{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 3\n", "\n", "\n", "`Original content created by Cam Davidson-Pilon`\n", "\n", "`Ported to Python 3 and PyMC3 by Max Margenot (@clean_utensils) and Thomas Wiecki (@twiecki) at Quantopian (@quantopian)`\n", "____\n", "\n", "\n", "## Opening the black box of MCMC" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The previous two chapters hid the inner-mechanics of PyMC3, 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", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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1lixZwoUXXsiTTz7JU089FVEsjhkzhnfffZeuXbsGzpXfS2232/n6669p06YN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\nR45k06ZNT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%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\");\n" ] }, { "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", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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5e+21F59++inr169n27ZtAIwePZpIJMJ5553H/Pnz+eGHH1iwYAF33XUXn376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\nUJfu3Wuybdt5li//O+J4lSopyMpqzo03akotpozGb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zzC3z1CQUEOXKixoXGH9C60LkEe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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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" ] }, { "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", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "observed (2-dimensional,sample size = 1): [[0 2]]\n" ] } ], "source": [ "# 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" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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EEMWT6yOjgT7QsUj4qu9eFgn57AYu+ixSsbKyAq0Uc37RmUzKyJSy5ffkLEVT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NRZU4ksaywLMrb3jGuGROuFX3NHW8D/TBkQa/d7wumRmkoZgCXtHMK0iRJQwr6ZyYKPBw/w79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\nmSRHhiT7zJE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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" ] }, { "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 PyMC3 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 PyMC3 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", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 115.85679142 152.26153716 178.87449059 162.93500815 107.02820697\n", " 105.19141146 118.38288501 125.3769803 102.88054011 206.71326136] ...\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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" ] }, { "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 $\\text{N}_0$ and $\\text{N}_1$ (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 $\\text{N}_0$ or $\\text{N}_1$, and we assume that the data point is assigned to $\\text{N}_0$ with probability $p$.\n", "\n", "\n", "An appropriate way to assign data points to clusters is to use a PyMC3 `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 form a uniform variable on $(0, 1)$. We call call this $p_1$, so the probability of belonging to cluster 2 is therefore $p_2 = 1 - p_1$.\n", "\n", "Unfortunately, we can't we just give `[p1, p2]` to our `Categorical` variable. PyMC3 uses Theano under the hood to construct the models so we need to use `theano.tensor.stack()` to combine $p_1$ and $p_2$ into a vector that it can understand. We pass this vector into the `Categorical` variable as well as the `testval` parameter to give our variable an idea of where to start from." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Applied interval-transform to p and added transformed p_interval_ to model.\n", "prior assignment, with p = 0.50:\n", "[0 0 0 0 1 1 1 0 0 1]\n" ] } ], "source": [ "import pymc3 as pm\n", "import theano.tensor as T\n", "\n", "with pm.Model() as model:\n", " p1 = pm.Uniform('p', 0, 1)\n", " p2 = 1 - p1\n", " p = T.stack([p1, p2])\n", " assignment = pm.Categorical(\"assignment\", p, \n", " shape=data.shape[0],\n", " testval=np.random.randint(0, 2, data.shape[0]))\n", " \n", "print(\"prior assignment, with p = %.2f:\" % p1.tag.test_value)\n", "print(assignment.tag.test_value[:10])" ] }, { "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. We will include both standard deviations in our model using a single line of PyMC3 code:\n", "\n", " sds = pm.Uniform(\"sds\", 0, 100, shape=2)\n", "\n", "Notice that we specified `shape=2`: we are modeling both $\\sigma$s as a single PyMC3 variable. Note that this does not induce a necessary relationship between the two $\\sigma$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 these 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 $\\sigma_0 = \\sigma_1 = 10$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Applied interval-transform to sds and added transformed sds_interval_ to model.\n", "Random assignments: [0 0 0 0] ...\n", "Assigned center: [ 120. 120. 120. 120.] ...\n", "Assigned standard deviation: [ 50. 50. 50. 50.]\n" ] } ], "source": [ "with model:\n", " sds = pm.Uniform(\"sds\", 0, 100, shape=2)\n", " centers = pm.Normal(\"centers\", \n", " mu=np.array([120, 190]), \n", " sd=np.array([10, 10]), \n", " shape=2)\n", " \n", " center_i = pm.Deterministic('center_i', centers[assignment])\n", " sd_i = pm.Deterministic('sd_i', sds[assignment])\n", " \n", " # and to combine it with the observations:\n", " observations = pm.Normal(\"obs\", mu=center_i, sd=sd_i, observed=data)\n", " \n", "print(\"Random assignments: \", assignment.tag.test_value[:4], \"...\")\n", "print(\"Assigned center: \", center_i.tag.test_value[:4], \"...\")\n", "print(\"Assigned standard deviation: \", sd_i.tag.test_value[:4])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice how we continue to build the model within the context of `Model()`. This automatically adds the variables that we create to our model. As long as we work within this context we will be working with the same variables that we have already defined.\n", "\n", "Similarly, any sampling that we do within the context of `Model()` will be done only on the model whose context in which we are working. We will tell our model to explore the space that we have so far defined by defining the sampling methods, in this case `Metropolis()` for our continuous variables and `ElemwiseCategorical()` for our categorical variable. We will use these sampling methods together to explore the space by using `sample( iterations, step )`, where `iterations` is the number of steps you wish the algorithm to perform and `step` is the way in which you want to handle those steps. We use our combination of `Metropolis()` and `ElemwiseCategorical()` for the `step` and sample 25000 `iterations` below.\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-------100%-------] 25000 of 25000 in 130.7 sec. | SPS: 191.3 | ETA: 0.0" ] } ], "source": [ "with model:\n", " step1 = pm.Metropolis(vars=[p, sds, centers])\n", " step2 = pm.ElemwiseCategorical(vars=[assignment])\n", " trace = pm.sample(25000, step=[step1, step2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have stored the paths of all our variables, or \"traces\", in the `trace` variable. These paths are the routes the unknown parameters (centers, precisions, and $p$) have taken thus far. The individual path of each variable is indexed by the PyMC3 variable `name` that we gave that variable when defining it within our model. For example, `trace[\"sds\"]` will return a `numpy array` object that we can then index and slice as we would any other `numpy array` object. \n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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duJUZH+3lvpXZlNfa3LYpdy4Oj/1w1EWD+sqGY9TZHG79dz/YfoJ6u4N7vz7E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A/2YLRURGkyahBa3HgFhmyaj8aqal5mierQCp3/7z+KfQN+9+ZyZ5eNes99F0lfeINhml01HIAy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\nXWRtcALV72xO2+/mWD1+cs4iDk8sOtbkw9ep98h9Ll3zwobt7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NpCE62AUXMvohxiY42f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\nOpR5pvz4mRGT9axCmUTsJsUDoc/SWi3UPNJrpOOLNk/G9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12.5, 9)\n", "plt.subplot(311)\n", "lw = 1\n", "center_trace = trace[\"centers\"]\n", "\n", "# for pretty colors later in the book.\n", "colors = [\"#348ABD\", \"#A60628\"] 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 = trace[\"sds\"]\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 = trace[\"p\"]\n", "plt.plot(p_trace, label=\"$p$: frequency of assignment to cluster 0\",\n", " color=colors[0], lw=lw)\n", "plt.xlabel(\"Steps\")\n", "plt.ylim(0, 1)\n", "plt.legend();\n" ] }, { "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. 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 as part of the `trace` object. To continue where we left off, we pass the `trace` that we have already stored into the `sample()` function with the same step value. The values that we have already calculated will not be overwritten. This ensures that our sampling continues where it left off in the same way that it left off. \n", "\n", "We will sample the MCMC fifty thousand more times and visualize the progress below:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-------100%-------] 50000 of 50000 in 215.4 sec. | SPS: 232.2 | ETA: 0.0" ] } ], "source": [ "with model:\n", " trace = pm.sample(50000, step=[step1, step2], trace=trace)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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n+OwPsRVb8JYjz7zlUstnKywyPK/lxNxPiPz0R6/TKxWlaDtGdVuQ6OzF41Lm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\n/p/ZPmTratBeFy/I9GJFKlsyd/VwSxpX2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12.5, 4)\n", "center_trace = trace[\"centers\"][25000:]\n", "prev_center_trace = trace[\"centers\"][:25000]\n", "\n", "x = np.arange(25000)\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(25000, 75000)\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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\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", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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p6RbCbhatwNnW3gI5B7gW2Aa4I5czcJxa8cJ3rikp3SG//35DNg4cp0FwX+A4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\ndV375zcmLSEnVu3dqq5S6a0NyfYyqTllw4mmFnYea8z7OnTKsyM7Tgz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(11.0, 4)\n", "std_trace = trace[\"sds\"][25000:]\n", "prev_std_trace = trace[\"sds\"][:25000]\n", "\n", "_i = [1, 2, 3, 4]\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" ] }, { "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 `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", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Vwpg5lm92EnW5ROD2fWZv3pE1szMp6rc3aFpfQVsssN3iJ9ziI2O2sr65gLP/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QwQ72eITT8SlCIxPIWy1M2RQVrZ6ky0NNo8V3uI33eJ/T8WlOx6eQtVqYMynkrQY5q4PEoId8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\n9Vu8eaakktvWytr9u1l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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib as mpl\n", "figsize(12.5, 4.5)\n", "plt.cmap = mpl.colors.ListedColormap(colors)\n", "plt.imshow(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" ] }, { "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", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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EQf1IHjmEmKTEQHsutbtLiMtMp6GujujYWBrrGzDnSB4zjMRAx7S+soryVRup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\nW5XNe6+p4F+eqeNg2vuxMD/EvbfWjvmezndVuaEx519VkUV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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cmap = mpl.colors.LinearSegmentedColormap.from_list(\"BMH\", colors)\n", "assign_trace = 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" ] }, { "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", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6OTmRmpqa55o373vDhg1JTEwE4Pr160ycOBEfHx88PDwICQmxaMe6LMDGjRvp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\nip54OdBOv+hslBrQiuuDasuuHXqH0O0birKX3sB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26T/vvY9hf3uRGOV/SHL8L24lbvJY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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 = trace[\"p\"].mean()\n", "\n", "plt.hist(data, bins=20, histtype=\"step\", density=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" ] }, { "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", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-------100%-------] 10000 of 10000 in 0.9 sec. | SPS: 11550.9 | ETA: 0.0" ] }, { "data": { "image/png": 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AqgD4AopF7V8oivudhnSvQZly3ARgDIBnGGN/aM77lFzVBeYuNf1WKJaRUeAr4r9Bmeb9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\nxZaP0xsr/LPQ0Wbi0xbl8WeKtNjte+BF2DBiuD+RKFJEhNs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AwBZM59YKtKhh37+L7Cff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2AAAg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\nk5s0v0AVhcCyGnn67An6XFern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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pymc3 as pm\n", "\n", "with pm.Model() as model:\n", " x = pm.Normal(\"x\", mu=4, tau=10)\n", " y = pm.Deterministic(\"y\", 10 - x)\n", "\n", " trace_2 = pm.sample(10000, pm.Metropolis())\n", "\n", "plt.plot(trace_2[\"x\"])\n", "plt.plot(trace_2[\"y\"])\n", "plt.title(\"Displaying (extreme) case of dependence between unknowns\");\n" ] }, { "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", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Probability of belonging to cluster 1: 0.01062\n" ] } ], "source": [ "norm_pdf = stats.norm.pdf\n", "p_trace = trace[\"p\"][25000:]\n", "prev_p_trace = trace[\"p\"][:25000]\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" ] }, { "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. PyMC3 provides a function that will approximate, if not find, the MAP location. In the PyMC3 main namespace is the `find_MAP` function. If you call this function within the context of `Model()`, it will calculate the MAP which you can then pass to `pm.sample()` as a `start` parameter.\n", "\n", " start = pm.find_MAP()\n", " trace = pm.sample(2000, step=pm.Metropolis, start=start)\n", "\n", "The `find_MAP()` function 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 function call is the Broyden-Fletcher-Goldfarb-Shanno ([BFGS](https://en.wikipedia.org/wiki/Broyden-Fletcher-Goldfarb-Shanno_algorithm)) algorithm to find the maximum of the log-posterior. As an alternative, you can use other optimization algorithms from the `scipy.optimize` module. For example, you can use Powell's Method, a favourite of PyMC blogger [Abraham Flaxman](http://healthyalgorithms.com/) [1], by calling `find_MAP(fmin=scipy.optimize.fmin_powell)`. The default works well enough, but if convergence is slow or not guaranteed, feel free to experiment with Powell's method or the other algorithms available. \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", "#### Speaking of the burn-in period\n", "\n", "It is still a good idea to decide on a burn-in period, even if we are using `find_MAP()` prior to sampling, just to be safe. We can no longer automatically discard sample with a `burn` parameter in the `sample()` function as we could in PyMC2, but it is easy enough to simply discard the beginning section of the trace just through array slicing. As one does not know when the chain has fully converged, a good rule of thumb is to discard the first *half* of your samples, sometimes up to 90% of the samples for longer runs. To continue the clustering example from above, the new code would look something like:\n", "\n", " with pm.Model() as model:\n", " start = pm.find_MAP()\n", " \n", " step = pm.Metropolis()\n", " trace = pm.sample(100000, step=step, start=start)\n", " \n", " burned_trace = trace[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, $x_t$, 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", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0zDT0eBV9znwIncZd0HjKo55f0quID60ddnrUgyfLE3ntwcIuJ3qu9btZjzpl\nKE2UDCWVrw/iLzmbvF/dj1I41unBLksflDYSs//6GONffgAz1v0bglqtOKbTGCpqiYHlGxOJ5Jsv\nRWSn4waiiIO3P+m2gA/gXioUAEwKUSPacx57wRnymOxwdJs0qFWoqmFt1cJu6r18RAnR4UDVV+6/\nS8vOLMViDk7oCJazFCIgG+h0DXWf8BCEUpNB1xVKRYcD2Ssfxebx5+LQ6uf6FMGkI0u0Rx1gdep0\nRNk/WY68+Ea569SVcgF6KtFIP19DpqbBOyQIcUvPlD9PeZZFixXV30r5UbYOveJvrfWwWkzNN7+T\n6kaapHgkXikvLOXqUW/ZdQA13/55zNp1XS47OQ+ZOp5sO3XqBQ+/CofRDNFuR3U/y99ONJwRQ6Xf\n8VgYdEN9ypQp+LtUNtSXTYiCj1rAsHL5pgufJenYw2ZQhvr+PMWHScOGHSh5+UO3gvvVX//BlEVM\nunE5Zv3yHgIoY4xGM4wqmUikL5RGXUH6ArAlGqu17EDqsNkYrx/rUaekNtW986iLooj8R14lA4BP\nZBhS77qGOYYJSXnoUa/64mccvONpZN/4MAqffpu8rzPbyIJPAFDSZITWJP0WdGIXPXi3788jEy91\noD95v3jNe24Z4naTGe3ZBaj84meUrf1yQBYocVL/21aiVwyeNJb0h+AJozFn4ycYcfuVJARuN5pQ\nvvYr8tn+1qg7rDZkr3yUJCypNX7wH5HIfF+1P22Sj7dYkX3zY2jddYDUcHZC/w7HA1dDvfrbPxkP\nZPDkseTvcJgsbguLuULfJ75UonVH8VHGOxS58FTFzzhp2rKHvE645BzM+v19st3faxZ0h8NidQv3\n9xRZEO12NKzfTrZjlswnrzVJcWT1S2tLu8dJbgAwXi2vmun0qPvFRJLv2W40MbISGjrMDUjVSES7\nHQ6rDbrDcrWDoPGyRzPxctlgqP9zm8cewp5gnR7D3fYHjkzGsKsuJN9TT84QPaVPDxiVDEEQMOG1\nh+AdLpXgNdc14dA9z7sZkUpVNVx/W8PRamLQq/01CD1lAiLmy4unuN4/NB1dGGrmhr7X2aZp3r6P\nPOO8w4KZqmfdedVp6UvodNlAI4Y67VGPDEXYTPn53bIrm/FWV6/7DfW//Q1AMjhp+aST7sZbh43t\nf8HjWUPdhzLU6eRHDeXMomupmxubmf9peppgs4a6NBlLumEZkyeh8pXth7qfNkl11/fnKSZi6xSq\nqijhrBYxdpTfAAAgAElEQVQDAMk3r4D/8ESyTSfPavOKsffiO3DwjqdR/p9jq8ZES3yCJ45G6LQ0\nZl/td+sZe6N1Tw7UajUMhhNbytlbRFFEXdlRdOyVEsN1/Vzi2avnQwYeZ5JmoI8a18+Ix6S4IBx+\nWx6cwk+bCgDQJMbCLz4appoG2A1G6PJKEEJ5ghrWb0fWtQ8AkG6W6V+8AkD6Equ++JkcN/qRW5Fy\n59XdtokxnKucHnXZGIoNVF6GmvWos9IXY0UtMQp9YyKZJaA1iX33qJe/+xWqKY/IqIdWuS1hHTgm\nBSo/HzhMFpiq62FubGFqxypR97OclFq+9kv4RoVjxG1XoKSJTfITAeTUdmDuiFCmQsKYx25D7U+b\nUP/rFvJeyNQ0TPv0JWRd+4A047bZkXPr40i69mJo84qgyy2GvqSC0bK27DyA6Z/9i7lm6ZufoXlb\nJkY9tAqh08Yz+4xVdegoKkfEvFOg8uq+i9MPhLiLz2T2qTW+GPPY7QhPn479l98LgDUOPMFuNMOm\n62DCkF1R+NSbciKfIGDKh88j6vRZaNy0C/uvvA+AtHrumMdug6BSoeHP7SREC0h9yqlddTWoBhKH\nxYqWXazW0t5hQPEL75LtkCnjYNN2EAPQXNvAPDxdoaUv0WfOISHdlh37yT3kExGK4Ilj5M+UV0F0\nOCCoZP9DE1W/O3LhqQiZmkbuA5tOD6u247gsxa49VOg2merJM9e69yAxdnxjIpl+LggCgsaPJCs3\na3OLmepOTho37ULZ218gbukiDLv6Irfr+sVGktchk8eioXNfe3aBnBPUicNiZaQhQKdRf6QSot1O\nfhe/hBjmtw0am4KQaeOl+91qQ8136zF81WXd/u09ITocTFsCRiZ3czRIu5woyQvpRNLA0SOkz8RG\nYeLrjyDr6n8AABo3ZKDiw2+RfNMl8rkUZAWuE6cmKmE0fPYUqHy8ETl/Jkr//Ym0/++udepdeVTN\n9U1M1LSvVH35C3kdv/xsRC9OJ4tCVf/vD4x+5BZ4BQa4fY6uWhQyfTxZfdMpfaGrC3mHh8I/ZRj8\nRyTCUFYFu96A3HtfwLTP/gVrSzsKn3mbOffhx15H5IJZ3Y4RTFtKKsj95RcfDZ+IUGY/LX2hF2Fi\nPeoK0pe+eNQpw9TpIAueMBpTP16D1r05CJs5CeGzp+LvaRfBptPDWFEDbc5hpuy0OtCftNMTaZvD\namOOi794MRP9ovto0+bdxGnWvG0fUu5knXq9QeviUfeJDIMmKR7Giho4zBbkPfgyc7ypuh5BZjt0\n0KGtzT065aSi1YQ2s+T8Swz2Rbi/d5/b6ERntqOs1b1sqspuR3xF53clCAibOQnaQ0WkmIEmMRaa\nYcr3mfZgIaw6PewGI4KDg9H+uWSH6Qr6t0TjoHvU6Trqc4aHwEetwtQwNWJqJO+YKAgImC6HzEKp\nWXnrXrl8o6WpFbn3rSHbjZt2kYod2pzDRDOr0vhiGLVccFewixDVSTXU9bJGPSrQveOIooiwhlp4\nmyUDvbrdzHhfugvV+tHJq9WeFdYHgIYNGYy3O/6Sc5B4xflux6m8vRijhl7WXQmH2eKmqS18+i1U\n/+8PFDe5z4YPVOvc9Onhs6diwisPkr81Yu4pmPG/1+EbFY7Ja58ikwnj0RoUPv0War/bgI7CMreE\ns9bd2cz30VFcjqLn1qJ5+z7k/eMl5lhLcxt2nnUD9l9xL/O9KGGqb5JDzoKAuAsXKR4Xcdo04lU3\nVdeTigVOzWTVl7/g8FNvuXkKLS3t2HrKUmyZfAEKnni920S6mu/W4+gHctWFUQ+tQtTpUtg9Yt4M\nEro1VddLSYkAKr/4iRyfes91mLfrG6J71ZdW9VtovCfasvLcKrQArIY1ZMo4+MXJhmR3iUUOm435\nbNQi2cNHl2zVJCfAJyyYaKAdJgvzELU0t8lhbpUKEXNPgSAI8IsfuJWAu0Jp7YeeHvh0JaLoxXOZ\nCQjgIn/Jc/e6mWoakL3yUbTszEL+Q6+QBLn95bLh5xsrRysYeZxC1E1fWukmawOkh7WrZ80VOgxf\n+dmPx5xUaqyqJ5W6vMND4eNcXbUbmAIBClHLjsJy8prWvEefOQfJN19Ktg8//RZjoCglN7smCjdT\nspeI+ZKON3T6BKgDpCiTsaJGMTlTFEWm4kvwJNkx1R8JpZaWdqafJV5xPsLnTCdjtr2j60oldA31\n0GkTqHO611H3iQiFIAgY/9I/yXuNG3ei6stfUPjM28yCVID0PC96lh2/u9Oo0xKMIBdvOsAa6jS0\nR50t0didoS6PXcbKWmSvegzFL74Ph9UGW4delgupVMwzN/qsORjz6G2IPisdXkEBiD57HtlX9/Nm\ntFG6/YRLz6X+tp4NdX3JUXaiHB7C/G209IXuT13lGXiCaLcz9f2DOu/7EMqr7royLSDJnmJiYhAf\nH9/lvw8LzHg1S49Xs/RQB0d2e6yn/0YNT8S6Eis571s5BuR3+OGHdXtQdftzqLr9Oeg+/AEJiYkI\nNTvIe0dW3IegdqPiOWsf+jeq73wedQ+8huiJY+UE9LKqLtdS6AsDbqgLgnC2IAiHBUEoEgThge6O\nXZgqzWgNecVQdYaAmqLj0KyW5SS0/KX6q99gbmiGKIrIe+BfboaSc3Uu2mMQe/4ZHnnQfKPDia7W\n0tyGphYdbJ013kP8vKDxVjPHG6vqsHfpbTh01rVY9eLDOP3nddBUVaHVKMtz6OongS4eIO/gQGK4\nOoxmxhvRFbr8EuTc+iSZHYfOnIQJLz9AdKyu9PQgpmnbn+fmAQSA3HueR+u6n+FlYY3AAzU6Rp8e\nODYFPpFh8A4Jwuw/P8RpG/+LU77+N/HM+CfHY/y//ul2fgCAIMA/ZRgJD9p0eqZSBb06oy6vmDH6\n6v/cRpawbtzQffJR3c+bSKgxfPZUppY9jcrXR/ZcudQObsvKQ+69L6B87Zdui9g0rN8ueURFEUff\n+xr7r/4nrArlzACg5JWPyOuYJQuYiI/K2wsxSxaQ7dofN8JwtEYu6yYISLzifKj9/eRqFw5Hr+tr\n95XmbfLiGjHnLWTWPHAiGeqerRVgrKwj/cg3LgrBk2TDjzYUnSsP+o+QQ7wGaoXS5u1yVafQ6ePJ\nw5r2PHc3YTAcrUH2LY/j0N3PofbHvxT1yZ7SppA8193COKIoMvr0mHPnuR0TTMlLlEqkHX7yTTKB\nEm12tGUeguhwMEaRb4xsnDA6dYWE0q70ytpDRW6eNVfiLjyDGKX6kgpUf80uQlT9zR/Yd/k9aNzs\n2QqmdN8OHN2zNx0A/OiopUIJXDY5dQSzb8wjt5IJiGixMvlAShU16Oogot2Olh2yBt1ZslLl402i\nxQBQ+fnPbmULjRW1xNjxDg9higJ4WkvdYbNBl1+iWDmq5rs/iYEXMmUcgsalQhAEJF17MTmm4qNv\n3ZL+re06Ms6q/HwQlCZHX6ytUq1yWrLo0ykfiph7ChONKHj0NUa3nHSdfN2qL37ptgIRDd3/lfqf\nt4JnXlCrmUk7LX1xJoxaepC+FL/4Pup+2oQjr32MwmffhvZgkVwicswIJu/NlbgLzyCva3/ayFSy\nS7pmKXG6dJQc7bGcJXP/dfZTv7gokpdjaW4jYw1tqBur6+GwWNEX9GVVZHzxiQqHX6eMzjXCDbAy\n2BbK2aKE1e5g1AjJoX7dHO05KkHA5VOkyboA4O70JCweHY74o3LkwZnwHHv+QpLn4DBbkHPrE26/\ngSiKjM2piY+RpdSiiI7D/edVH1BDXRAEFYC3ACwGMB7A5YIgjKWPcdZRD9N4YXKcVGmjg9JHNsYm\noIZK4oyYP4PMWnT5Jdi5+AYUr3mP6Nto6n7dAm1eMWq+lz0Cw666wLO2q9WMB7CmRJ55xrro02t/\n2oQdZ1xLwtA+FjOm7N2Oa998DtmX3U1m57RGPkBBU9lTspMrh+55npQV1AyLw7SPXmC0b670JqG0\nmXqwxF5wBqmuIdrsSP74Y6x68WGc8dNXiKyTvpdqrRmVf8sGG13uzSvAH8ETRrt5BOMuOhPjnr0H\nEfNmIPHqC5G25n6c+ut7WFTyF+bt/BrBk2RvBB2WdjUYmv6WdchNVGKosbKu21rAjRt2yG1xkb24\n4p8i5zI4Q+7p6elopSQfrpMf1xJNTZt3Yc95q5hkSEAqxehMhBS8vTDx9UfcJltxF8ne/rpfNqPy\nc9mbHrngVBKaI2U44Z74N1A0b5fD+rHnn47YC9jIhFdQAAJSk1gDuZsSjXR98YCUYfCNiSRGHo1z\nUhIwQl7kRl8qT6IaN8v9gk46ZbTKNcr3mSiKyL75UdT9uBHV635Dzi1PYPOEJdh17kpm1T9PEEWR\niQTQSa1d6V2btuwhumGv4EDmfnJCJ8y51tlu2pYpTUQpWvfkwNLUinGQHnzeYcFQ+8lSvZDJ8vig\nzS9xe4DT9x1d/lDn4lF3TeQDAK/AAIy47QqyXfzSf4jh0Lh5Nw7d9QyatuzBgRseZGqzdwUTnfRA\n9gIAmgQ6Ssr+7qLDwejyaY86IE3WJ74plx1t2Z1NxhZmISfnfetwwNKpIdceKiI5Gb6xkQgcI08C\nIufLVTLK3vocmycuwcG7niWGF714SlDaSJJTAHjuUS94+DXsOP0a7D53JbP+iMNmY6qEJFCR2PgV\n50DtLxmZHYVljHQUYD2x/skJUPv5EkeTaLfD2qZjnE10xGP0I7cRj72DMn5ilixA2pr7EX22vFJu\n3v1r0JyxD3aTuVuNOrMiqUL/U/Ko+8VHQ0Xdi7QU1Kmf70n60kY9R4++9zWKX5JzYEKpvDAlIubN\nINXFTNX15FnuGxeFgNHDEZDaOa45HD0afVqFiIKgVjNjnbGyFnaTmaxH4Tx3Xxcic00kdUJ71AHJ\nNklbcz/ZbuuhYl9Vu5ksLBkT6AN/H7XicQ6rrdeRucWjI/DqeaPwztIxWDQqHMPDNUg4SuU2nCJF\nhgS1GpPffpI4nToOl7rJs2w6PakeqA7wh9rfD0HjR5L9/ZlQOtAe9ZkAikVRPCqKohXAOgAXuh4U\nWVeNeSNCoVZ1hu0po6w5Og61VOJi4MhkjHt6NTHWzbWNKH39U7J/2DUXyQlmDgeyrvkn8UgEjEpm\nMs97gpajNB6RByZnxRdRFJH/4MvIWfUYWQTEFcveA8i99wUA0syY/B0uDwLANdmp+4RSW4eeeL0E\nLzWmffoSUwdWCSahNKegW3lNC5UIGHPuPJzy1avMrNjXbMLkzAxctfZFDC+SPAH122XjnvYUdUfy\nTZdgxjevY8K/HkDSdRcj7JSJ8Oo0yujviDbUXR/kTi+cw2xhtKCi3d7tIERHOMLnTO+2nc4awAAY\nbSzdFtdrKV27o6gM+y69m8m2p71BQWNTFPWg4bOnEo+PpbGFWZKdlhUEUYa6JwbPsWLT6dFOJQNH\npE9H0rUXMccETxoDQaViZBbdedSZhOvUJAiCID+0KJz9kV6N0jnhEUURzdQEjk46pb1oXU2IGzfu\ndPcqiyLas/KQecldKHjs3x4v2mIoqyLeeK+QIGbCrPQ9tB/IR/bKR8l29OK5UPm4S+0CRw8nCWqG\nsipihDksVhQ8/Irb8a17cmCiIlP07wGgM1wufaeixeqms6TzHuKWLSavtblFjKGk5NEEgOG3XE4M\nTXNdE8rfWwdTfRMO3fk0OcZh6vRe9SDb6imRVInuHCGm6nriHfQOD1EcS4PGppAJscNohvZQERwW\nqxyVEQRmzHL+trQRFXbqZGYSHrNkATMJtXcYUPPN79h17kq07DrALEcuGeqUPMMDQ93c0Ewm9R2F\nZSh98zOyr3rdb2Ryog70Z5wB3sGBGL5KlvsUPruWOJwAtuKLM6LlTRnjhvIqYkR5BQUwDiS1xheT\n3niMSa5UB/hj3DN3AwDGPXcvE33JXH4XNo1djMzL7lZc/0AUxR4jOkqGOl2aEQDzm1uaWmA3mBSr\nbznvIbvJ7LZ2A71YmDORtCtUPt6IPme+2/thMyZ15qC4L2rm/Ftdy3nqmIiC/DlaW22sqIW+uNzN\nuO1q/Yme0B6kvnMq6hk8YTTjjBj10CqEz5pC3usoKuu2QEQ5Vap7eJiyN72jqBx/T70Qf0+9iMml\n84QJsYFIjZD6l5/dhpga+XneMVp2DgaOGYGxT60m2xUffYsGyrlHe9OdORHBlKHeVRJ4XxhoQz0B\nAF2KoarzPUJ2djZmbfkdC1Llm4Q2oFqiY1GrYyUYyTddgulfvAyvkCDmfU1yPMY8cQdG3CHLBmjP\nSeIV53cpC1GCNpx1VDJGdKeh3rwtk8mK90uMxak/v4v2NU+hcIJsqDb+tQPtB/IZj42rRh1wTWCV\nDXWl6jbMQDk8wS3xSwn/EYnkO7O2tHe5CILdaEZblhyGCz9tGvxio3DaXx8j4K4b0RIpe0ZVdjvO\n/u5ThDQ3QixgH0jHCh1+pvuEa6Jk87ZMOGw2tOzJIV4JJ10NQjadnjzoBG8vpsqPEgGUMegsHZiR\nkcF4OiyNLcwKhvRvmHjl+eRhZSivRus+edlw1hukbOQIajViLzidbJOEysgwRJ8le5oCxxxfj3rL\nrgNk4A+eOBo+EaEImTaeecg4DVNGo96doU5NhJxGuFJ1JmciWECKLH1xGvm6/BLiFfMOC2aSzhkJ\nRLV7O0RRxBFKihQ2awpCT5lAnAOAVFd751nXe1RBifamh82Y6BJZYD3qusOl2HfFvbJ3LTYSox5Y\nqXhetZ8vM444jbry99YRrxltBGoPFcFQWoF8h2R80ImkTrqTx9H3XfSi00hdcmurlpTA9A4LZgxi\nGq8ADUb+8yayXfb2F8i5+TE3SVFHwREUPf+u68cZmLHUQ4+6b0wEMQ4tjS3MZICRJSo4UZyEncrm\nSBmr6ojUwS8+GhoqOdH527oa2zR+cVFI3/o5Rt5/IzPhFC1WHLjhIWYNgKC0kfCNln8zkweGeu1P\nG5lKIuXvroOhohY2vQHFL8re35Q7rnKThKbcdS2JnNjadSh86k2yj5b/OauLOOUtAPt9eivkD4RM\nTUPqfTeQ7VEPriT3hSYhBmOfvIM53mGyYPvmLche+aibDMdU00DkXF5BAYw2m7RBQfrin8Qa6qxG\nvZWp+EJX3jLXNkIURSmq0806ICE9eNQBMGO6k9CZkjORXX1YekYcfuzf2LnoOuw86wYio5SMd+WJ\nMqNTr6xV9PLqu1i4qie6mhyp/XyRdMMyAEDUGbMRd9EiqP39mAg5nV/oSjmV8NmVoV7x8XewNLXC\n3NCM7JsfRf5Dr/Sp1GR7TgHUnc+vlshoVIAtEjLsmouYCM+hu5+TV96lDfXOSR69EJ2nZTU9YdCT\nSbdu3Yr1BZvwy8dvYc2aNVi7di12H5JnpcXGFuzbLQ9WGRkZyMjIQNTCWZj954coiw9GvkMPQa3G\npDcew+4DWch36BHSqZPKd+il/d5eiF9+Nvm86/mUtv0SY8jnDZ2aRu2RbLQWS5VNWnfnkP0R82Zg\nzuZPkWfRosHfht8uuwmHJ04n+/MfegU2bQfyHXoc9rUTz1JX13NqKNfd8RBeT5qJvH++xBzvDPHn\nO/QoDvZSbL/rtiAIKE8KJQ/q9gMF2PrXRvzw1L9Q9/NmiKKIjIwMrP/4c2IIlsYHIbNIemB7hwRh\nc3wU3jjvAnx9492whYUh36FHua4el3z0OgS7HfkOPQpig3DDxhrc/uNhrN+81ePv23U7YPRw8n04\nVwzcunET9pfJg1K+Q4+DbfVoz8pH46ad5HjSvzZuVDy/0xjMd+hxJEpDqsN01R6noZjv0GP3AUn6\n4LDbsSc/l7ne5p9+JZ83VtaS9gy/9QrErziHbLdn5ZLzb90oSxSK/Bxdfh9xF53p9vfVnzYOO/fK\nnuNDhhayX3e4tFffd1+2//rqf+R6EXNnICMjAzt27EDqPddJ35doRHmSFAnwi48i7XdWxVA6/679\nclQk19ju9v07r+c/PAEZGRk42C4bu3tyc5CRkUHKMuY79KgcG08MtIyMDOS0yBOoPXkH3a7/25vv\nEyO1QG2B/oZzMevX/2DBgR9RMy2FXF9fXI4PF1+OT1asIh5apb9ny8+yBvdIlAb5dvn327FzJzne\ncLQG/73oOuQ0S04B7/AQ2B64mkn+dD3/kSgNaY82txjrP/kKP7/0Btnfvnw+yhIlQ0m027H+v1+h\n3CFNJn1jo9zOVxysls+Xc5jsl7yH1dL3LxoQMHoEgsaPcuuPZQnB2LFD9jq5nr98WCjKEiSjya43\nYMcu6Z6FICDh0nPJ+Y7+52s0bt7dZf9zygjzHXrktDV0eT16W+XlheIQL9JeU00D2d9Bna84UNXl\n+YrDfMnn2/YexN+//0m2NcPiUOAwyOeva5Tuh13y8yvfYXRr3/7yEoy8/0bM3bEOeP5WFAVLfdXa\nqsWu/ZnkfEFpI3GgVp5omeube7w/13/8BfP75Bpb8c3qR1D2zpewNEpjRXGYN4bffJnb59UaX2iv\nPJN8vubb9fh97YfIyMggDpB8hx55dslg9AkPkcfrzuhxvkOPw16yo4k+f+o918Fyz2Ww3H8Fkm9a\nwewfdvVFmPn922g6azqOxMoTiAPV5djw2TrmfBu/+Y5sd9X/nB51ur9qkuOZ9niHBaMAJuQ79LC1\n65jxO3BkMlQa6bc/1NEEm06PjsOl8v5xqWR/vkMPlcYXgWNSevx9CgQzigJk52G+Q49Cb+n7Cpow\nmpxPl1eMpm2Z+OM//0W+Q6oU07hBOtfmH34mEf1CjYh91HiRT/VHY0UNtv61kekP+Q59t/drV9ui\nwwHtwcOkfU5dvHP/uKdW4/T8P2C45SLs2Cn1/7CZk8nxTpmw0vl3UNsdpTmK13eOz87zVXz8HXaf\nvwobv/uxV8+vjd98J/fvpFRs+nsbs3/Hjh1oX7EQvp1OjZymavz2hrRKsaW5lVzf6VE/pG8m7320\nbxtuu/VW3HbbbUzRlL4w0OUZqwHQrrDEzvcIq1evRsP6Ypx+863wCQ+BVduBTU9J4Tmb2gvqyfOg\nipClALROLWBEIlZu/x51P29G4JgUhE5Lg3NvfYcDB65/CGkq6bPRi+fCNyoc6VGszs1V90ZvaxJj\nyedra+uBqUBw6hQsmCd5LXUFJWR/wopz4B0ciPT0dMQ0GfDLj4XYvfAcXJubBaFzyWAASFMFICQt\njXj2meslxJDzGavrYaioRej32xHq8EPlpz9i5P03kuOPvPYxOd/wGbLOsbu/BwDmnb4QpYckr2PZ\n2i9hq6yDpqUN2fgBY5+6C+mrLkPR9lw4fWcLzjoTadQ5hMSJCLa1oRqA+vH7kHbvY5JHqb2VtCd7\n+DQ06q1o1FtRGT8SN82UvUw9tY/eDhw9gnwfHYWlEEURUyLjYVTJ/cG5v2nLbjRu3EW26f10+53n\nr/luPdkfPXmq237XbWd4O00VAO8mydCZFp8Mg90HUMlh3SnRCYhKnw2HzQZzbSNpjyYhFqHTxiPt\nM2nbWbklPT0deOw9OFNMT7/ofCYaQbcndPp4TBuWwkSJLnhwNePtX7R8KcQH3oJotcFUVYdFk6cy\npTp78/17sp18pAkRnX9jxLxTMCZdlpjM+ftzzNP4Es+3X2wU+T6c3kal89taX4EzLnH6BeciIDUJ\ntZ0lQZ2fF3y84RsbifT4aNgm67HxgbcAAKlNJsyZPRuZr60jx0+4dBlz/o6oBGQ8918AwBgD24Y5\nc+Zg9wufwBmYXXztFUi74Dyp/TGRuP63z6QqP4+9DrvBiDTBH9h2CNvnXIrkm1Zg1upr3b5v8cG3\n4Hw0Lrp0GbQ5h3H4V0muNcEvlPTPgkdexag2G6AKgDrAH6d88YqbV07pfi7cLkW/qr78GcKRCoy1\nSjKZwHGpOOu5h1AgvobKT38AACTklCPWK6Lz94jERJfznb70AmR+LuX0tGcXIP3VhwBIJeJEux1p\nqgBokuPhFaBB8MTRSNt1gPl8evpcjFW435zMnTcPY1/0wv6rJM2q8/dMvfs6jPznTbA0txEv8qHV\nzyJ9y2eMJCE9PR2WlnZs7vTCTwgIxxlLz2f2d/d9zRg1Fq0tkpFgqq5H+lxpf+73L5D2jF0wv8vP\nn3XFJdjxvqTXbt2Tg4nzZ0LtvMeT4jE7JRHFGyXZoLmmEXNuvATmumfhVPsvWn4hI0egzy8IAs6+\n4WrMmjINey++HQ6TRe7vajUCRw/H/JgIiA9Inm1zfRPO6Obv1R+pQHJpE6AKgKBWk98Puw6jLKuU\n/L0THv8H1P5+in/veXfejOzcStR1rt8Q+MmfiFkmoqYzNydNFYBTzpQkM97hoaS9zolUmioAUSPk\nKILr33vBA3d12f7w06biqtOkvzXn9ieBzuozI1stzPEle4rgNE3T587FOIX+56zMQz8f/JPj2fao\nVJgSk0girbr8I+R435gIWNt1SCuTojDm2kboCstk++KsOQgcPQKO25+S2j57GlTeXj0/jxfMR/jS\n81H1udSnJgZG4owrpUlL8ITR5Py6vBLk/eNFpv0NG3ci/d2nUf/nNjjvwtlTp2PmXNkDnD5vLg5+\nJf12xspajNLayHjt/D6iLLIZ6On4r80rhrVNhzRVgFSSsXOMp4/3CQ/BXKot4bMmI22tdG1nFSyl\n839Qkw90yp3PO3MBkak49zssVmzMf5S034n2YCEC3/oO6Vs+Y47v7u9JbTAiuPMc1ckp0AybgPR0\n9/5acrgWJS+9jzRVAJJFyetuaWol13eOUQvPX4LwpXvgPzwBl6eNQsyS+VB5eSEr69jWNRloj3om\ngJGCICQLguAD4DIAPysdqD0o6UHphMvWyGiIajVqdWY4utBTewX4I/Hy85hC+4BkmNMJm7SO11Po\nEK6qQQ4zOhc76iqkmRAs/ZAt0XEonHSK23kDRg1Hm9HK1GV3vZ6puh5HP/yGCa3RmmM6aY4OmfYE\n/eDX5hwmmfuAlMFuqmlg9Onhc9gkNro04+izZiHlLvd69JUj5PDPH4XNMNm6Dg92h198NAndW9t0\nsE1E3SAAACAASURBVDS1Mt8BHY6sWvcbk4ToxEB9TzR0Qk1Xi17R+MZGkmWgra1aWFra0VHgLi1x\n6tLNtY1EEuIbHQG1xheh0+USZm37pVXb7CYziRYA7qFxGkGlQuwFcqWA8NOmMUY6IOke6b+H1vb3\nN6a6RnJ+wcebWSIckDS9dJ1i74hQCJ1aa5u2g0lsc2I3mMhERFCriWba9TfyT4ojycleQQFEvy9a\nrNg6cznTh+llrQHAL4GVntCh9Oate6XFuTr/ppQ7rmI+KwgChl15AeZs/gRRi04j7ztMFpS99Tm2\nz7uCVGsRRRHNO7JIXxO8vRAyeZyiBEiqDCK3edonazwKnTMlGnOLSXKeV3AgJr72MFReXoxcw26U\npVl0YqKTkElj5GoThWVEykUnkjrlVUpaYKXSjK5EnjEb4elyTkjYqZORet/1nQsMPczkYhQ88brb\n55lE0tQktyT17qBlT7Q0TamGuhKBY0YQ+aCluY1JZPdPjmfzMOoaYa5rYmQZdN5TV4ROG4+Jrz/G\nvBcwMglqP1/4RoYRCZa1pb3bih10WcWoM09DLFVlxCkTCByXioQV53TbnrFP3UUmn4byahx55SNG\nNkmkL1TtcroghGtN874Qdfps8ppexAxwkQ4qlGYElKUvGhfpCwD4ULXU6QRpn+gIt9+WlhYGjklB\n/LLFmPLBc0i+6RImebIn4paeRV6HzZpCoru+UeFEjmM3mtxWwG3asgcOm41N5J7I/v30pNBQUeOW\ndA7ArbiBJ9AL6oWfNs0jSXEoVbFPe/CwYsUrk81BchJVAhBSVuZW+EJ3uJT0X82wOIx7/j55zCo4\n4nHukFXbgTYq56E6ORVlLSbFY2k5nL5I6tvsgl5SvxEEAVPeewajH7oFcRee0eM6Lp4yoIa6KIp2\nAHcA2AAgD8A6URQZ4aMzJOCsd0zXstXFSp3MahfRYuhdCSFBpcLUD59H1BmzMerBm5mqD55CVwnw\na5H1ajGBPmShAkBK5qR1kv4+aoT7Sz/QrgXnMNpWALAkxOO6b/Jxzdd52HVUTqqg6/wayipR9cUv\nzOdojShdhk4p0a4raA2qK3aDEXn/eJHRptLVJtpNNrI6q7daQHKYBiPvvwmOtDHMeaqGy8amzmzH\n5pK+raAnuCRndRSWMQZD4uXnEUkDvcAInSREf080+tLeGeqCSgX/VFqnXoG/17vXF3Ya6rQR4Hw4\nB4xMkh/yTa0wVtSi43ApMej9RyS6LVTlSvJNl5BJQ1fa5cBjTCit/uYP7L34jm6TdBxmC0rfkD0X\nYTMmEq9cVwiC4FKi0b3iCa191STHk6oMdNUdgF2oBGBzCOiIQ/CkMfBzSZr0Cgwgv4PDbCEDriiK\nTJnMxMvPU1xECJCMk+mfv4wZ377J1raubcSBGx7C/ivvw+5zVyJzmay1DZ40BmqNL7PSqvM7MByt\nIUa0T1Q4ItLdJ/hKBCtM7PxThmHW7++Te51eERKArFFXKEfqFRRAEqdFu50sokKPPc6EZSWjvKtE\nUhpBEDDhlQcRMjUN4adNw+R3n2aMk4mvPUyOrf1uAxq3sCUb+1LxxYlS5RdRFFmNejfJqYJKhTCq\nIAGtIdckxbmV/qQTcgM7Sx96QtyFZ2DUgzeTbefERlCrFauTuCKKImq++5Nsxy9bjDGP3uZWFWzM\n47czSZ1K+MVGYfTDtyjuCxiVDE3nxNcngk4mlY0/7/BjN9Qj589Evig5idr25TIrj/dUwx+Q+rXr\n3+mqUQcA3yhZp05PAHyjI9zGLvpZ5LwnYs9biHHP3tOrhagi5kzD6EdvQ8ySBRj71J3MPqWJh/Pv\nsLXr0L4/j03kHs/+/fTf2FFYRirxqDSyFttwtKbX1VPohQ09LRzhEx5CJsGizY72A3lux1S0meB0\nyU6rLMS+81Zi1zk3MWVbtTnUglJTxiH5hmU9rpHgit1oRtY1/yTVmPRBwWiLiEazwYp2k3tOID0m\nOGVySsmkA8WAa9RFUfxTFMUxoiiOEkVxTVfHOWtj09n8tmFykliNtveJAoGjh2P6F68g9e7repVE\n6oT2cAe2twIOB4J91dB4q5kBOGDUcLeqDInBktHSGhUDn7MXMvu22gNgsDogAthEGbG+sZGyt6RN\n57ZYQAfjUZcNUP8RnhvqfrFRiOj0MPrGRiJtzf045RvZa9W4aZdcC31cKtMBaW96argGXioBKm8v\njHvjcZg0kne7PHUspqUl4rrp8kD1U16jxws4ucJWfilnvoOwGZMQQi1d7ST5huXkdVclGnu7qiEA\nBLiUaFRaOty5AhxdmtGZqCqoVEzkpy0rl1lNzhMjR5MQg/n7vsfpBX90mbAb1E2JRtFuR3PGfuTe\nvwY7Fl2LI//+LzNIl7//NQ7d9Qxadmbh4OpnFKseNGfsR8bp16Dio2/Je55OhGlvMl0b34nepTSj\nE68ADWMEaVwM9dBTJjDbKl8fhM2eyiywwrSDNqg6DTZdfgmpdy54e/W4ejEgVbmZ/ecHmPTW44xE\no3HTLtYTJAhIvl6S4NAPfOcEk/UKdh1VccW5EiBpz7wZmP37+8w6DX6dKzq7ouRRB8Ak3rZ3PhRZ\nj7r0sA0YlczUzFdpfJnqSN3hn5yA2X98gJnfv+U2YYhadBrilsrlUvP/+S/G+9bdehQ9oVT5xVzf\nRJJhvYICiB61K+gIhUiNLf5J8cyk0FzXyHgwg8b2nPBPk7L6Wkx6+wmk3ncDRv1DTsJVqvwiOhxo\n259LEt3as/KIB9YrKABRZ86BZlgcht96OflsxPwZiFo4y6O2DLvuYkx6+wmMuPNqpN57A0Y9eDPG\nPXcvZvzvDWI4MgY5FaXqDyPGJzKMRI5Fu52USDUcrSbOEcHbq8tJliAITPEJtb8G3grtomup07aI\nb0wk89saSitlR51a7ZGzpztS7rgKUz983q39rqUmw2ZPRcJl8mJIDRt3djtR8YkKJ0Y53Vedq4g6\n3+9uPQlXRIcDrZTkzTXq3h1hs+RnllOnTnOUSiSduGc7eU2vvN5OVeNyrv3AqBEUVh2mcVhtyL75\nUaZCT9GyFcQrX9bi7un3H5FI+rmpqg42vQFmylD37aHi3rEy0Br1HpkyZQoaIH/5dGlGrxR5EK7V\nmTEpbuCX+qbxCtDAOzwE1pZ2qO12BHRoERMtGaDManEKD9aEEF8crJMGf+2KZdCs/5sYRHtU8gBx\nlCpFpPLygl9cVJerJTofltY2rTwz9vPpcqGerpj++cvoKCyTEmQ6PSzxK85FzTe/M8cFzpqKjzNr\noFYJWDIuEkWNlOwlSpadjJgwAn+9+QrKNuzC2Avm49HTR8BotWNdTj1MNgfKWk04WNuByfFslR5P\noMPQ+qIyNkQ9NgVRC09Fm8uqjzFLFqDs3a+I/MRYWcsYfaLDAcMRtgSgJ9DH6Y9UYGSjEa5LiCh5\n1OnZfsi08SR027YvF7DLDzSl+r9KqLy8gG5Cakq11EWHA6Wvf4KK//7AlHXT5Rajeds+TFr7JBr+\n3I7Dj8mTNofRjIYNGYinSvGVvPwhSl7+kLle6MxJJBmsJxivlMLDgan44hIpCkhNIp+h63gDwMj7\nbiQGVuj0CQieMFqxpKETTUIMOjon26aaBoRMGccY1tFnzmF+t+4QVCrELz8bUYtOQ+Fza1H1mVzj\nXvDxRsLys5G8cgWpzOQbEyk9FEQR5sYWOKw21qAb57mhDgBpa+7Hkdc+RsS8GUi95zq3cKsgCAid\nOQl1P26UjnfqbrswSIOnjEPNt1IOh7YzusaG+aV7UuXlhaCxqSQCFzQ2tUfvrKeMfXo1mrbshrVN\nSuo78spHGPP47QBcV3ge3qvzalzkhYBLBZnRw3t06rhKvMi5k+NJaVlAkkfoCqjfNa13hrogCMy9\n50SaYEmOLWed77wH/oWqz36CSuOLpOuWwUKVUoxZsoDUy0+9+zrY2nQwN7Zg3HP3HHNbaLpaHdan\nHzzqAHDGRefjyGv/BSDlJMWetxBl73xJ9kekT+/2nvcOCyZST01yvOLv7EtJX2jD1jc6HA6L7Cxs\nolaa9U9J7Hb9kmMhmPKoq3x9MOHlB9BRXE6i7XU/bpSlgj7ebk4nQRCgSYxjJMWALLF0eoUN5dWM\nTMaJvrQSVV/+gqgzZiN8tuQ51+WXEE+0T1R4r6JaYadOJrX7lVZrLu+UnnibTQjNlSujNXVWdlN5\neTERf2fUUJMYC6fZrFRy1240w1TbAFNNPSo//QmNf8kJtGMeux15E9OBIumeKWsxYoqLraLy8Yb/\niAQiY9SXVMCqIH0ZKAbdUHdiqqqDpbmN8ZYEjR4OdH4XdC3144kmMZYYxcFtLYgJHA7ARZ+u8GBN\nDJFDS9us/rjlnutQ+vKHaJg2HW0RsrFS1W6Cxe6Aj1rypPslxDCGujrAn5Rq6ygsk8pC0fr0EcN6\npdEEpAdssEtIbcxjt6Fxw3ZyAwLAZ2IUDuVIbfn6YD2CfOWH8OhIdgGam8+bDHHJJDL4Bfp6YdGo\ncPxaIBmFP+Y19slQD6A86m37c+VBydsL/iMSEblwFlNmLHBcKjSJsQgYMYx4Kw1lVaw0oraRyAy8\nw4I9Wn4cYCVGutwixaXDiaFO1VCnB0Bap96+P4+pN+uJR90TlGqpl775GfM90bTszMKO+Vcyv72T\nup83kQe0obyKMdK9ggIw+uFbMOyaizw20Lor0Wg3mJhVCgNS2QdA5IJTiSfN1Yuj9vfD8JWXwlPY\nWurSpIqpC9yNRKwrvEODMeFfDyDhknNQ+ekP8E9JwrCrL2SkCoC00qxvVLgkWxBFmOubmLJpShP/\n7og6fRaiTu/eMxo2czIx1KVGqNza5YRe+KhlVzZ0h0vlvq5SMQ/moImjyYPTE326p/hGhWPM43ci\n997nAUglJ+OWLkLwxDHsqqQKZW67Q8mjzkQLutGnOwmePBaCjzepjAVIRpRvdAQElQrqQH/YOwxw\nmCzMgmielND1BNqjbqprgt1kRs23kszFYTSjfO2XzPHxy2UDW+3n2yv9dG/wiVA2Vnwi+8dQj1w4\nizLU98Dc2ILqr+XxYsRtV3bfvrBg4ljpSppCl2hk349kVkWmV8f2pM/0lahFs6EZFgdjZS3GPHEn\nAlKT4BsbSfof/ZwJGpvCLODkRDNMwVAfPwp2g4lEEPVlVYiYy8rtdIdLsXfpbbC2anH0g28wd8fX\n0CTEuMleeqNWoKPArXtzoCs4wtwXzhrqI4ryIFjl+8vWrkN7Vj6CJ45hnAbOko90eWVXj3rhM2+j\n/N11ivKelLuuwYjbr8SIXPlZ1JVOPWDUcNlQLy5nPOpDXvrSE3TZmtY9OcQTKajViBoznOxzraV+\nvKAH9qD2VsQESjN2esW4QAVPybQE2SjNrdfjj1lnInrnz/h86fXy6nUA7CJQ3S5PQjQuNYiTV15C\nVi+z6fQw1TTAUKosDzgWfKPCMerhW8m2KAgoSpANPilPQPYwjHIx1AG43bAXpskeu10V7ajT9X6y\nRQ+CdIgvYGQyVN5eCJ40hgm5OhP8/EfIHle9i06dkVf0ImRJH9ucsR/5nWXJ/FOGuS3VzBjqlGeW\nlr5oc4uYhSo89aj3hCYpnoQ7LY0t6CgqZxY68YkIRdL1yzDi9itJX6SNdHrlxMYte4j8pZLyFIdM\nTUP69i+RdP2yXnlRfeNpjzqrUS968T2ibfUKDkTMOfOY/ckrV2DSO09i5vdvu000ewuTUNpZS117\nSH74HovRGTZzEia99QRG3nt9l8Ywo1Ova/w/9s47zI3qbPv3qPftvXt3bW+xd927sTHYFFNMN/Wl\nBhIIIaQBSQjJm5AAIV8gb4CQhBp6L6Ea22CMDe5ed2/vvWvV5/tD0swZabSSdlW953ddvi6NNDMa\na49Gz3nO/dxPQAVxk4GUaxx2jEKZnuzz72aoKOWXeVs78fWqqzmvcE1RrqCbKdkGnSx0DgU5G8/l\namRYux37bvkVRk40wOjuacEwQRXSA8Lvoqm1AyzLClYzxvNQdyNVKb1qfdREcbOvVSNypWsykF7q\n5q4eDOw6KOjwKdg3M5XLhIYbMb/08Z4PloNj/Zx3v6mtC4d//jAcJmdcYJg9U1CgLHodRNMjT+mc\nG4Wv72t6snDlmpByhurvKoZMp8Xyr17C6oMfoMDlTS7TapC8pNprX1+JHrFJib68WLAqOdYgLCg1\nNrZi1+U/4gqhHSYLGp9+DQDQR3Qt99co0BN1biaXzXeYLNh99U9gcnVnZlkW9S7pS8lhb1lM9xff\nYPjwCW7CpC3J57z/ySJtUnZq6R1A/d9fEg3S8669EKX3fA8AUJSs5p6v7/eWvgDeOnWhj7r4uAkV\nUQ/USdre/IT4QchBdipfWBeKjPqY1Y72IINFMnA2DPQhQ68E63BgmHD8EAsailM0uI7QaX94tBcP\nbm8XBOluSIN/cmLAyGXIv/5iYRObY/UeGXVexz9Zsq88D61znF+8fYtWwqzWIFUjx4w0YVCulEmQ\nnzh+4SAAFCSpuQmLg3Vq1YNFnZfJua2QuINJRiJB5npXDQDDIPM8ZwMJUrfv6fwSrOOLG0FDEmJZ\nVF9e4tWqmZzVkxl1eaKBa1LD2uyCAkKVD81wsDASiWCCc+D23xLdeQuxat97KH/wbsz41Q+w4LW/\nCpbtDLOmY9G7T3CBKmuxouuTr+AwW9DyMp+9Kv7x9V5FmoEgyKh38OOh/7uDaPzHa9z2zAd+6J2J\nVsiRfdHagIuXxkMggWjrgsNmE8gUQrW64QvyR3/kaJ1gpSjYAslA0M+cJihUHu9vJ9WokHfthaKv\n6WcIs4cpy+dj2eYXsGzzC0jxEygFC8MwqHj4Z3yjsPoW7DjnZk7/rM7PEkwaAkGmJwqJTRaMHK1D\n+9ufca8HOkHzLNBV5/F1AuQY557LyYA8IfgVRTFIyZK5o0fQjTl56VxB4Jh39QUhkyP5w5fExVem\nPVgkUqkg6+t2VwKAaXdc7TezK0/iJwxiTZEA+J5YpyV7dfJ1o58RvkAdcE4MPa+LdJzirsPHBF/M\n3UZfViyIHcgiflNHN7679E6vzrfNL74LS/8Q+ght+UTuxbMe/xXn5mZq7cSea38G26gRx3uM6Bm1\nQmq1YtqxGq/jer7YgcF93vp0QHg/J2Wno7VNXEwpUSuRuHA2sjacicq/3IvyB+/mxkwR0VipoW8M\ndod3TR3ZXG7keAOntAB8y75CRdQD9epqfmbYReiGtKWFyNTzN+HJZtRHzDZc//phXPfqYbx3OPCA\nkZypOaUvCow1t3NyFEVKos9Z+JXVGVhNdFx1VxPLJIzg+QZiqYXMZmZtWAtVRqrguZGjdULHlxBl\n1AFgS/0gXr3oevzffQ9j8/rLcPaMFDx9SRkeO386/nh2MaqydFDKJLhmTiakksCWuy4o529ubx/q\nxvbGgXH29oaRSER1qKS8Y/ovb8P0X34fc5/7k9NeDsLPxbM76Wgt6RoReKAuT9ALglq31ldfViy4\nGY41tQl0cp6WbIlzvQtgQx0Ykp+P2/oUAGb88jbB8mjKivlYuuk55N9wCfKvvxjzX/0r5IkGZJzH\nd8zreP8LdHy4hdN3qnIy/EotfCEspHRmG+1jZtTc9Xvuhpq6ehFyrjh3QucP+Do8pC+jJxq57Jwq\nO93nD3bI3p8I5noIRwPd9CLR5evJwkilSJzvdCspl/gvmCz7w4+x4I3HvLKU5I+jG31ZcchkHZ5o\ni/NR9eQDvK0nUdw8njvLeJA/6ofv+TM3WdaXlwhcrsbDM1Ans5ZiAV0oPx+VoJi0F71EoF5w86VY\n9sXzmPvCw5j1+K8w7YfXhux9/SFP0Hk5nAGhkwUsX74cqSL3Hc20PGScc5rIEUKyLjoTjEwKWYKe\nS+h4IqY1licZOGmTWKJNNyN80hdfpK3xDtQNPlZkPSclmsIcyLQaQUbdvZJpGxnFrst+xBXKSlQK\nrhDdPmLE4V88zDVXUqanTKiI1lBRiuqn/5ebQA4dOIb9t96PDw45fw/ya49CYXEmVFU5GWBk/H7d\nn/MxIrmqpcr1dnMChKvn6WuXY/F7T6LqiQcEjnEAkKiWc059ZjsrmtAlk18D3x3ksvQygy5sNQpu\noh6ok5CaP930QqRq5ZBLnV+MQZMNo5bgLIRIdjYPcdKNV/Z3+vRl94S0N8qtP450rRzDh8gCoRKf\nM3mGYXD3inzM9MhInzMzBYvy+GW4BqKgNPO805F37YXI2nAmZj7gbAYhzKjXcS3sgeA81MfDwbJ4\n9UAnwDAwqzW4ek4m7lqRD61CCoZhMDfHgIfPLcV7183GZVXiLcLFWJhnQFm6xvUewB++aMChzhE/\nRwkRW44mb45ygw7Tbr8a6Wv5ZgaCbIGH9MVYRxaSBpe9FAvs9WXFAo3cwK4aLuMuT06ETKsW7J8w\nT+hQAoRO9uJGbDk2aVEV0ojPyI0qIxXlf/gxyh+8m8sMkD9k3Zt3ouFJvhtg3jUTz9IJMuouWcDJ\nh//Jt7zXaVDx8M8n5NIU1HV4ZNQFXsRhzqYDQukLmREdz0d/spCOC6qc8b/DDMMgZfl8LHzjcSz+\n8B/IvmQdsi87B/nXbQjb9fki4+zTMP+lRwV9E4DgrRndkP930vmh5Gc3BVzv4570uCEtYVVZ3pOg\nUP5dSbeekeP1nGSLkUqRvGweGIkE6WcuQ86lZ49bXBlqGKlUIC8BnCtE/ixng0HMXaroto0B3Y/S\nVi/Gqr3vYvXed32uXopp1N3PuWtLSBi5LGS/wcGgnZbn9b6+3KI8i0TdmXe3/z3gTGaxLIumZ9/m\ne2PIpKh++vco+QnvOORufAU464Qmep9OO30xyv94N7fd/dnXsP/1aYBlUUrIXrIuPEPwXSM99Mla\nGoHtansXF0ST7njaaeNPKoqS+N/pOhHnF/J+I5S9hLeQFIiBQH3fvn2isxHd9CJIGAaZOv61iWic\n3ZDWgj2jVhzq9LadEyNpxTxYFM7MfmpXB9RHjwkdGvzcgBUyCX5z5jSkaZ03TLVcgo1VmSgkBgUp\nfZGqlKh46GeoeuIBKFxNGsigdDhMGfWdTUOcA41aLsGGSvFlvmC/mFIJg9+cOQ3ZBuff0WJn8etP\n69A0IF6wIYaOqFXgnxt/uZH02fa0aJyo9AUQftndftS6smLBzZBsBkEG8G4SRSwlQ51RF/t8Zvz6\nBwH//bRFuQL5izsrz8ikyNm4fsLXRWqjLb0DqHv8BdT//T/ENd4esNvKZFBlpXHZMXNnr8DxJZRF\nkeO+vwv36hwQnDVjsORdcyF0ZcU4maxE3jXi0hYxEudVYvbf7sfsx37pFYhFipTl87Dwzb8J6lEM\nVTPGOcI3nnVAznPNRPq6FSJ7i0N6QgNCeYGY9EVXFjp5BBmom1o7uZWohDllnGY3WnhmzxXJiSGb\ndG/btg3qnAzB76EiLRnZl47fsIlEmZY8br8HeZLBK+gnP2/P1RJtcX5YVsACIW0N3wRKU5QLmU58\nQuQpfXGv7siTDJwMzD5mgrmjB80vvMPtN/OBO5F+5jJkX7xW1Mp1shLEvGsuRBHRUG72N1sw7+tN\nKD3GNyHKOHcV0taIrN5KJILfTKlaydtN2uwwuax/hUm58WOl4hQ+JiMd7tzItGrRBEe4C0mBGAjU\nAfFg1y13yDLw8peJeKm7OdEjnCFtru33saeQEakSR4nuot0vvyvwUA8kU5KskeOxC2bgxgXZ+PO5\npUjRypGbqIRbPdIxbMGY1fdqgcDF49AJbvlXqtX4lN0EA8uyeHU/v1x07sxU6JWhu/kkqeX4w1kl\nSFA5zzlstuPej08GvELiWVUvUSmgKfDW3ZFINSoua+m2aAScMgtOwyaReNn8+cMzsJeqVdAUZAsC\nddI+Sizo1M0oglQjzLL7WracKHqPjHrGuasEjjOBkHm+9/Jw+roVk9LSM1KpwLXi+O+f4B6nrFyA\nvKvPn/C5g0GikPPZMYdDILtzy6fCiS9L1ckWyY6HIjkByze/gKqnfus1PuKBhKqZWPz+k8i8YA3y\nb7jEp3zBH2I/tqU/vyXogNKt41ekJgm002J/22A91MdDkZYkKsFIWblQZO/IQjY9AkJXSEpCTqgK\nb7k86DqF8WAkEq8MqTKd/431XC0JZyGpPzLOXcU9TlrsXVzqRp6oF6xquJMBDMMIElpNz73Fee/L\nE/XIvdLZzV2iVKDgpku9zhuoTGw8pt97q+B35rSP34Zy1LnirsxKQ0J1GVJFvP6dv6HCCZeYl7qg\n34yfjPrMdP4zOtrlHagD4qv7UyKjXl1dLWiwAQBgGK6RRZZAp+6dUXewLGo6RtA14juId7AsanuF\nH/xX9QOiBQMAMGqx462aLjy8tRH3fVKLAwt5uUDnB1s4SyMgcG/cFI0cl1dloMTllqKQSpDjmoSw\nAJoHfK8WKFKTuFkbaRGlLc4LSbbiYMcoDnc5g3+5hMHFleLdGCdDtkGJ368rhkrmHHJdI1ZsrQts\nsqT1CNR1pYUBLXVqi7x16saGFr5gOT8raG0Z6e1dLtFCN6MIjEQiyFqQfyMxb1qJTIaEOfyynVSr\nCWlRMOC8ybl1yIxU6rOz4HiIBUJ5IZA+iGl4kxZVYc6//hC01ehk8NUkIxLSF7GsKxBaLbMvVqwI\nPHMca2iL81H91O9Q/ocfT7g9typXGKgnLpyN1NXBd64uuOlSrPj6Fazc+bogk+05vkNdICyRyUSD\ng9RVMRCoexSUhjLbuHy583e46ParkXfdBhTdfjUKb93o56jgUaR5Buq+M+qexdWRJHlxNSr+/AsU\n3HI5prvcS8RgGIazMWTkMiTM4Z3HSHe0hqd4eWP25edASnQvzbv2Qq4AFHAWNIdC8sNIJJDeexda\n870nPBlnrQQjkUBfUeolSRLrsC7sTtrp7JciUB+M/xtblsYH6sd6jD4KSgu9npsyGXWyBTfgDG7c\ns6UsAx9IiTm//GdvB378wQnc9vZRtA6KyylaB80wWh2C5wZNNuxt8/aNBoD/91UTntzRis9OY7Hg\nOAAAIABJREFU9KG2dwxd2fnoyHHOxhxmC9e2mZFKJ+WhWpgsLn8RQ0zKEKrg7pX9fJByRmkyUrTh\n0TVOT9PgCkLfTsqRxsMzoPYne+GOE7FoJD2Y/c2wxfDMqOtcgZWYxAUQz6gDQj91fUVJyANUhmEw\n67FfIX3dclQ98cCEin40hbkCGYimKDckzh6eGceUFfMx76VHQ6plDeg6RLp1ypMTRZ8PNWKTFWVG\nakSyM1Mdda5w8lz6s5snnPDQFucLmhwB3uNKV1oYcnkEuSoFOGs7yAAsWnhm0EPV7EjwHgYdKv70\nU8z45ffDIjtRpgk/W4Ugoy783kYzow4AeVedj7Lf3unT/91N+R/uRu5V56Hq/34jcHwiV5RJi8/8\na4UJGXmCHnnXXMBtJy+duD7dkw/rh/HuVd9Df4rws80411kgzDCM10TaK7kLj0C9pcPp5uUyCFCk\nJPqV7aVo5ZxE2WxziMZkYn0bpkRGfd++fV5aQ3J5gcyoe0pfLDYH3qpxteA22/Gv77wb0ADAcR8B\noZj8xWxzYHvToNfzDctXeT2nLcmfVLVvIWkJ1D++ZlvshhAKfXptrxG7WpwTFgkDXDY7vEEKafV4\nsnf8yYkbRioVZKQCrbIXs2gUeKgH4fjCnbMgh8vmH3aM8t0m01M4ZwoSXzZgaWcu4x6nnhaeTFjq\nygWY+9xDohKWQCH1n/k3XBySCYWBkJakrVmCuc8/7FVwGwnEJBCG2dPDXsgKOPWOMg+7vnAWkpJs\n27YtIu8Tq+jLi7neFGlrloTcVlKRkihoZBZsR9JA8JSfpSybGzWtNEk4M+qRGreeclJyUuQ5wQ40\naRRtdDOKUPnne7x+C8iCUjcpKxeIJnam/fBaJC6YBU1RLqbdcU1IrmvQZMNXDQMwaXV4+5rvQ+K6\nJ6rzswVyntTTlwiOE8uoqzyaHgllL4HFSmWE/OWIiPxFNKMegUA9+t9suApHlQo4zM5AnPwwsg2+\ni0m/bR4S6Jy3NQziUMcIKjKFBTVk5nZ+rp4LTL9uGMCdy/KgkPHBR03HCKx255JHpl6BH6/IR36i\nCnrHdGz58A3OjxqY/A+rr4JSMcSCUzIQnShv1/BWlSsKE5GT4N8ffTKUEI2S6vrGYHOwkAVg9Zg4\nv5JrCuNpjeYLofOLK1CfRCEp4NQ2q/OzuPO5A3VGIoE6N1NQvAKIS18AIGnBLMx59o8wtXUjdxLF\nmeEm/4aL4TCbwchkKLjhkpCcs+DGS2AfM0GeoEfBDZeE3drKF6JFhRGQvbhRZaZiZJBf1QtnISmF\nR6bVYPFH/8LAroMB2foFCyORQJmRysmpdCHUp7vxLO6LBX064B2Yh0OjHm6U40hfyIx6ILVSsY7Y\nqrwveaMiOQGL338qpO//0r4OLt7KKCvEik3PofPDLUhbu1wgbUs9bQEYmRSszQ6JWikqERT2MumA\nkUzKBRioz0zT4Mt6pw3x0a5RrC/zqEkQUVBMCelLdXU1JHKZwKyfzKiTXuqdIxbYCN3QppN9Xud7\namcrWA/rRbKQdH1ZKhf8G60OfNsyJNh3dyv/w7koLwHV2Xoka+SQ67RcK3U3kw/USZP98TPqYsVf\n/qqY/TFstmELoRO/aFb4l/wTVDKku7q7Wu0sGv1MUNyU/ORGFNxyOcofvFvQhng8hF7qLumLoAo8\n+EAdAOfxPb+0TDBpEJO/jOdgknHWShTccLFACxhrSGQyTLvjWhTddmXIGqfIdFpM/8X3UHTblVEL\n0gFx6YthVvgLSX29f6Qy6m6t71RGW5SLnEvP9pKthAryex+Ov6un9CXltAUhf4+J4CV9CVGzIyBy\n49ZTRkIWk5L1UQnV5RFrJhUuPM0UlJmpSF8Xmc95b+uwIFF4YUUa1LmZKPzeFdB6TCDkiQaU/e9d\n0M0oQtn/3iX6u6H28FIXZNQD/K0XZtS9nQEVyQlegbkyzF1JgRgI1N3kXHoWAKfWjuy6pZRJkKJx\nBnYOFuh2FY0Om234tpkPst1Z2aPdRm5G5DxGWEhamqrBadP4m8cWD/nLHiJQd3fVdOPZrW+yN+Bs\ng5Lzie8xWjFstvncNxwZ9c9P9MHims2WpKi9/N7DRUlK8PIXZVoyyn57J/Kvvzjg9xGzaJys9AUA\niu+8Dit3vo7lm18Q3DA8bbA8q+0psYW49CVygbpXYVqEAnVK+Cm89QrI9FokL5+HlJXz/R8QJGRG\nXZWTMeGkQ6gJp/QlUnhLX4jPOjsdFY/8HFkbzkT5g3d7Hhp3KDNSISESRblXnT/hIu1gGDHb8PCX\nfL3YglwDTi8ef1KX/z8XYfnW/yDvKnFnMBVRezLW0iFcPQ8wo16SqoErJEPzoFk0JvOUv0wZjToA\n5P3PRVi2+QWc9u2bXk0FsvR8MLStwRmEf1U/AKsruz4jTYMLK/gfvX991waL3Vk8ShaSJqpkSNXI\nBV1BdzQNcvKZfqOVM7qXMkBVllBCY6goRdISp3eoVKOedPGOVMIgj5CaNI6jU5cnGgQ3DHmiflJt\na1mWxQdH+BbB55alRkSbCzgnS25OBlhQOhE8LRq/qDiH66om1WpEvWEDRVOQg+3f7hQ85ylz8exI\nSoktPAN1qU4T0aVs0vmFUcgnPHEMlqmuUY8EGWetxOlHPsLCNx4PS+BDFtNlnLsqYvduf3j+Jnna\nNU6GSI1bMv6QqBReyZbcjetR9cQDEXFoCjcMwyDJ1VBIolYi7+oL/BwRGv62vQU9o84GlwalFD9e\nmT/pMSxP1HO2x3bjGAb38b0xAp3IKmUSTCP81I+J+Kl7WjROCemLG4ZhoC8rFg0+lxTwzz27ux1N\n/SZsOslnwk8vTsLG6gzolc5lqI5hC94/7AxCSX16aaoGDMOgMEmNIpfsxGJn8clxp4sL6QJTlq6F\nRuG9rFX91G9Reu+tmP/a/5tUoOwmuIJSPqs+EccSkoMdI2gedGr+NXIJVk+LnNtEaSr/RfD0tw81\nOqII1TbEd0TVlkz+xuCJp/TFlz6dEhso05IFRX+GyumRtYckPJn1M4oiksmiRI5w/j0T5pRj9t9+\njZKf3YzSn93k/4AIIfeQuoRS+hIp3La2gHMyHSuToHBR+Zd7UfzjGzD/5b/47O8QSrbW9eMLQsnw\no+X5nGpiMjAMI5C/WPt5xYVY0awvygR+6t7yF62H80sk6jCiHqhXV/s26nezoTIdJa5ZjtXO4neb\n6nGwwxl0SRhg1bQk6JUyXD2H/yO9tK8DQyabR6DOB4jnlfMD8q2aLtgcrFD2kitu5aNMT0HxD6/l\nZqGTpTCZzKgHbtHozxPUH+8T2fTTS5JFJyXhgpS+1PaN+fSzDwVFd1zjtTQlUSpQeOsVkz63p2bS\nMzCPRIdNysRhJBKBVVkkZS+AsA19ikhr9HBBNeqnBtmXnIWSH1/vsyNlNAhnw6NIjVttSQHS1i4H\nI5eh8JbLI/Ke0USdm4nSn92E5HGaJoWK+r4x/OUrXpJyZmkylheFLiMttoqtyskIqg5sZtr4zi86\nQvoiTzJEJMESFykcmYTBT08rwO3vHIPVwaKRaD8/N0ePJNdsbH1ZKt493I22IQuGzXa8vK9DkLEl\nJRdnlibjud3tGDTZ0DVixZbafkEh6TwPfXq4EDq/jJ9RT1uzBI3/eBXA5Kr8+41WfN3AW1Cunzlx\nCchESNbIkayRoc9og9nmQOugGflJ4XGbSV25AKsPvA/7mBkOswUOiwUyvTYsRWQaD406zajHPqqc\nDK5rLekZHwn0ZcWY9+IjGG1oiWnnHwolUKQaNRQpibD0DkCq04TFRz3cMAyDec8/BPuYOaYL/eON\nXqMVv/yklpMiZ+gU+P6S0Db6E0uOBVu/UZbOxwZHu0fBsqxgVcVQOR0SlQIOkyVi9pxRz6i7Ner+\nKEpW49p53oHP6cW8nkwuleDGBXwB4buHe3Csm1+6mE4USyplElxA6Nr/+V0reo1OzZRWIcX01MgU\nVpLSl/q+MS/HGpLU0xZi3kuPovpff0D2xWsn/J6fnOjl3HPK07UCTVakKCWy6id6w6dTB5yZU5lW\nDUVyAlSZaSEL0j01k4q0ZEhURHGpjyZIlNgh+xKnk5MiNQnphLd9pEg7YykKb7osbO4jYlCNOiVc\nMAyD8j/9FEmLq1Dxp5+G1Ns90uOWBumhY8xqx/2f1qHbpUvXyCX47dpp0IZ4Jd+z6zAQfL+ZbIOS\nk1EPm+1o82i0qUhNQtUTDyD36vNR/sefTPxigyDqgXowXDIrXTDbUcokWFYoXFpbXpiAcpfGyOZg\nYXa5mrgLSUnOL0uF0uWh3mfkq3urs3SQBuDtHQrSdQqo5c5rGDLb8cr+znH3Tzt9MTLPXTVhWygH\ny+LDI73ctqdPaKQoiVBBaSRhGEbgNBOMLo4SHfKuvgArd76OlTvf8Nu5jkKh+Cdz/WoseucJLztj\nytTE7mDx0JZGrvGkhAF+uaYIRcmhTxCKZdQ1QdpYMwzjt/FRxtmnofKRX4jaZoeDqAfqgWjU3Uhd\nEhj3bOe8slSo5cKAlWEY3LIox+tYdyEpiUElw1nTvVvvetoyhhMJwwiu4Zld7dhc6+0PHwh1vWM+\nu7C62d0yjE6XxaVeKcWKEOrDgqGEyOIHatEYa4hpJqfdeR1kCXpkbTgz6u2lKYGhKciJSmfUaEE1\n6pR4hI7b+KNrxIKffHgCXzfyUtvbl+Zhvo8awMkiKn2ZgI01aVUt5qceaeJCo06Sm6DCUxfNRMug\nGbM8OpC6Kc/QYmVRosBPnSwkJbl4VhreP9INsp5xXpgGkS9uWpiNur4x7G93Fsg+srUJqVqFz/+f\nGPvbhvHT/54EADxw5jSBUw4Jacm4tjSZW1GINGS9wIkeIxwsC8kpUF2ffdFaZF14RkTdQygUCoVC\niSW+bhjAo181YdjMd4+/uDItrKv44hn14B3yZhIZ9QMdI1469UgT9WgiUI06SapWgeps/bjylBsW\nZAta05f60Jxn6pWCBkiZegWyDZHVpsmlEtx/RhEKEp16dauDxW8+qwu4aycAfE50af3waI/oPl0j\nFuxs5me250S4iJQkTSuHwbUyYrQ60D5kidq1TBRfmkkapFNiGapRp8QjdNzGDy/v68ADn9dzQbqE\nAa6fn4WbRdQOoUSZkQJGxqssGJl0QrViZelarhllY78JO5qG/BwRXk7ZiCLboMSVLrvGNK18XDnL\nFVUZ3B/FX3escKFTyvC7ddOQpHYucgyb7fjZf0+iyY8TjBu3XSXgbM1rtNi99vn4WC+3clCdrUNe\nYnicVgKBYRhh46MwF5RSKBQKhUIJLyzL4lWi1i5dJ8ef15diY3Vm2FfNGalU0EhOU5gzIftErUIq\ncMN7bnc7HOMYfYSbqAfqwWjUg+Wq6gz8+9Iy/POSMi8tO0lRshqPnz8D959RhKvnRs9SL1OvxO/W\nFnPFpf1jNvz0vyf8Bus9oxa0ERlpq4PFrlbhDNDmYPHfY3ymPdKWjGLEe0Ep1UxS4hE6binxCB23\n8cGAycZZMKrlEvz9wpmoyAhcxjtZSC/1yTSGvLwqg5MG1/WNYRshpY40UQ/UwwnDMMhNUI0bpLuZ\nlqLGssJEgVwmGkxP0+D364IL1slsupvthE86AOxoGuScbZLVMiwtjL6/bSlRULq1fgB7W4fHtads\nHzZjVGSlgEKhUCgUSvTpGOaThll6JQyqyJZCkjr1YK0ZSZI1clxYLsyqh7M543hEPVCfiEb9VKcy\nU+cVrP/6s1qfg+RAu3egvrN5iPNKB4APiSLSdTNSoj4hAYS+9h3DFvz8o5O4+8MTXhMPlmXxj52t\nuO7Vw/if1w6jZzQ29OxUM0mJR+i4pcQjdNzGBx3DvO94ll4xzp7hIWnRbO5x8tK5kzrXpbMzoHHF\nYc2DZmyu7Z/U+SZK1AN1ijiVmTr8YV0xVK6ll7Yhi2hADggDdZfUHqMWOw60D7uONXNdVxkA58yI\nvuwFcEp9rpmbKZg01HSM4u4PTuCJHS2w2B1wsCwe/7oFbxzsAgAMmmz46Fivr1NSKBQKhUKJEmRG\nPTMKgXrO5eei8tF7MPuJ3yDtzKWTOpdBJcPFs3jN+wt72gUJ0EgR9UA9nBr1eKc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Nod+O3n9WgftgiOMVodtPiUIkqg43anQJ+eMM6eviHlL3tjRKfuT/riRiGV4L7TC7l+Bm1DZjz2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\nIiIiMiEW6kREREREJvT/YvXijE994isAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12.5, 4)\n", "\n", "import pymc3 as pm\n", "x_t = np.random.normal(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] = np.random.normal(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" ] }, { "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", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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2958Vq2Aikh+NPSEiIkkzYMAAVqxYwerVHU65lZROnToxYMCAoq0/W0tEeNi8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\nD0qv2kYmz1cpuo6V61hXXRABjAbmuvt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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" ] }, { "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 not 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. PyMC3 has a built-in autocorrelation plotting function in the `plots` 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", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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3v2dYj+SYcv7zJ3Rw8Myqd9jjvSkt0KLSkYvxAXHKUy5lilPhK/UYxWVWIuX8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\nWyycfvrpbLzxxnTs2JF99tmH9957D4B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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "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" ] }, { "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." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### `pymc3.plots`\n", "\n", "It seems silly to have to manually create histograms, autocorrelation plots and trace plots each time we perform MCMC. The authors of PyMC3 have included a visualization tool for just this purpose. \n", "\n", "The `pymc3.plots` module contains a few different plotting functions that you might find useful. For each different plotting function contained therein, you simply pass a `trace` returned from sampling as well as a list, `varnames`, of the variables that you are interested in. This module can provide you with plots of autocorrelation and the posterior distributions of each variable and their traces, among others.\n", "\n", "Below we use the tool to plot the centers of the clusters." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VWEq7ZFgDek+PnYIFs1GfL0wBCDzf7q6e4L0F6Dlyip7jZwadd/6cCrJKCsks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\n13otEVkrIo8Wg8wisltE1jv7+pUikTkiIj9zZNgoIhcVsswiMsfZv2u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AAA6hZhuuIiuwgzpcWEVWYAfvRXATM9sAAACAQ4Ky2j+1T7CKrMAO6nBhVV1Z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\nWBWMCWXW2QYAAAAcEqzB9qw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.plots.traceplot(trace=trace, varnames=[\"centers\"])\n", "pm.plots.plot_posterior(trace=trace[\"centers\"][:,0])\n", "pm.plots.plot_posterior(trace=trace[\"centers\"][:,1])\n", "pm.plots.autocorrplot(trace=trace, varnames=[\"centers\"]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first plotting function gives us the posterior density of each unknown in the `centers` variable as well as the `trace` of each. `trace` plot is useful for inspecting that possible \"meandering\" property that is a result of non-convergence. The density plot gives us an idea of the shape of the distribution of each unknown, but it is better to look at each of them individually." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second plotting function(s) provides us with a histogram of the samples with a few added features. The text overlay in the center shows us the posterior mean, which is a good summary of posterior distribution. The interval marked by the horizontal black line overlay represents the *95% credible interval*, sometimes called the *highest posterior density interval* and not to be confused with a *95% confidence interval*. We 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\". 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 last plots, titled `center_0` and `center_1` are the generated autocorrelation plots, similar to the ones displayed above." ] }, { "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 `testval` 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, testval = 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 PyMC3 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", "PyMC3 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", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "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" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }