68VuwaNiMz4Qxbz7ZBKizEQibDobE33pPmY2lXR11GSqLmjZKE\nhcwSSVJOFVk5OCNzbcLvv/+OtbU1CoVCPaKmGr5JySngctNR2Da34NQPM3GethxQCpFefZDLkqjr\nvNu/Oc3q2ZGvKCRXUUhqdr6GX9bW1qTnKHOrJCSweBzCrF69mujoaO7evcuTAUE0BGycG5JzKw4H\nz9ZIkkS9xk2xb9SC1lM/Z+e0zigUj/PIyuPjkATOJWdzNjmLef2bl3lt0YHDhYeuEdTaVeO8ZZER\nqst3c+je1FlnO4rzUF7A39fT6dHUGYdK5JGpTEp7+HjK2BDjaCHxyoBq14VUAlrUM0CN1U9BocQ3\n0dfp1tSpxvogEAgE5oxBdKwAli5dyqxZswD0mk5q0P1psm9c5NKKufz74zwAPIdMI/6Xj7m88k3i\nfnqPQnk+F1Ky0fiatbDA2qk+hfI8rqz/hLz7STQeOJExY8YwcuRIpk57iYgrDzQ2b75yPJJLP7zO\n6e9eo0G7Huqq/jx3l1e3Xyb+3kOe+2E/g4aO4FJcPG37DObZpbuISFD6mnHlFP7+/uzY+CPXd36P\nRbGv/Z49exIcHMzSpUuxtHUAoMnTL3Fj9wour5jL/Pnz2ZmQh2unQC798AZP9n+KAZNmlxmQHr+R\nwaqYWxQUSpxLzlaXaWPbmTsMXnOS2Tsuc+Xew1LrzLhyiofyx6NekkSlpt+WRF3ni/BrfBVZuf2c\n9DGhIvomMiNPd5ZHWb6EX3nA/n/v87/Qq6TnKspcrFGUfEUhPx2/TXxqjqHMFFQhQsfK8NSm9oSO\nlXExiI5VfHw8Tk5O1K9fH6DUAEGlYwVgaV8HB49W6mm1rOsXaNBzuPpYpWvU9qVF6uOs6xeQdRiD\ny6NjO/fm6usb9X8WADs3T+zcPLlracX/BTbn++sufB5+lW5PDkIe/wB7d3D1649VXaXEQ36R9hZf\nOaWuT555nw5DnsdizCfq8xlFzodevsOzL73GjgylPxISfx89zJCB/fn666+Jjo4mKSOP823+Q468\nkPy0FBoHTcLJuxOvjG/Hgc83Ye3cAJ+ZS9T1/7EvjLFDlEs7i+sEzV7+OwBt3Eapr1dYywDfEtev\nOnabjCunOH4FLt/VfJ4qnaiMK6fIuR2v8bwvSPV4Pq4VbRvUIdD2FjfScrHx8mVMhwYcPly27te6\n7QfYGXMLJ+9ORF9N01vHysm7E9Kj85eupQMeAJyIOcIdZ7tK6VhlXInDybsTF1Ky+XnHAbzrO2i9\nPjNPwZ6QCDzLaM9YxxkubdTP66lPTtGxa09Wj32i3Ps/W7+b/f/eY7N3Jw5M62xw+0IjIjmTlEWH\nRnU4EXNU6FiZESJfp+Yh+sy4GETHytLSkm+++QYHBweOHTvG2LFjWbVqlUY9RXWsqouWrvYk3FeO\n2LR2sycuVfvozZ3oP0g79zgStm/ckmYjZ5Vb/5C29dl7+XFu1LN+7gxv50aDOjacT87ijd1xWu/r\n29yF6KtpJcpXjfUhM6+A/ZfvMbNXEw1ZBpXW06u9mvD90Zvq8h0v+GJvrTntVlQXqjjbJnbkj3Mp\nbDp1p0zfDkzrrK7nw4Et8G/hUuq1KVn5TPz1fIn7daW4vb9P6oijrRW7L6ay7PANAL4f1ZbWbg7c\ny5ZzNzufzLwC2jZwwMlOp98GWtvp39KFt/t5ldh7cswvZ8jKL+C7UW1p4+agc/2G5KG8gOM3MujW\n1Emjf7edTWFVzC2Na3V51l9GXCX00VRoVeiWLQi/StiVB3Rt4sjnwa3U5ULHSmCqCB0rQXkYXcdK\ntfJuwIABJcRBjYUqqAKILyWoAnDvOwb3vmMqXP/d7HyN419P3+HX03cY9oQbDtalz7KeScrUWp6v\nkHjzUTBWx9aSmT2blLim+CzWyJ/PMLVbY571a6STzd8duaGe0gSlHIO22aQD/z4OGJMz88jIVaiD\nmL2X73HkahofDmyBjZWMlKz8Evcn3HvIQ3kBjnZWNHW2rdD0sLZQ/9298fw+yZcJm8+pyxo52vDL\n+Pbq46sPHvJ15HWmdvOg86PNnPMVhfx1KZVeXiVzxyIS0ujs6cSQtvU1yrMeLQo4m5SlDqwKJYkP\n9l+heT17XurhqbMv+vLRgQROJykXZnwR7M2Gk8m80beZ3lO1Rfv4Xo5Sb82QHL6mXGgQe1P7uy2o\nGJs3byYwMJBGjXT7d11RHjx4wAsvvMCpU6eYMGECX375pdbr/Pz8iIiIoF49zXy+ffv2cfnyZV57\n7TWt9507d46kpCQGDRpkcNsFAlOn3ByrCRMmkJKSQnh4OOHh4WoNq6ioKDZs2FAkMVxJWFhYhaUW\nqgNDLtx/PK2mnd0XU/nrUumr/DLytK/mm7Xjsvrvu1m674O49niSztceK5KXlXHlVKn5RkXzpLac\nvsO4DWfZe0m5unJJ1HVibmSw/fxdHuTISwR7AC//eYk3dscxbdtF9lzWfcUjwC//KP3JL3isXZWZ\nV0Bcsfyg5EfCrLmKQj7+aSeztl/m8t0c5u2JJytPQVaegk2nkvnh71s8v+WC1rbu55T+nIsO5ibe\nf0jszUy2ndW+wbihkCSJJZv3qIMqgP/bd4Xzd7J56Y+LnE3KKnHPYS2jn9rqVTH/QIJhjAWy8hTK\nug0sjVHbWbFiBcnJyRW6p6Cg/FXCKmxtbXnvvff49NNP1WXa8lcsLCxYuXJliXyd4ODgUoMqUObk\nhoSElGmDuefniByrmt+evpQbAcXExNCnTx/8/f2ZO3cuAIsWLcLf35+JEyeiUCjIzMwkKCiIfv36\nMXz4cLKySn741zaydZBCKAttU4UA3x25qbX8g/1XGLzmJFfulZ2cnFNMaNNSB+l1VSC45vhtjfI1\nx28zftM5Pn+09VBpLI2+UWYAU5ydF1JJyswrMeX16vbLWq8fse40+/69R37B4y/3MevPMmb92TID\nXFCORCVl5mntr6JPqvgChari+M0MtpzRPk1bKEGMlgULn4QkaixC0EbRsOff1Bweygv45UQS1x/k\nlnpPeZxJymLM+rO8uO0ieQUisAJISEhg9OjRBAQEEBgYyLVr1wDlF11QUBD+/v4sWLAAgOvXr9Oj\nRw9ef/11evfuzdixY8nNzWXHjh3Ex8czY8YM+vfvT25uLqdOnWL48OEMGDCAcePGceeO8h0ZPnw4\n7733HgMHDmTFihVs376dPn36EBAQoLFrRHEcHBzo2bMnNja6abr9+eef9O3bl7g45Yj6pk2bmDdP\nucioaJvDhw9HLpfzxRdf8Oeff9KvXz8NSR5B9TBnzhyRZ2VEDKJjZWNjw8aNGzl06BAjR44sd0ub\nmo4q4Tvxvv5fSoZGNRI180/twYc2nLw74VaBKaHSBiXuZpcfNJ0uNv2Zkavg6LV0CkpZ1fbClgta\npyiLk56rlKlQ9Ulp50sjJSufF7Zc4JkNZ0ueLNK+ZTn/UlQBGihH2nZeuEvyo+OKcP3CHoA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9KfS0X4eFCLEmXaWq4qvSQ7K8NniZYXRJiT9pPKl/G+Denb3IXnOpdcjNHUxc7kcvYEhkPoWBme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\n/tRW7o3c3FwKCgqws7Ojfv361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"text": [ "" ] } ], "prompt_number": 68 }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are really two figures here, one for each unknown in the `centers` variable. In each figure, the subfigure in the top left corner is the trace of the variable. This is useful for inspecting that possible \"meandering\" property that is a result of non-convergence." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The largest plot on the right-hand side is the histograms of the samples, plus a few extra features. The thickest vertical line represents the posterior mean, which is a good summary of posterior distribution. The interval between the two dashed vertical lines in each the posterior distributions represent the *95% credible interval*, not to be confused with a *95% confidence interval*. I won't get into the latter, but the former can be interpreted as \"there is a 95% chance the parameter of interest lies in this interval\". (Changing default parameters in the call to `mcplot` provides alternatives to 95%.) When communicating your results to others, it is incredibly important to state this interval. One of our purposes for studying Bayesian methods is to have a clear understanding of our uncertainty in unknowns. Combined with the posterior mean, the 95% credible interval provides a reliable interval to communicate the likely location of the unknown (provided by the mean) *and* the uncertainty (represented by the width of the interval)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plots titled `center_0_acorr` and `center_1_acorr` are the generated autocorrelation plots. They look different than the ones I have displayed above, but the only difference is that 0-lag is centered in the middle of the figure, whereas I have 0 centered to the left. \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Useful tips for MCMC\n", "\n", "Bayesian inference would be the *de facto* method if it weren't for MCMC's computational difficulties. In fact, MCMC is what turns most users off practical Bayesian inference. Below I present some good heuristics to help convergence and speed up the MCMC engine:\n", "\n", "### Intelligent starting values\n", "\n", "It would be great to start the MCMC algorithm off near the posterior distribution, so that it will take little time to start sampling correctly. We can aid the algorithm by telling where we *think* the posterior distribution will be by specifying the `value` parameter in the `Stochastic` variable creation. In many cases we can produce a reasonable guess for the parameter. For example, if we have data from a Normal distribution, and we wish to estimate the $\\mu$ parameter, then a good starting value would be the *mean* of the data. \n", "\n", " mu = pm.Uniform( \"mu\", 0, 100, value = data.mean() )\n", "\n", "For most parameters in models, there is a frequentist estimate of it. These estimates are a good starting value for our MCMC algorithms. Of course, this is not always possible for some variables, but including as many appropriate initial values is always a good idea. Even if your guesses are wrong, the MCMC will still converge to the proper distribution, so there is little to lose.\n", "\n", "This is what using `MAP` tries to do, by giving good initial values to the MCMC. So why bother specifying user-defined values? Well, even giving `MAP` good values will help it find the maximum a-posterior. \n", "\n", "Also important, *bad initial values* are a source of major bugs in PyMC and can hurt convergence.\n", "\n", "#### Priors\n", "\n", "If the priors are poorly chosen, the MCMC algorithm may not converge, or atleast have difficulty converging. Consider what may happen if the prior chosen does not even contain the true parameter: the prior assigns 0 probability to the unknown, hence the posterior will assign 0 probability as well. This can cause pathological results.\n", "\n", "For this reason, it is best to carefully choose the priors. Often, lack of covergence or evidence of samples crowding to boundaries implies something is wrong with the chosen priors (see *Folk Theorem of Statistical Computing* below). \n", "\n", "#### Covariance matrices and eliminating parameters\n", "\n", "### The Folk Theorem of Statistical Computing\n", "\n", "> *If you are having computational problems, probably your model is wrong.*\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "\n", "PyMC provides a very strong backend to performing Bayesian inference, mostly because it has abstracted the inner mechanics of MCMC from the user. Despite this, some care must be applied to ensure your inference is not being biased by the iterative nature of MCMC. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### References\n", "\n", "1. Flaxman, Abraham. \"Powell's Methods for Maximization in PyMC.\" Healthy Algorithms. N.p., 9 02 2012. Web. 28 Feb 2013. ." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.core.display import HTML\n", "\n", "\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": 1, "text": [ "" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }