{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Computational Methods in Bayesian Analysis\n", "\n", "In the final example from the previous section, the problem was deliberately chosen so that a result could be calculated by hand: there were only two possible parameter values for the likelihood, so the normalizing constant of Bayes' formula was just a sum of two terms.\n", "\n", "For most problems of interest, Bayesian analysis requires integration over multiple parameters, making the calculation of a posterior intractable either via analytic methods or standard methods of numerical integration.\n", "\n", "However, it is often possible to **approximate** these integrals by simulating\n", "(drawing samples) from posterior distributions. For example, consider the expected value (mean) of a vector-valued random variable $\\mathbf{x}$:\n", "\n", "\\\\[\\begin{gathered}\n", "\\begin{split}E[{\\bf x}] = \\int {\\bf x} f({\\bf x}) d{\\bf x}, \\qquad\n", "{\\bf x} = \\{x_1,...,x_k\\}\\end{split}\\notag\\\\\\begin{split}\\end{split}\\notag\\end{gathered}\n", "\\\\]\n", "\n", "where $k$ (the dimension of vector $x$) is perhaps very large. \n", "\n", "If we can produce a reasonable number of **random vectors** $\\{{\\bf x_i}\\}$, we can use these values to approximate the unknown integral. This process is known as *Monte Carlo integration*. In general, MC integration allows integrals against probability density functions:\n", "\n", "\\\\[\\begin{gathered}\n", "\\begin{split}I = \\int h(\\mathbf{x}) f(\\mathbf{x}) \\mathbf{dx}\\end{split}\\notag\\\\\\begin{split}\\end{split}\\notag\\end{gathered}\n", "\\\\]\n", "\n", "to be estimated by finite sums:\n", "\n", "\\\\[\\begin{gathered}\n", "\\begin{split}\\hat{I} = \\frac{1}{n}\\sum_{i=1}^n h(\\mathbf{x}_i),\\end{split}\\notag\\\\\\begin{split}\\end{split}\\notag\\end{gathered}\n", "\\\\]\n", "\n", "where $\\mathbf{x}_i$ is a sample from $f$. This estimate is valid and useful because:\n", "\n", "- By the strong law of large numbers:\n", "\n", "$$\\begin{gathered}\n", "\\begin{split}\\hat{I} \\rightarrow I \\mbox{ with probability 1}\\end{split}\\notag\\\\\\begin{split}\\end{split}\\notag\\end{gathered}$$\n", "\n", "- Simulation error can be measured and controlled:\n", "\n", "$$Var(\\hat{I}) = \\frac{1}{n(n-1)}\\sum_{i=1}^n\n", " (h(\\mathbf{x}_i)-\\hat{I})^2$$\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example: negative binomial distribution\n", "\n", "We can use simulation to estimate the expected value of a random variable that is negative binomial-distributed. The negative binomial distribution describes some postive discrete random variables; In particular, it can be used to model the number of Bernoulli trials that one can expect to conduct until \\\\(r\\\\) failures occur.\n", "\n", "\n", "\\\\[\n", "f(x \\mid p, r) = \\frac{x+r-1}{x} (1-p)^x p^r\n", "\\\\]\n", "\n", "Where:\n", " \n", "- \\\\(0 < p < 1\\\\)\n", "- \\\\(r \\in \\{1, 2, 3, \\ldots \\}\\\\)\n", "\n", "and:\n", "\n", "- \\\\(x \\in \\{0, 1, 2, \\ldots \\}\\\\)\n", "\n", "![negative binomial (courtesy Wikipedia)](http://upload.wikimedia.org/wikipedia/commons/8/83/Negbinomial.gif)\n", "\n", "Most frequently, however, it is used to model **overdispersed counts**. That is, counts that have a larger variance than would be predicted under a Poisson distribution. In fact, the negative binomial can be expressed as a continuous mixture of Poisson distributions, where a gamma distribution acts as the mixing distribution.\n", "\n", "\\\\[f(x \\mid p, r) = \\int_0^{\\infty} \\text{Poisson}(\\lambda) \\, \\text{Gamma}(r, (1-p)/p) \\, d\\lambda\n", "\\\\]\n", "\n", "Lets use simulation to try to estimate the mean of a negative binomial distribution with \\\\(p = 0.7\\\\) and \\\\(r = 3\\\\):" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Simulate gamma means\n", "import numpy as np\n", "r = 3\n", "p = 0.7\n", "\n", "lam = np.random.gamma(r, p/(1.-p), size=100)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "7.3" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Simulate sample Poisson conditional on lambda\n", "sim_vals = np.random.poisson(lam)\n", "sim_vals.sum() / 100." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The actual expected value of the negative binomial distribution is \\\\(p r / (1-p)\\\\), which in this case is 7. That's pretty close, though we can do better if we draw more samples:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "7.01889" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lam = np.random.gamma(r, p/(1.-p), size=100000)\n", "sim_vals = np.random.poisson(lam)\n", "sim_vals.sum() / 100000." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This approach of drawing repeated random samples in order to obtain a desired numerical result is generally known as **Monte Carlo simulation**.\n", "\n", "Clearly, this is a convenient, simplistic example that did not require simuation to obtain an answer. For most problems, it is simply not possible to draw independent random samples from the posterior distribution because they will generally be (1) multivariate and (2) not of a known functional form for which there is a pre-existing random number generator.\n", "\n", "However, we are not going to give up on simulation. Though we cannot generally draw independent samples for our model, we can usually generate **dependent** samples, and it turns out that if we do this in a particular way, we can obtain samples from almost any posterior distribution.\n", "\n", "## Markov Chains\n", "\n", "A Markov chain is a special type of *stochastic process*. The standard definition of a stochastic process is an ordered collection of random variables:\n", "\n", "$$\\begin{gathered}\n", "\\begin{split}\\{X_t:t \\in T\\}\\end{split}\\notag\\\\\\begin{split}\\end{split}\\notag\n", "\\end{gathered}$$\n", "\n", "where $t$ is frequently (but not necessarily) a time index. If we think of $X_t$ as a state $X$ at time $t$, and invoke the following dependence condition on each state:\n", "\n", "\\\\[\\begin{aligned}\n", "&Pr(X_{t+1}=x_{t+1} | X_t=x_t, X_{t-1}=x_{t-1},\\ldots,X_0=x_0) \\cr\n", "&= Pr(X_{t+1}=x_{t+1} | X_t=x_t)\n", "\\end{aligned}\\\\]\n", "\n", "then the stochastic process is known as a Markov chain. This conditioning specifies that the future depends on the current state, but not past states. Thus, the Markov chain wanders about the state space,\n", "remembering only where it has just been in the last time step. \n", "\n", "The collection of transition probabilities is sometimes called a *transition matrix* when dealing with discrete states, or more generally, a *transition kernel*.\n", "\n", "It is useful to think of the Markovian property as **mild non-independence**. \n", "\n", "If we use Monte Carlo simulation to generate a Markov chain, this is called **Markov chain Monte Carlo**, or MCMC. If the resulting Markov chain obeys some important properties, then it allows us to indirectly generate independent samples from a particular posterior distribution.\n", "\n", "\n", "> ### Why MCMC Works: Reversible Markov Chains\n", "> \n", "> Markov chain Monte Carlo simulates a Markov chain for which some function of interest\n", "> (*e.g.* the joint distribution of the parameters of some model) is the unique, invariant limiting distribution. An invariant distribution with respect to some Markov chain with transition kernel $Pr(y \\mid x)$ implies that:\n", "> \n", "> $$\\int_x Pr(y \\mid x) \\pi(x) dx = \\pi(y).$$\n", "> \n", "> Invariance is guaranteed for any *reversible* Markov chain. Consider a Markov chain in reverse sequence:\n", "> $\\{\\theta^{(n)},\\theta^{(n-1)},...,\\theta^{(0)}\\}$. This sequence is still Markovian, because:\n", "> \n", "> $$Pr(\\theta^{(k)}=y \\mid \\theta^{(k+1)}=x,\\theta^{(k+2)}=x_1,\\ldots ) = Pr(\\theta^{(k)}=y \\mid \\theta^{(k+1)}=x)$$\n", "> \n", "> Forward and reverse transition probabilities may be related through Bayes theorem:\n", "> \n", "> $$\\frac{Pr(\\theta^{(k+1)}=x \\mid \\theta^{(k)}=y) \\pi^{(k)}(y)}{\\pi^{(k+1)}(x)}$$\n", "> \n", "> Though not homogeneous in general, $\\pi$ becomes homogeneous if:\n", "> \n", "> - $n \\rightarrow \\infty$\n", "> \n", "> - $\\pi^{(i)}=\\pi$ for some $i < k$\n", "> \n", "> If this chain is homogeneous it is called reversible, because it satisfies the ***detailed balance equation***:\n", "> \n", "> $$\\pi(x)Pr(y \\mid x) = \\pi(y) Pr(x \\mid y)$$\n", "> \n", "> Reversibility is important because it has the effect of balancing movement through the entire state space. When a Markov chain is reversible, $\\pi$ is the unique, invariant, stationary distribution of that chain. Hence, if $\\pi$ is of interest, we need only find the reversible Markov chain for which $\\pi$ is the limiting distribution.\n", "> This is what MCMC does!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gibbs Sampling\n", "\n", "The Gibbs sampler is the simplest and most prevalent MCMC algorithm. If a posterior has $k$ parameters to be estimated, we may condition each parameter on current values of the other $k-1$ parameters, and sample from the resultant distributional form (usually easier), and repeat this operation on the other parameters in turn. This procedure generates samples from the posterior distribution. Note that we have now combined Markov chains (conditional independence) and Monte Carlo techniques (estimation by simulation) to yield Markov chain Monte Carlo.\n", "\n", "Here is a stereotypical Gibbs sampling algorithm:\n", "\n", "1. Choose starting values for states (parameters):\n", " ${\\bf \\theta} = [\\theta_1^{(0)},\\theta_2^{(0)},\\ldots,\\theta_k^{(0)}]$\n", "\n", "2. Initialize counter $j=1$\n", "\n", "3. Draw the following values from each of the $k$ conditional\n", " distributions:\n", "\n", " $$\\begin{aligned}\n", " \\theta_1^{(j)} &\\sim& \\pi(\\theta_1 | \\theta_2^{(j-1)},\\theta_3^{(j-1)},\\ldots,\\theta_{k-1}^{(j-1)},\\theta_k^{(j-1)}) \\\\\n", " \\theta_2^{(j)} &\\sim& \\pi(\\theta_2 | \\theta_1^{(j)},\\theta_3^{(j-1)},\\ldots,\\theta_{k-1}^{(j-1)},\\theta_k^{(j-1)}) \\\\\n", " \\theta_3^{(j)} &\\sim& \\pi(\\theta_3 | \\theta_1^{(j)},\\theta_2^{(j)},\\ldots,\\theta_{k-1}^{(j-1)},\\theta_k^{(j-1)}) \\\\\n", " \\vdots \\\\\n", " \\theta_{k-1}^{(j)} &\\sim& \\pi(\\theta_{k-1} | \\theta_1^{(j)},\\theta_2^{(j)},\\ldots,\\theta_{k-2}^{(j)},\\theta_k^{(j-1)}) \\\\\n", " \\theta_k^{(j)} &\\sim& \\pi(\\theta_k | \\theta_1^{(j)},\\theta_2^{(j)},\\theta_4^{(j)},\\ldots,\\theta_{k-2}^{(j)},\\theta_{k-1}^{(j)})\\end{aligned}$$\n", "\n", "4. Increment $j$ and repeat until convergence occurs.\n", "\n", "As we can see from the algorithm, each distribution is conditioned on the last iteration of its chain values, constituting a Markov chain as advertised. The Gibbs sampler has all of the important properties outlined in the previous section: it is aperiodic, homogeneous and ergodic. Once the sampler converges, all subsequent samples are from the target distribution. This convergence occurs at a geometric rate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Inferring patterns in UK coal mining disasters\n", "\n", "Let's try to model a more interesting example, a time series of recorded coal mining \n", "disasters in the UK from 1851 to 1962.\n", "\n", "Occurrences of disasters in the time series is thought to be derived from a \n", "Poisson process with a large rate parameter in the early part of the time \n", "series, and from one with a smaller rate in the later part. We are interested \n", "in locating the change point in the series, which perhaps is related to changes \n", "in mining safety regulations." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "disasters_array = np.array([4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,\n", " 3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,\n", " 2, 2, 3, 4, 2, 1, 3, 2, 2, 1, 1, 1, 1, 3, 0, 0,\n", " 1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,\n", " 0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,\n", " 3, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,\n", " 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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pdAw7lWXfdoT8ecAZwBLgZZ21SpIkSRoxwwbzLZJsQRPMv1BV9wDVXbMkSZKk0TJsMP8gcC2wDXB+kj2AoeeYS5IkSZrYpBd/thd7/ryqdh1Y9hPgqV02TJIkSRolk46YV9X9wFFjllVV3dtZqyRJkqQRM+xUlrOSvCHJ7kl2XPfotGWSJEnSCBn2PuavbL++dmBZAQ+f3uZIkiRJo2moYF5Ve3bdEEmSJGmUDfsBQ1sn+YskK9vv90ry7G6bJkmSJI2OYeeYfwy4G3hi+/1q4K86aZEkSZI0goYN5o+oqncD9wBU1Z1AOmuVJEmSNGKGDeZ3J9mK9tM+kzwCuKuzVkmSJEkjZti7srwd+Cqwe5KTgQOBI7tqlCRJkjRqhr0ry9eSrAIeTzOF5eiqWtNpyyRJkqQRMuxdWf6tqm6uqtOr6stVtSbJv3XdOEmSJGlUTDhinmRLYGtgpyQ7sP6Cz+2BXTpumyRJkjQyJpvK8qfAMTQhfBXrg/la4P0dtkuSJEkaKRMG86o6ATghyeuq6h9mqE2SJEnSyBn2dok/S7IdQPsJoKcleUyH7ZIkSZJGyrDB/G1VdVuSJwGHAJ8APtBdsyRJkqTRMmwwv6/9+izgA1X1BWDhRBsk2TLJt5N8P8klSY7blIZKkiRJ89mwwfz6JB8CDgfOSPKgIba9CzioqvYD9gcOTfL4jW+qJEmSNH8NG8wPB84EDq2qW4EdgWMn2qAat7ffbtE+amMbKkmSJM1nw37y538DpyXZOcmSdvHlk22XZHOa2yw+Enh/VX1rA2VWACsAFi7aedh2d2758Wc/YNmFxx40I3XMRN0Tmc12zfaxT1Vf22tfPdBca+9UTefxzffXSt3r6983qe+G/eTPw5JcCVwDnNd+/cpk21XVfVW1P7AbcECSR22gzMqqWlZVyxZss2hqrZckSZLmiWGnsrwTeDzwn1W1J/B04BvDVtJOfzkXOHSqDZQkSZJGwbDB/J6quhnYLMlmVXUOzQWd40qyOMmi9vlWNGF+0ukvkiRJ0igaao45cGuSbYHzgZOT3AjcO8k2DwM+0c4z3wz4TFV9eeObKkmSJM1fwwbz5wJ3Aq8HXgI8GHjHRBtU1Q+AR29S6yRJkqQRMexUFgCq6l7gAuBaYG0XDZIkSZJG0bDB/HxgyyS7Av8GHAl8vKtGSZIkSaNm2GCe9l7mLwD+oaqeD+zbXbMkSZKk0TJ0ME/yBJr55ae3y4adny5JkiRpEsMG82OAtwCfr6pLkjwcOKe7ZkmSJEmjZahR76o6j+YTP9d9fzXwZ101SpIkSRo1EwbzJO+rqmOSfAmoseur6rDOWiZJkiSNkMlGzP+5/fqerhsiSZIkjbIJg3lVrWq/npdkcfv8pplomCRJkjRKJrz4M423J1kDXA78Z5KbkvzfmWmeJEmSNBomuyvLMcCBwPKqekhV7QA8Djgwyes7b50kSZI0IiYL5i8HXlxV16xb0N6R5aXtOkmSJEnTYLJgvkVVrRm7sJ1nvkU3TZIkSZJGz2TB/O6NXCdJkiRpCia7XeJ+SdZuYHmALTtojyRJkjSSJrtd4uYz1RBJkiRplE02lUWSJEnSDDCYS5IkST1gMJckSZJ6wGAuSZIk9YDBXJIkSeqBzoJ5kt2TnJPksiSXJDm6q7okSZKkuW6y+5hvinuBP6+q7yTZDliV5KyqurTDOiVJkqQ5qbMR86r6aVV9p31+G3AZsGtX9UmSJElzWZcj5r+SZCnwaOBbG1i3AlgBsHDRzjPRnJGy/PizH7DswmMPmoWWaJ2p9sl45aezb2diX/4szg/276abL6/Vho4DZu5YZvN13Ji650u/q1udX/yZZFvgc8AxVbV27PqqWllVy6pq2YJtFnXdHEmSJKmXOg3mSbagCeUnV9VpXdYlSZIkzWVd3pUlwEeAy6rqvV3VI0mSJM0HXY6YHwi8DDgoyffaxzM7rE+SJEmaszq7+LOqvg6kq/1LkiRJ84mf/ClJkiT1gMFckiRJ6gGDuSRJktQDBnNJkiSpBwzmkiRJUg8YzCVJkqQeMJhLkiRJPWAwlyRJknrAYC5JkiT1gMFckiRJ6gGDuSRJktQDBnNJkiSpBwzmkiRJUg8YzCVJkqQeMJhLkiRJPWAwlyRJknrAYC5JkiT1gMFckiRJ6gGDuSRJktQDBnNJkiSpBwzmkiRJUg90FsyTfDTJjUku7qoOSZIkab7ocsT848ChHe5fkiRJmjc6C+ZVdT7wi672L0mSJM0nzjGXJEmSemDBbDcgyQpgBcDCRTt3Usfy489+wLILjz2ok7rUjensQ38epmYmXq/x6pjq8on2NZ2mWsdca+9M2JjXZGOOYzr7qmsbqruL+qfz9Z0u03mOTOfvjT6eO9C/n9P59prM5u+NWR8xr6qVVbWsqpYt2GbRbDdHkiRJmhWzHswlSZIkdXu7xE8BFwD7JFmd5FVd1SVJkiTNdZ3NMa+qF3e1b0mSJGm+cSqLJEmS1AMGc0mSJKkHDOaSJElSDxjMJUmSpB4wmEuSJEk9YDCXJEmSesBgLkmSJPWAwVySJEnqAYO5JEmS1AMGc0mSJKkHDOaSJElSDxjMJUmSpB4wmEuSJEk9YDCXJEmSesBgLkmSJPWAwVySJEnqAYO5JEmS1AMGc0mSJKkHDOaSJElSDxjMJUmSpB4wmEuSJEk90GkwT3JokiuSXJXkzV3WJUmSJM1lnQXzJJsD7weeAewLvDjJvl3VJ0mSJM1lXY6YHwBcVVVXV9XdwKeB53ZYnyRJkjRndRnMdwWuG/h+dbtMkiRJ0hipqm52nPwhcEhV/XH7/cuAA6rqdWPKrQBWtN/uA1zRSYP6YSdgzWw3QjPOfh899vlost9Hk/0+mqba73tU1eLJCi3Y+PZMajWw+8D3uwE3jC1UVSuBlR22ozeSXFRVy2a7HZpZ9vvosc9Hk/0+muz30dRVv3c5leVCYK8keyZZCLwI+GKH9UmSJElzVmcj5lV1b5KjgDOBzYGPVtUlXdUnSZIkzWVdTmWhqs4AzuiyjjlmJKbs6AHs99Fjn48m+3002e+jqZN+7+ziT0mSJEnD6/STPyVJkiQNx2C+iZJ8NMmNSS4eWLZ/km8m+V6Si5IcMLDud9vllyQ5b2D5oUmuSHJVkjfP9HFoeFPp8yQPTvKlJN9v+/zIgW2OSHJl+zhiNo5Fwxun3/dLckGSH7b9vP3Aure05/MVSQ4ZWO65PodMpd+T/F6SVe3yVUkOGtjmse3yq5L8fZLMxvFoclM919v1S5LcnuQNA8s81+eQjfgd/9vtukva9Vu2yzftXK8qH5vwAH4HeAxw8cCyrwHPaJ8/Ezi3fb4IuBRY0n6/c/t1c+BHwMOBhcD3gX1n+9h8TEufvxV4V/t8MfCLto93BK5uv+7QPt9hto/Nx5T7/ULgKe3zVwLvbJ/v257HDwL2bM/vzT3X595jiv3+aGCX9vmjgOsHtvk28AQgwFfW/b7w0b/HVPp8YP3ngM8Cb2i/91yfY48pnusLgB8A+7XfPwTYvH2+See6I+abqKrOpwlbv7YYWPeu6sGsv3/7HwGnVdVP2m1vbJcfAFxVVVdX1d3Ap4HndtpwbbQp9nkB27XvmLdtt7sXOAQ4q6p+UVW3AGcBh3bddm28cfp9H+D89vlZwO+3z58LfLqq7qqqa4CraM5zz/U5Zir9XlXfrap15/4lwJZJHpTkYcD2VXVBNX+5/x/wvO5br40xxXOdJM+jGVwZvPOc5/ocM8V+Pxj4QVV9v9325qq6bzrOdYN5N44Bjk9yHfAe4C3t8r2BHZKc2/6b8+Xt8l2B6wa2X90u09wxXp+fCPwmTVD/IXB0Vd2PfT5fXAwc1j7/Q9Z/qNp4/Wu/zw/j9fug3we+W1V30fTx6oF19vvcs8E+T7IN8CbguDHlPdfnh/HO9b2BSnJmku8keWO7fJPPdYN5N14DvL6qdgdeD3ykXb4AeCzwLJoR07cl2Zvm3x1jebucuWW8Pj8E+B6wC7A/cGI7R80+nx9eCbw2ySpgO+Dudvl4/Wu/zw/j9TsASX4LeBfwp+sWbWAf9vvcMl6fHwf8XVXdPqa8fT4/jNfvC4AnAS9pvz4/ydOYhn7v9D7mI+wI4Oj2+WeBD7fPVwNrquoO4I4k5wP7tcsHR1x2Y/1UCM0N4/X5kcDftP/SuirJNcBv0PT57w5svxtw7oy0VNOmqi6n+Zcm7ZvsZ7WrJjqnPdfnuAn6nSS7AZ8HXl5VP2oXr6bp63Xs9zlmgj5/HPAHSd5Ncx3Z/Ul+CazCc33Om+R3/HlVtaZddwbN/PST2MRz3RHzbtwAPKV9fhBwZfv8C8CTkyxIsjXNCX0ZzcUFeyXZM8lC4EXAF2e4zdo04/X5T4CnASR5KM18tatpPhH34CQ7JNmB5sQ/c0ZbrE2WZOf262bAXwAfbFd9EXhRO794T2AvmguCPNfngfH6Pcki4HTgLVX1jXXlq+qnwG1JHt9eb/Jymr8HmiPG6/OqenJVLa2qpcD7gL+uqhPxXJ8XJvgdfybw20m2TrKA5u//pdNxrjtivomSfIpm5HOnJKuBvwT+BDih7axfAisAquqyJF+luZL3fuDDVXVxu5+jaDp6c+CjVXXJ2LrUD1Ppc+CdwMeT/JDmX1xvGniH/U6aX94A76iqsRedqEfG6fdtk7y2LXIa8DGAqrokyWdo7sJ0L/Daqrqv3Y/n+hwylX4HjgIeSTNN8W3tsoPbC/1fA3wc2IrmTg1fmZED0JRNsc83qKru9VyfW6b4O/6WJO+l+RtewBlVdXpbbpPOdT/5U5IkSeoBp7JIkiRJPWAwlyRJknrAYC5JkiT1gMFckiRJ6gGDuSRJktQDBnNJmifS+HqSZwwsO7y9Taskqee8XaIkzSNJHkXz6bOPprl/8veAQwc+hXJj9rmgqu6dpiZKksZhMJekeab9ePA7gG2A26rqnUmOAF4LLAT+Aziqqu5PspLmo6S3Ak6pqne0+1gNfAg4FHhfVX12Fg5FkkaKn/wpSfPPccB3gLuBZe0o+vOBJ7afSLiS5iPCPwm8uap+0X5q7TlJTq2qS9v93FFVB87GAUjSKDKYS9I8U1V3JDkFuL2q7krydGA5cFESaEbHr2uLvzjJq2j+HuwC7AusC+anzGzLJWm0GcwlaX66v30ABPhoVb1tsECSvYCjgQOq6tYkJwFbDhS5Y0ZaKkkCvCuLJI2CfwUOT7ITQJKHJFkCbA/cBqxN8jDgkFlsoySNPEfMJWmeq6ofJjkO+NckmwH3AK8GLqKZtnIxcDXwjdlrpSTJu7JIkiRJPeBUFkmSJKkHDOaSJElSDxjMJUmSpB4wmEuSJEk9YDCXJEmSesBgLkmSJPWAwVySJEnqAYO5JEmS1AP/H5YM+/zQ3OMzAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "\n", "plt.figure(figsize=(12.5, 3.5))\n", "n_count_data = len(disasters_array)\n", "plt.bar(np.arange(1851, 1962), disasters_array, color=\"#348ABD\")\n", "plt.xlabel(\"Year\")\n", "plt.ylabel(\"Disasters\")\n", "plt.title(\"UK coal mining disasters, 1851-1962\")\n", "plt.xlim(1851, 1962);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are going to use [Poisson](http://en.wikipedia.org/wiki/Poisson_distribution) random variables for this type of count data. Denoting year $i$'s accident count by $y_i$, \n", "\n", "$$ y_i \\sim \\text{Poisson}(\\lambda) $$\n", "\n", "For those unfamiliar, Poisson random variables look like this:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 4, figsize=(18,4), sharex=True, sharey=True)\n", "for i,l in enumerate([1, 5, 12, 25]):\n", " axes[i].hist(np.random.poisson(l, 1000), histtype=\"stepfilled\")\n", " axes[i].annotate(r'$\\lambda$=%i' % l, xy=(1, 1), xytext=(30, 350), fontsize=20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The modeling problem revolves around estimating the values of the $\\lambda$ parameters. Looking at the time series above, it appears that the rate declines later in the time series.\n", "\n", "A ***changepoint model*** identifies a point (year) during the observation period (call it $\\tau$) after which the parameter $\\lambda$ drops to a lower value. So we are estimating two $\\lambda$ parameters: one for the early period and another for the late period.\n", "\n", "$$\n", "\\lambda = \n", "\\begin{cases}\n", "\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", "\\lambda_2 & \\text{if } t \\ge \\tau\n", "\\end{cases}\n", "$$\n", "\n", "We need to assign prior probabilities to both $\\lambda$ parameters. The [gamma distribution](http://en.wikipedia.org/wiki/Gamma_distribution) not only provides a continuous density function for positive numbers, but it is also **conjugate** with the Poisson sampling distribution. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, axes = plt.subplots(1, 4, figsize=(18,4))\n", "for i,p in enumerate([(1, 10), (1, 100), (10, 10), (0.1, 100)]):\n", " axes[i].hist(np.random.gamma(*p, size=1000), histtype=\"stepfilled\")\n", " axes[i].set_xlabel(r'$\\alpha$=%i, $\\beta$=%i' % (p[0], p[1]), fontsize=18)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will specify suitably vague hyperparameters $\\alpha$ and $\\beta$ for both priors.\n", "\n", "\\begin{align}\n", "&\\lambda_1 \\sim \\text{Gamma}( 1, 10 ) \\\\\\\n", "&\\lambda_2 \\sim \\text{Gamma}( 1, 10 )\n", "\\end{align}\n", "\n", "Since we do not have any intuition about the location of the changepoint (prior to viewing the data), we will assign a discrete uniform prior over all years 1851-1962.\n", "\n", "\\begin{align}\n", "& \\tau \\sim \\text{DiscreteUniform(1851,1962) }\\\\\\\\\n", "& \\Rightarrow P( \\tau = k ) = \\frac{1}{111}\n", "\\end{align}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementing Gibbs sampling\n", "\n", "We are interested in estimating the joint posterior of $\\lambda_1, \\lambda_2$ and $\\tau$ given the array of annnual disaster counts $\\mathbf{y}$. This gives:\n", "\n", "$$\n", " P( \\lambda_1, \\lambda_2, \\tau | \\mathbf{y} ) \\propto P(\\mathbf{y} | \\lambda_1, \\lambda_2, \\tau ) P(\\lambda_1, \\lambda_2, \\tau) \n", "$$\n", "\n", "To employ Gibbs sampling, we need to factor the joint posterior into the product of conditional expressions:\n", "\n", "$$\n", " P( \\lambda_1, \\lambda_2, \\tau | \\mathbf{y} ) \\propto P(y_{t<\\tau} | \\lambda_1, \\tau) P(y_{t\\ge \\tau} | \\lambda_2, \\tau) P(\\lambda_1) P(\\lambda_2) P(\\tau)\n", "$$\n", "\n", "which we have specified as:\n", "\n", "$$\\begin{aligned}\n", "P( \\lambda_1, \\lambda_2, \\tau | \\mathbf{y} ) &\\propto \\left[\\prod_{t=1851}^{\\tau} \\text{Poi}(y_t|\\lambda_1) \\prod_{t=\\tau+1}^{1962} \\text{Poi}(y_t|\\lambda_2) \\right] \\text{Gamma}(\\lambda_1|\\alpha,\\beta) \\text{Gamma}(\\lambda_2|\\alpha, \\beta) \\frac{1}{111} \\\\\n", "&\\propto \\left[\\prod_{t=1851}^{\\tau} e^{-\\lambda_1}\\lambda_1^{y_t} \\prod_{t=\\tau+1}^{1962} e^{-\\lambda_2} \\lambda_2^{y_t} \\right] \\lambda_1^{\\alpha-1} e^{-\\beta\\lambda_1} \\lambda_2^{\\alpha-1} e^{-\\beta\\lambda_2} \\\\\n", "&\\propto \\lambda_1^{\\sum_{t=1851}^{\\tau} y_t +\\alpha-1} e^{-(\\beta+\\tau)\\lambda_1} \\lambda_2^{\\sum_{t=\\tau+1}^{1962} y_i + \\alpha-1} e^{-\\beta\\lambda_2}\n", "\\end{aligned}$$\n", "\n", "So, the full conditionals are known, and critically for Gibbs, can easily be sampled from.\n", "\n", "$$\\lambda_1 \\sim \\text{Gamma}(\\sum_{t=1851}^{\\tau} y_t +\\alpha, \\tau+\\beta)$$\n", "$$\\lambda_2 \\sim \\text{Gamma}(\\sum_{t=\\tau+1}^{1962} y_i + \\alpha, 1962-\\tau+\\beta)$$\n", "$$\\tau \\sim \\text{Categorical}\\left( \\frac{\\lambda_1^{\\sum_{t=1851}^{\\tau} y_t +\\alpha-1} e^{-(\\beta+\\tau)\\lambda_1} \\lambda_2^{\\sum_{t=\\tau+1}^{1962} y_i + \\alpha-1} e^{-\\beta\\lambda_2}}{\\sum_{k=1851}^{1962} \\lambda_1^{\\sum_{t=1851}^{\\tau} y_t +\\alpha-1} e^{-(\\beta+\\tau)\\lambda_1} \\lambda_2^{\\sum_{t=\\tau+1}^{1962} y_i + \\alpha-1} e^{-\\beta\\lambda_2}} \\right)$$\n", "\n", "Implementing this in Python requires random number generators for both the gamma and discrete uniform distributions. We can leverage NumPy for this:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Function to draw random gamma variate\n", "rgamma = np.random.gamma\n", "\n", "def rcategorical(probs, n=None):\n", " # Function to draw random categorical variate\n", " return np.array(probs).cumsum().searchsorted(np.random.sample(n))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, in order to generate probabilities for the conditional posterior of $\\tau$, we need the kernel of the gamma density:\n", "\n", "\\\\[\\lambda^{\\alpha-1} e^{-\\beta \\lambda}\\\\]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "dgamma = lambda lam, a, b: lam**(a-1) * np.exp(-b*lam)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Diffuse hyperpriors for the gamma priors on $\\lambda_1, \\lambda_2$:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "alpha, beta = 1., 10" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For computational efficiency, it is best to pre-allocate memory to store the sampled values. We need 3 arrays, each with length equal to the number of iterations we plan to run:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "# Specify number of iterations\n", "n_iterations = 1000\n", "\n", "# Initialize trace of samples\n", "lambda1, lambda2, tau = np.zeros((3, n_iterations+1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The penultimate step initializes the model paramters to arbitrary values:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "lambda1[0] = 6\n", "lambda2[0] = 2\n", "tau[0] = 50" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.68361227, 0.57781372, 0.56232418, 0.52190586, 0.5420745 ,\n", " 0.58513557, 0.58869045, 0.60488907, 0.62667459, 0.42310934])" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#disasters_array[tau[0]:].sum()+alpha\n", "np.random.gamma(57,0.01,10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can run the Gibbs sampler." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "# Sample from conditionals\n", "for i in range(n_iterations):\n", " # Sample early mean\n", " lambda1[i+1] = rgamma(disasters_array[:int(tau[i])].sum() + alpha, 1./(tau[i] + beta))\n", " # Sample late mean\n", " lambda2[i+1] = rgamma(disasters_array[int(tau[i]):].sum() + alpha, 1./(n_count_data - tau[i] + beta))\n", " # Sample changepoint: first calculate probabilities (conditional)\n", " p = np.array([dgamma(lambda1[i+1], disasters_array[:t].sum() + alpha, t + beta)*\n", " dgamma(lambda2[i+1], \n", " disasters_array[t:].sum() + alpha, \n", " n_count_data - t + beta)\n", " for t in range(n_count_data)])\n", " # ... then draw sample\n", " tau[i+1] = rcategorical(p/p.sum())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plotting the trace and histogram of the samples reveals the marginal posteriors of each parameter in the model." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "param_dict = {r'$\\lambda_1$':lambda1, r'$\\lambda_2$':lambda2, r'$\\tau$':tau}\n", "for p in param_dict:\n", " fig, axes = plt.subplots(1, 2, figsize=(10, 4))\n", " axes[0].plot(param_dict[p][100:])\n", " axes[0].set_ylabel(p, fontsize=20, rotation=0)\n", " axes[1].hist(param_dict[p][int(n_iterations/2):])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Metropolis-Hastings Algorithm\n", "\n", "The key to success in applying the Gibbs sampler to the estimation of Bayesian posteriors is being able to specify the form of the complete conditionals of\n", "${\\bf \\theta}$, because the algorithm cannot be implemented without them. In practice, the posterior conditionals cannot always be neatly specified. \n", "\n", "\n", "Taking a different approach, the Metropolis-Hastings algorithm generates ***candidate*** state transitions from an alternate distribution, and *accepts* or *rejects* each candidate probabilistically.\n", "\n", "Let us first consider a simple Metropolis-Hastings algorithm for a single parameter, $\\theta$. We will use a standard sampling distribution, referred to as the *proposal distribution*, to produce candidate variables $q_t(\\theta^{\\prime} | \\theta)$. That is, the generated value, $\\theta^{\\prime}$, is a *possible* next value for\n", "$\\theta$ at step $t+1$. We also need to be able to calculate the probability of moving back to the original value from the candidate, or\n", "$q_t(\\theta | \\theta^{\\prime})$. These probabilistic ingredients are used to define an *acceptance ratio*:\n", "\n", "$$\\begin{gathered}\n", "\\begin{split}a(\\theta^{\\prime},\\theta) = \\frac{q_t(\\theta^{\\prime} | \\theta) \\pi(\\theta^{\\prime})}{q_t(\\theta | \\theta^{\\prime}) \\pi(\\theta)}\\end{split}\\notag\\\\\\begin{split}\\end{split}\\notag\\end{gathered}$$\n", "\n", "The value of $\\theta^{(t+1)}$ is then determined by:\n", "\n", "$$\\theta^{(t+1)} = \\left\\{\\begin{array}{l@{\\quad \\mbox{with prob.} \\quad}l}\\theta^{\\prime} & \\text{with probability } \\min(a(\\theta^{\\prime},\\theta^{(t)}),1) \\\\ \\theta^{(t)} & \\text{with probability } 1 - \\min(a(\\theta^{\\prime},\\theta^{(t)}),1) \\end{array}\\right.$$\n", "\n", "This transition kernel implies that movement is not guaranteed at every step. It only occurs if the suggested transition is likely based on the acceptance ratio.\n", "\n", "A single iteration of the Metropolis-Hastings algorithm proceeds as follows:\n", "\n", "1. Sample $\\theta^{\\prime}$ from $q(\\theta^{\\prime} | \\theta^{(t)})$.\n", "\n", "2. Generate a Uniform[0,1] random variate $u$.\n", "\n", "3. If $a(\\theta^{\\prime},\\theta) > u$ then\n", " $\\theta^{(t+1)} = \\theta^{\\prime}$, otherwise\n", " $\\theta^{(t+1)} = \\theta^{(t)}$.\n", "\n", "The original form of the algorithm specified by Metropolis required that\n", "$q_t(\\theta^{\\prime} | \\theta) = q_t(\\theta | \\theta^{\\prime})$, which reduces $a(\\theta^{\\prime},\\theta)$ to\n", "$\\pi(\\theta^{\\prime})/\\pi(\\theta)$, but this is not necessary. In either case, the state moves to high-density points in the distribution with high probability, and to low-density points with low probability. After convergence, the Metropolis-Hastings algorithm describes the full target posterior density, so all points are recurrent.\n", "\n", "### Random-walk Metropolis-Hastings\n", "\n", "A practical implementation of the Metropolis-Hastings algorithm makes use of a random-walk proposal.\n", "Recall that a random walk is a Markov chain that evolves according to:\n", "\n", "$$\n", "\\theta^{(t+1)} = \\theta^{(t)} + \\epsilon_t \\\\\n", "\\epsilon_t \\sim f(\\phi)\n", "$$\n", "\n", "As applied to the MCMC sampling, the random walk is used as a proposal distribution, whereby dependent proposals are generated according to:\n", "\n", "$$\\begin{gathered}\n", "\\begin{split}q(\\theta^{\\prime} | \\theta^{(t)}) = f(\\theta^{\\prime} - \\theta^{(t)}) = \\theta^{(t)} + \\epsilon_t\\end{split}\\notag\\\\\\begin{split}\\end{split}\\notag\\end{gathered}$$\n", "\n", "Generally, the density generating $\\epsilon_t$ is symmetric about zero,\n", "resulting in a symmetric chain. Chain symmetry implies that\n", "$q(\\theta^{\\prime} | \\theta^{(t)}) = q(\\theta^{(t)} | \\theta^{\\prime})$,\n", "which reduces the Metropolis-Hastings acceptance ratio to:\n", "\n", "$$\\begin{gathered}\n", "\\begin{split}a(\\theta^{\\prime},\\theta) = \\frac{\\pi(\\theta^{\\prime})}{\\pi(\\theta)}\\end{split}\\notag\\\\\\begin{split}\\end{split}\\notag\\end{gathered}$$\n", "\n", "The choice of the random walk distribution for $\\epsilon_t$ is frequently a normal or Student’s $t$ density, but it may be any distribution that generates an irreducible proposal chain.\n", "\n", "An important consideration is the specification of the **scale parameter** for the random walk error distribution. Large values produce random walk steps that are highly exploratory, but tend to produce proposal values in the tails of the target distribution, potentially resulting in very small acceptance rates. Conversely, small values tend to be accepted more frequently, since they tend to produce proposals close to the current parameter value, but may result in chains that ***mix*** very slowly.\n", "\n", "Some simulation studies suggest optimal acceptance rates in the range of 20-50%. It is often worthwhile to optimize the proposal variance by iteratively adjusting its value, according to observed acceptance rates early in the MCMC simulation ." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example: Linear model estimation\n", "\n", "This very simple dataset is a selection of real estate prices \\\\(p\\\\), with the associated age \\\\(a\\\\) of each house. We wish to estimate a simple linear relationship between the two variables, using the Metropolis-Hastings algorithm.\n", "\n", "**Linear model**:\n", "\n", "$$\\mu_i = \\beta_0 + \\beta_1 a_i$$\n", "\n", "**Sampling distribution**:\n", "\n", "$$p_i \\sim N(\\mu_i, \\tau)$$\n", "\n", "**Prior distributions**:\n", "\n", "$$\\begin{aligned}\n", "& \\beta_i \\sim N(0, 10000) \\cr\n", "& \\tau \\sim \\text{Gamma}(0.001, 0.001)\n", "\\end{aligned}$$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "age = np.array([13, 14, 14,12, 9, 15, 10, 14, 9, 14, 13, 12, 9, 10, 15, 11, \n", " 15, 11, 7, 13, 13, 10, 9, 6, 11, 15, 13, 10, 9, 9, 15, 14, \n", " 14, 10, 14, 11, 13, 14, 10])\n", "\n", "price = np.array([2950, 2300, 3900, 2800, 5000, 2999, 3950, 2995, 4500, 2800, \n", " 1990, 3500, 5100, 3900, 2900, 4950, 2000, 3400, 8999, 4000, \n", " 2950, 3250, 3950, 4600, 4500, 1600, 3900, 4200, 6500, 3500, \n", " 2999, 2600, 3250, 2500, 2400, 3990, 4600, 450,4700])/1000." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To avoid numerical underflow issues, we typically work with log-transformed likelihoods, so the joint posterior can be calculated as sums of log-probabilities and log-likelihoods.\n", "\n", "This function calculates the joint log-posterior, conditional on values for each parameter:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "from scipy.stats import distributions\n", "dgamma = distributions.gamma.logpdf\n", "dnorm = distributions.norm.logpdf\n", "\n", "def calc_posterior(a, b, t, y=price, x=age):\n", " # Calculate joint posterior, given values for a, b and t\n", "\n", " # Priors on a,b\n", " logp = dnorm(a, 0, 10000) + dnorm(b, 0, 10000)\n", " # Prior on t\n", " logp += dgamma(t, 0.001, 0.001)\n", " # Calculate mu\n", " mu = a + b*x\n", " # Data likelihood\n", " logp += sum(dnorm(y, mu, t**-2))\n", " \n", " return logp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `metropolis` function implements a simple random-walk Metropolis-Hastings sampler for this problem. It accepts as arguments:\n", "\n", "- the number of iterations to run\n", "- initial values for the unknown parameters\n", "- the variance parameter of the proposal distribution (normal)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "rnorm = np.random.normal\n", "runif = np.random.rand\n", "\n", "def metropolis(n_iterations, initial_values, prop_var=1):\n", "\n", " n_params = len(initial_values)\n", " \n", " # Initial proposal standard deviations\n", " prop_sd = [prop_var]*n_params\n", " \n", " # Initialize trace for parameters\n", " trace = np.empty((n_iterations+1, n_params))\n", " \n", " # Set initial values\n", " trace[0] = initial_values\n", " \n", " # Calculate joint posterior for initial values\n", " current_log_prob = calc_posterior(*trace[0])\n", " \n", " # Initialize acceptance counts\n", " accepted = [0]*n_params\n", " \n", " for i in range(n_iterations):\n", " \n", " if not i%1000: print ('Iteration', i)\n", " \n", " # Grab current parameter values\n", " current_params = trace[i]\n", " \n", " for j in range(n_params):\n", " \n", " # Get current value for parameter j\n", " p = trace[i].copy()\n", " \n", " # Propose new value\n", " if j==2:\n", " # Ensure tau is positive\n", " theta = np.exp(rnorm(np.log(current_params[j]), prop_sd[j]))\n", " else:\n", " theta = rnorm(current_params[j], prop_sd[j])\n", " \n", " # Insert new value \n", " p[j] = theta\n", " \n", " # Calculate log posterior with proposed value\n", " proposed_log_prob = calc_posterior(*p)\n", " \n", " # Log-acceptance rate\n", " alpha = proposed_log_prob - current_log_prob\n", " \n", " # Sample a uniform random variate\n", " u = runif()\n", " \n", " # Test proposed value\n", " if np.log(u) < alpha:\n", " # Accept\n", " trace[i+1,j] = theta\n", " current_log_prob = proposed_log_prob\n", " accepted[j] += 1\n", " else:\n", " # Reject\n", " trace[i+1,j] = trace[i,j]\n", " \n", " return trace, accepted" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's run the MH algorithm with a very small proposal variance:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration 0\n", "Iteration 1000\n", "Iteration 2000\n", "Iteration 3000\n", "Iteration 4000\n", "Iteration 5000\n", "Iteration 6000\n", "Iteration 7000\n", "Iteration 8000\n", "Iteration 9000\n" ] } ], "source": [ "n_iter = 10000\n", "trace, acc = metropolis(n_iter, (1,0,1), 0.001)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the acceptance rate is way too high:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.979 , 0.9694, 0.9605])" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array(acc, float)/n_iter" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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Loz/eNIS563fSoVU2AC2zE/PHcX4wEW+ZdV8c4JF/LkrIuUUaK3d/CHioQvUqYHCMtgXA11IRl4g0fLqzlkYdWmVz4XFdEn7ebu1bMOmuc8Llcx+bRnFp+RMYPRIVERGpP5SsNVADqpmv7buvfsr2fYdSGI2IiIgcLiVrjdCURVv41gsz0x2GiIiIxEHJWiMVOV2IiIiIZC4law1Y0yZa3UZERKS+U7LWgF143BFV7tMqhSIiIvWDkrUG7N6L+1a5zx3WbN+fwmhERETkcChZa8COO7J8ROjnP72Ez8ZczBFtmofrzn/8/TREJSIiIrWhSXEbuCWPXIo7tMjOAmDGj4bR6/5JaY5KRERE4qVkrYHLaZYVVTZ1VhMREalX9BhUREREJIMpWWuEVvx8BG1zQjdV9x8qTnM0IiIiUh0la41Q06wm3Hx2bwD2FihZExERyWRK1hqpXrmtAJi9dkeaIxEREZHqKFlrpEpLHYA7X5ub5khERESkOhoN2kjlNCvP0z9e+QUndm/HfePn8+uvnRKe5kNERJIvb/TEpJ17zdjLknZuSZ2k3lkzs0vNbKmZrTCz0TH2H21mU83sMzN738y6R+y73syWB6/rkxlnY3Ri9/bh7RtemsnNL89i0oLNDPv1++kLSkRERCpJWrJmZlnAM8AIYABwjZkNqNDsceAVdz8JeBh4NDi2I/AQMAQYDDxkZh2SFWtj1K19i/D2oeJSZqwO9V07oVu7dIUkIiIiMSTzztpgYIW7r3L3QuB1YFSFNgOAqcH2tIj9lwBT3H2Hu+8EpgCXJjFWCRzZLifdIYiIiEiEZPZZ6wasjyjnE7pTFmk+cBXwFPAVoI2Zdari2G4V38DMbgVuBejZs2fCAm8senVuxeoKi7lPXriZBy4bQHZTjT0REZGqqa9d6iTzf+RY6xp5hfIPgPPMbC5wHrABKI7zWNz9WXcf5O6DcnNz6xpvozPtB+dz36X9ouq27DnENc99kqaIREREpKJk3lnLB3pElLsDGyMbuPtG4EoAM2sNXOXuu80sHzi/wrHvJzHWRuvAoZJKdXPW7kxDJCIiIhJLMu+szQL6mFkvM8sGrgYmRDYws85mVhbD/cCLwfZk4GIz6xAMLLg4qJMEO1RcOVkD+N17y1MciYiIiMQSV7JmZs3N7Btm9iMze7DsVd0x7l4M3EkoyVoMvOHuC83sYTP7ctDsfGCpmS0DugA/D47dATxCKOGbBTwc1EmCLd2yD4Chx3aKqn/8nWXpCEdEREQqiPcx6FvAbmAOcCjek7v7JGBShboHI7bHA+OrOPZFyu+0SZKsCQYY7D5YVGnfhl0Ho6b4EBERkdSL9zFod3f/L3f/lbv/uuyV1MgkJZ68+hQA7h/Rn/P7RQ/SGDr2Pb7+h4/TEZaIiIgE4k3WppvZiUmNRNLi1J4dWP7zEQw9tjO/+fop5LZpHrV/5mo9fRYREUmneJO1s4E5wdJRn5nZAjP7LJmBSeo0ywr9NejYKpsP77ug0n73SrOmiIiISIrEm6yNAPoQGpX5JeDy4Kc0MDnNsrhoQJeoun4/+Rdrv9jPfePn89a8DWmKTEREpHGKa4CBu681s5OBc4KqD919fvLCknRqmZ0VVS4sLuUbz81gw66DvDE7n1GnVFpMQkRERJIk3qk77gZeBY4IXn8ys+8lMzBJn998/ZRKdRt2HQxva9JcaYzMrL2ZjTezJWa22MzONLOOZjbFzJYHPzsEbc3MnjazFUHXkVPTHb+I1F/xPga9GRji7g8GU2+cAXw7eWFJOmU1ibXaVzlNmCuN1FPAv9z9OOBkQvNHjgamunsfYGpQhvKuI30IrV/8+9SHKyINRbzJmgGRU92XEHv9TmkgmlezkPuBwtirHog0VGbWFjgXeAHA3QvdfRcwChgXNBsHXBFsjwJe8ZBPgPZmdlSKwxaRBiLeZO0lYIaZjTGzMcAnBF9a0jA9841TOb5r25j7ZqzeQVFJaYojEkmr3sA24CUzm2tmz5tZK6CLu28CCH4eEbTvBqyPOD4/qBMRqbW4kjV3/w1wI7AD2Anc6O5PJjMwSa/hA7ow8a5z+Ot3zoy5/0+frE1xRCJp1RQ4Ffi9uw8E9lP+yDOWWE8eKs2BY2a3mtlsM5u9bdu2xEQqIg1OtclacOsfM+sIrAH+BPwRWBvUSQN3el5HRp54ZKX6yQs3pyEakbTJB/LdfUZQHk8oedtS9ngz+Lk1on2PiOO7AxsrntTdn3X3Qe4+KDc3t+JuERGg5qk7XiM0p9ocon8rtKDcO0lxSQb532tPY/PuAnLbNOeYH4WWep2hlQ2kEXH3zWa23sz6uftSYBiwKHhdD4wNfr4VHDIBuNPMXgeGALvLHpdmurzRE5N27jVjL0vauUUasmqTNXe/PPjZKzXhSKY6sl0OAHMeGM5pP3uXq07tnuaIRFLue8CrZpYNrCLUNaQJ8IaZ3QysA74WtJ0EjARWAAeCtiIihyWuSXHNbCgwz933m9k3Cd3+f9Ld1yU1Osk47Vo0A6B7hxZpjkQktdx9HjAoxq5hMdo6cEfSgxKRRiHe0aC/Bw4EqxjcB6wl1HdNGpmmWU1o0SyLVdv2M3XxlnSHIyIi0uDFm6wVB78pjgKecvengDbJC0sy2cGiEibM38jN42anOxQREZEGL95kba+Z3Q98E5hoZllAs+SFJfXFp+u09JSIiEgyxZus/RdwCLjZ3TcTmtzxsaRFJfXG5M83M3P1jqi1Q0VERCRx4hpgECRov4korwNeSVZQktnaNG/K3kPFAOTvPMjX//AxoGH5IiIiyVDTpLj/CX7uNbM9Ea+9ZrYnNSFKpslt2zy8PXFB+dRR05ZsjdVcRERE6qDaZM3dzw5+tnH3thGvNu4ee+FIafDeuC32ElQ3vjwrxZGIiIg0fHH1WTOzM8ysTUS5tZkNSV5Yksk6t27O6BHHpTsMERGRRqE286ztiygfCOqkkerZsWW6QxAREWkU4k3WLJhnDQB3LyXOwQnSMF16fOXF3S/op4WoRUREEi3eZG2Vmd1lZs2C192E1saTRqpJE6tUN23ptjREIiIi0rDFm6x9BzgL2ADkA0OAW5MVlNQvmrJDREQkeeKdZ20rcHWSY5EGIH/nAbp3UH82ERE5fHmjJybt3PXxBkO8o0H7mtlUM/s8KJ9kZg8kNzTJdK/eMoQfj+wfVbdwo6bfExERSaR4H4M+B9wPFAG4+2fEcafNzC41s6VmtsLMRsfY39PMppnZXDP7zMxGBvV5ZnbQzOYFr/8X/yVJqgw9tjPfPrd3VF2LZllpikZERKRhijdZa+nuMyvUFVd3QLDY+zPACGAAcI2ZDajQ7AHgDXcfSCj5+9+IfSvd/ZTg9Z0445Q0ueOCYwAoLR80LCIiIgkQb7K23cyOARzAzL4KbKr+EAYDK9x9lbsXAq8Doyq0caBsJYR2wMY445EMU9ZP7Yl3l6c5EhERkYYl3rnS7gCeBY4zsw3AauDaGo7pBqyPKJeNIo00BnjHzL4HtAKGR+zrZWZzgT3AA+7+YZyxShqcfWxnAHp1asmegiLa5jRLc0QiIiINQ4131sysCTDI3YcDucBx7n62u6+t6dAYdRWfkV0DvOzu3YGRwB+D99sE9Awej94LvGZmldYiNbNbzWy2mc3etk1zfKVTu5ah5Owf8zZy0ph30hyNiIhIw1FjshasVnBnsL3f3ffGee58oEdEuTuVH3PeDLwRnPtjIAfo7O6H3P2LoH4OsBLoGyO2Z919kLsPys3V7Pnp1Co7+iZtYXFpmiIRERFpWOLtszbFzH5gZj3MrGPZq4ZjZgF9zKyXmWUTGkAwoUKbdcAwADPrTyhZ22ZmucEABcysN9AHrZiQ0bIqrGjQ94G3KSgqSVM0IiIiDUe8fdZuIvQI8/YK9b1jtAXA3YvN7E5gMpAFvOjuC83sYWC2u08A/ht4zszuCc5/g7u7mZ0LPGxmxUAJ8B1331GrK5O023+omBxN5SEiIlIn8SZrAwglamcTSqo+BGqc+8zdJwGTKtQ9GLG9CBga47i/AX+LMzbJEF3b5bBxd0G4/My0lTz4pYqztYiIiEhtxPsYdBzQH3ga+G2wPS5ZQUn99OTVA6PK01duT1MkIiIiDUe8d9b6ufvJEeVpZjY/GQFJ/TW4V3Q3xq8P6lFFSxEREYlXvHfW5prZGWUFMxsCfJSckKSh2LK3oOZGIiIiUq1476wNAa4zs3VBuSew2MwWAO7uJyUlOql35jwwnJvGzWb++l384d+ruH9E/5oPEhFJgLzRE9MdgkhSxJusXZrUKKTB6NS6OX+97Uz6PvB2ukMRERFpEOJK1uJYrUAkLLtp+dP1wuLSqLKIiIjUjv4XlaT40sldgdDkuG/MWl9DaxEREamKkjVJiuH9jwhv3/e3z9IYiUjimFmWmc01s38G5V5mNsPMlpvZX4LVWjCz5kF5RbA/L51xi0j9pmRNkqJTq+ZR5Y27DqYpEpGEuhtYHFH+JfCEu/cBdhJa75jg5053PxZ4ImgnInJYlKxJUnRqnR1V3neoOE2RiCSGmXUHLgOeD8oGXAiMD5qMA64ItkdRPnH4eGBY0F5EpNbiHQ0qUisdW0Unaz+buJhXbhqcpmhEEuJJ4D6gTVDuBOxy97LfRPKBbsF2N2A9hNdJ3h2017IeklKazqRh0J01SYpOFZK1/B0H0hSJSN2Z2eXAVnefE1kdo6nHsS/yvLea2Wwzm71t27YERCoiDZGSNUmKpllNuOGsPB68PLSQ+8bd5X3WvvHcJ+SNnoh7pf+7RDLVUODLZrYGeJ3Q488ngfZmVvaEojuwMdjOB3oABPvbATsqntTdn3X3Qe4+KDc3N7lXICL1lpI1SZoxXz6e68/KA6CgqDRcP33lFwD0un8Sc9ZW+v9LJOO4+/3u3t3d84Crgffc/VpgGvDVoNn1wFvB9oSgTLD/PddvJyJymJSsSVJlNQk9DRpxwpEx9z81dUVC329vQRFPTFlGUUlpzY1F6u5/gHvNbAWhPmkvBPUvAJ2C+nuB0WmKT0QaAA0wkJR4+/PNvPTRar51xtFR9R8sS2w/nafeXc7z/1lNXueWDDq6IwA9Oras9XmWbdlLbuvmdKjQ907E3d8H3g+2VwGVRs64ewHwtZQGJiINlpI1SZmf/t8i5q/fRZvmTdmbpKk8vthfCMAz01ayYut8ANaMvaxW5yguKeXiJz44rGNFREQSTcmapNQ/5m2suVEdHNkuB4AVW/cd9jmO/bEWoRcRkcyhPmuSdP2PapvW9y+uRf+10tLoPuDqEy4iIummZE2S7tgjWle7f87anXV+j8LiUu79yzx+//7KSvu27TsU93lWbY++I3egsKTOsYmIiNSFkjVJulbZWZXq7h7WJ7w99u3FlfbXVt8H3ubNuRti7oucNqQmFW/C7SkoqktYIiIidaY+a5J091zUl70FxUxcsClcd+0ZPVm8aQ/vLNrCrDWHf2ctnqVUfj5xEc9ff3qN7W4ZN4v8ndELzm/cVcBR7VocdnwiIiJ1pTtrknRd2ubwzLWnMn30heG65k2z+NkVJ9TpvNX1RXvgsv7h7XcXb632PJ+u28lb8zbw7uKtLNm8F4CjO4Wm+7jq99P5+9z8OsUpIiJSF0rWJGW6tm/BVwaG1rlu0SyL3DbNw/u27imo1bnyRk+sctRm86ZNuOWc3rx+6xk1nudAYTFX/u907n59XlT9ref2Dm/XlOyJiIgkk5I1SanHv3YyC8ZcTHbTJpiVr3U9+BdT4z7H/82vevqPp64+hf/73tkADOnVMVw/KeIRbKQ3P43dz+3sYzuHt7ftiX+AgoiISKIpWZOUympitMlpVqdzfO/Pc2PW//32sxh1Sjf6dmkDEJUM3v7qpzGPWbhxd8z6ru3L+6nNXFN5/dLt+w6RN3oi01dujztuERGRw6FkTdJq5o+HAfDNM3rW+Vyn9Ghf62P+PHN9zPpmWdX/07jxpVkAfOO5GbV+TxERkdpQsiZpdUSb0IoD05Yc/hqhXdvl8MNL+kXdSauL444M3Zm74ay8cF1JxGS57s6CDbHvyImIiCSapu6QjLBh10H2FBTRtoZHpKWlTlYT47vnHcMPLulX43lvGtqLFz9aDcAl3ZF7AAAY+ElEQVTm3QWc8Wiob9ysHw+PGuBQ5h93DKVf8Bh1zJeP5+XpawDYdaCQTq1D7ce+vSTqmN0Hipifv4tz+nROWMIoIiJSJqnJmpldCjwFZAHPu/vYCvt7AuOA9kGb0e4+Kdh3P3AzUALc5e6TkxmrpN9JY96pceH0LXsLKCl1OrXOjuucD35pAJ1aZ/PY5KXhRA3gqanLWLl1f7j8zj3n0qJZFj06tow6fnCvjsxcvYPJC7ewZPMeXvl4baX3OPnhdwDo2bElH9x3QVxxiYiIxCtpyZqZZQHPABcB+cAsM5vg7osimj0AvOHuvzezAcAkIC/Yvho4HugKvGtmfd1da/80cmc++h5A+C5XPNrmVP5r/qdP1kWVywYlVHT7+ccwc/UOfvT3BTW+z7odB+KOSUREJF7J7LM2GFjh7qvcvRB4HRhVoY0DZat8twPK5mQYBbzu7ofcfTWwIjifNECv3jIkrnYfrSgfedmuRfwjSls1r/53ku+ef0yV+9rW4n0qem3GOk58aDLFJaVs33eIt+bFniZERESkOslM1roBkUPt8oO6SGOAb5pZPqG7at+rxbGY2a1mNtvMZm/bdvgd1CW9hkbMaVada58vH3lZUBT/TdaakrX/ufS4KvcdrGYh97/fflaV+4pKSvnR3xew91Axy7fuY9DP3uXu1+exdW/tJv8VERFJZrIWq6e1VyhfA7zs7t2BkcAfzaxJnMfi7s+6+yB3H5Sbm1vngCV9WmVn0bxp/H8du3eIf73ONjUka9UZHDGxbkVHtsupVFe2BFafiNUVRjz1YXj7wCE9yRcRkdpJZrKWD/SIKHen/DFnmZuBNwDc/WMgB+gc57HSgJzf7wiymlQ9krKwOHod0OO7tov73BXvrN0WsZRUTZplNWHlL0bG3Hdk28rJ2gfLq7/Du+9QcdzvLSIiAslN1mYBfcysl5llExowMKFCm3XAMAAz608oWdsWtLvazJqbWS+gDzAzibFKmk1csIkDhSXsryKZue2Ps8Pb/wyWk4pXdoU7dveP7M8jo46P+/iqksjIaTquDNY8venl2THbltl1oIgd+wvjfm8REZGkJWvuXgzcCUwGFhMa9bnQzB42sy8Hzf4b+LaZzQf+DNzgIQsJ3XFbBPwLuEMjQRuHPQVFUeWPV37BgcJipi0tv2PV78jYIzer0rFV+TQfZQvJf/OMo4HoBdtro+IUI+f1i+8x/DdfmMGpj0w5rPcUEZHGKanzrAVzpk2qUPdgxPYiYGgVx/4c+Hky45PMcU6fzny4fDvTlmwLT5Mx/6GLuea5T7jwuCPC7X5y+YAal4KqqEvbHD6+/0I+WvEFl590FBC6K1bTnG6R/vX9c9ixv5Av9hVydKeWlfZ3i1hLtGy1g++efww79hXyl9mVl7Ry90oT6N7+6hw27DzIW3fW7s6hiIg0bFrBQDJC786t+HD5dn733vJw3YHC0CPReet3heuG9z+i0rHxOKpdC756WvfDju+4I9vGrJ/8/XNZsnkPpx3dIVw3ZdEWAP5v/kb+8z8X8tNRx/POoi3cFbEA/YHCkkp96SYt2AyEVmloUk3/PREROXx5oycm7dy1uQlQG1obVDLCLeeEHkdeM7h8QfeCotCggrKkDUJ3yTJJvyPbMOqUbpgZdw/rA8B3/jQHgNZBMpbTLIvT8zpEHXf8Q9ELcuw6UN6PbfMeTe8hIiLllKxJRihbp/PXU5aF68rmOCtL2sZ8aQA5zbJSH1ycSj16dplrh5Qnni2bVb6Jve6L8hUPXp1RvqJC5KLxIiIiStYkI8SaY23k0x9GlTfsOpiqcA7LH/69Kqr81dPKZ59pE2PJqwt//X54++mp5Y9/DxUndizNl377n7hu+4986kNG/e4/CX1vERGpOyVrkhEqdraPZdveQymI5PD998V9o8otssvvAsbqg1Zc6uFJdA9FzCNXdiexrtyd3QeLWLBhNwCXPvlBlSs/HCgsZtGmPczP302p7uyJiGQUDTCQeqP/UbE7+WeKqwf35NG3l9TqmF9PWVZpuav8nQc5oVvNk/5+vmE3j01eyrPXnUbzppUfD/9l1npGv1m+AP2SzXs5/7H32byngA/vu4AeHctHtW7fW95nrvePJnHT0F48+KUBtboWkZoks2O3SEOmO2uScTpFzIsWqWwQQqZq16IZ7957Xo3tHvvqSeHtE2KsxFA2QKEml//2P/x72TbmrNkZVT9h/kbemreBqUu2VjqmbPDCOb+aFlVfVBp9N+/Fj1Yn/HGsiIgcHiVrkjHmPXgR1w7pyXv/fX7M/dUtR5UpenduxXl9c3n5xtMr7ft/3zyNU3q052uDevCHb50GQIk7HgxM6NCy2WG9Z8VHyHf9eS53vz4vPIVIPLbuqfyIedz0NYcVj4iIJJaSNckY7Vtm8/OvnEi7iKSlNut4ZoImTYxxNw3m/H6V54O79IQj+ccdoTmgyx5zrty6j/Fz8gG47sy8w37fwuJS8kZPrNVjpqFj3wtvX/PcJ5X2N4mjH6GIiCSfkjXJaFcM7Mb9I47j0StPTHcoCZUTjH59aupyfjj+MwDWfrE/vD9v9ERem7EuKqGqSkFRCZt2Vz9S9tdfO7lSXU2ja382cXGN791YmFkPM5tmZovNbKGZ3R3UdzSzKWa2PPjZIag3M3vazFaY2Wdmdmp6r0BE6jMla5KRJt51NhPuHEr/o9py23nHRE2W2xB0aFm5X94/5m2MKv/o7wvYsOtgeMRoVQqKSigsrr7NVVWs3vDMtBVMXVz+uPT+EcfFbCcUA//t7v2BM4A7zGwAMBqY6u59gKlBGWAE0Cd43Qr8PvUhi0hDoWRNMtLxXdtxUvf26Q4jaWJN5fHKTYNjtt1Sw5Ql2/YdYuPuqlc9OLl76JHrPcP7Vtr32OSl3Dxudrh823nHRLU78aHJ5I2eGO5X11i5+yZ3/zTY3gssBroBo4BxQbNxwBXB9ijgFQ/5BGhvZkelOGwRaSCUrImkycOjjo8qn3lMJ2b8aFildtc8W96fbOHG3Tz/4aqovmkPvrWQ61+cWeX7/OW2MwG4a9ixzPzRMPoc0brauO4e3ie8vfdQaKmv95duq/aYxsTM8oCBwAygi7tvglBCB5R1VuwGrI84LD+oq3iuW81stpnN3rZNn7GIxKZkTSRNrjszj4l3nU3HVtncecGxNMtqQpe2Ofzwkn5R7XYfLApvX/b0f+LuS/bvH57PjB8NCy/RZWYc0TaH68/Kq3Ws+TsP1NyoETCz1sDfgO+7+57qmsaoq3R70t2fdfdB7j4oNzc3UWGKSAOjSXFF0uj4ru349CcXRdXdccGxPDZ5abj8lYHdKC4pZeAjU2o838pfjOSL/YcoKCylZ6eWMdt884yjOT2vI5c8+UGV5znuyDYs2bw3XH7kn4u5ZnBPmmY13t/vzKwZoUTtVXd/M6jeYmZHufum4DFn2eR2+UCPiMO7A9GdEkVE4tR4v3lF6omXp6/h2B+/zd6C4hrbZjUxjmiTU2WiVqbfkW24+vQeUXVT7jk3vF02D1yZwpJSZlWYfLcxsdBkdi8Ai939NxG7JgDXB9vXA29F1F8XjAo9A9hd9rhURKS2lKyJZKDjuyZ/aa2xV50UXurqzdvPok+XNuF9R3dqxak9owd4FJcmZs3Semoo8C3gQjObF7xGAmOBi8xsOXBRUAaYBKwCVgDPAbenIWYRaSCUrIlkoL/cdiafjbm42jZzHhjOuX3r1s/pO+f15qPRF3Jqzw6V9t01rE9UedeB8r5zP/nH541qlKi7/8fdzd1PcvdTgtckd//C3Ye5e5/g546gvbv7He5+jLuf6O6za3oPEZGqKFkTyUCtmzelbU71y091at2cV24azJR7zuWEbm35z/9cUOv3MTO6tW8Rc9/5/Y5g9aMjw+VH/rkIgNXb9/PHT9YC8MHy7bV+TxERqR0layL1RPcOsZOqPl3a8M/vnUP3DtX3UzscZkbn1qEJfJs2MZ6ZtoILHn8/vP/PM9Yl/D1FRCSaRoOKZLCW2VkcKCzhh5f047Zze/P4O8s4t09nmjVN3e9Zsx+4iLzRE9m4uyBqlCrAvxZuTlkcIiKNlZI1kQz21h1D+feybdxyTmhB+9FaDkpEpNFRsiaSwfp0aRM1SjPTDO9/RM2NRESkTpSsiUittclpSsdW2bRurq8QEZFk0wADEanR89cN4tohPcPlvQXF5DTN4t3FW8kbPZGZq3ekMToRkYZNyZqI1Gj4gC78/CsncuPQvHDd0i172Rcs9H7f+PmHdd6S0sYxT5uISF3oGYaIxO3OC47lpY/WVKr/RsRdt5oUFJVw3E/+FS5/f3gfvj+8byLCExFpkJSsiUjcOrVuzmu3DKFPlzac/vN3w/W/mLSEy07qWuUEu5H+PDN6brYn313O94f3ZdW2ffTq3IrQMpxSnbzRE9MdgoikUFIfg5rZpWa21MxWmNnoGPufiFhnb5mZ7YrYVxKxb0Iy4xSR+J11bGdy2zSvtBzVRb/5d1zH//a9FVHlvl1aM33Fdi789b/5+9wNCYtTRKShSFqyZmZZwDPACGAAcI2ZDYhs4+73lK2zB/wWeDNi98GINfi+nKw4ReTw3HtRX+6JeHx5oLCEvNET+cO/V0a1Gzd9DTe+NBN3Z/76XezYXxi1v2v7FszP3w3A/PW7EBGRaMm8szYYWOHuq9y9EHgdGFVN+2uAPycxHhFJsLuH96lU9+jbS8LbewuKeGjCQqYt3Uav+ydxx2ufVmq/52ARf/x4DQDjPl7LwcKSZIUrIlIvJTNZ6wasjyjnB3WVmNnRQC/gvYjqHDObbWafmNkVyQtTRBKtoCiUcJ045p2o+vydB6PKzbKMT9ftYuPugnDdqzPWJj9AEZF6JJnJWqxewlWN078aGO/ukb9S93T3QcA3gCfN7JhKb2B2a5DQzd62bVvdIxaRWpv/4MWV6nYeKIzRstw3hvRk0l3nUFRS+SuhXYtmCYtNRKQhSGaylg/0iCh3BzZW0fZqKjwCdfeNwc9VwPvAwIoHufuz7j7I3Qfl5uYmImYRqaV2LZvx3HWDourOfPS9Kkcs9urcil985UQGdG0bc/8ZvTslPEYRkfosmcnaLKCPmfUys2xCCVmlUZ1m1g/oAHwcUdfBzJoH252BocCiJMYqInVw0YAuTLnnXL50ctca267evj9m/TPfOJV/3DGUHh1bJjo8EZF6LWnJmrsXA3cCk4HFwBvuvtDMHjazyNGd1wCvu3vk85D+wGwzmw9MA8a6u5I1kQzWp0sb7rukX8x9ix6+hLY5lad1/GxM+SPUy046ilN6tE9afCIi9VVSJ8V190nApAp1D1Yoj4lx3HTgxGTGJiKJF+uu2DfP6EnL7KbsKSiutK9tTjOW/WwERSWlqQhPRKRe0tqgIpJQZ1boc/azK0K/d105MDQY/L8G9Yjan920Ca2aazEVEZGq6BtSRBJq5ElH8fGqLwBY+NNLwvWPf+1khg/owiXHH5mu0ERE6iUlayKSUPsPlT/ubJmdFd5u0sQYeeJR6QhJRKRe02NQEUmoG87KC29rUXYRkbpTsiYiCZXTLKvmRiIiEjc9BhWRhPvN10+mS9ucdIchItIgKFkTkYS78tTu6Q5BRKTB0GNQERERkQymZE1EREQkgylZExEREclgStZEREREMpiSNRGRJDCzS81sqZmtMLPR6Y5HROovJWsiIglmZlnAM8AIYABwjZkNSG9UIlJfKVkTEUm8wcAKd1/l7oXA68CoNMckIvWUkjURkcTrBqyPKOcHdSIitdZgJsWdM2fOdjNbW4tDOgPbkxVPEinu1FLcqVeb2I9OZiB1EGtRVK/UyOxW4NaguM/MliYwhvr8d6AqDfGaoGFeV0O8JqjhuuyXtTpX3N9fDSZZc/fc2rQ3s9nuPihZ8SSL4k4txZ169Tn2CPlAj4hyd2BjxUbu/izwbDICaCCfY5SGeE3QMK+rIV4TpO+69BhURCTxZgF9zKyXmWUDVwMT0hyTiNRTDebOmohIpnD3YjO7E5gMZAEvuvvCNIclIvVUY07WkvLoIQUUd2op7tSrz7GHufskYFIaQ2gQn2MFDfGaoGFeV0O8JkjTdZl7pT6vIiIiIpIh1GdNREREJIM1umQt05aAMbMeZjbNzBab2UIzuzuo72hmU8xsefCzQ1BvZvZ0EP9nZnZqxLmuD9ovN7PrUxR/lpnNNbN/BuVeZjYjiOEvQedqzKx5UF4R7M+LOMf9Qf1SM7skRXG3N7PxZrYk+OzPrA+fuZndE/w9+dzM/mxmOZn4mZvZi2a21cw+j6hL2OdrZqeZ2YLgmKfNLNZUGQ1STd9hZvaEmc0LXsvMbFeF/W3NbIOZ/S51UdesLtdlZj3N7J3g3/KiyL/r6VTHa/pV8G99cab9HY/junpa6P+1ucG/6ZER+1L+fR+Pw70mM7vIzOYE30dzzOzCpATo7o3mRaij70qgN5ANzAcGpDmmo4BTg+02wDJCy9P8Chgd1I8GfhlsjwTeJjSP0xnAjKC+I7Aq+Nkh2O6QgvjvBV4D/hmU3wCuDrb/H/DdYPt24P8F21cDfwm2BwR/Ds2BXsGfT1YK4h4H3BJsZwPtM/0zJzSp6mqgRcRnfUMmfubAucCpwOcRdQn7fIGZwJnBMW8DI5L9dyYTXtTyOwz4HqHBDZF1TwX/Zn+X7utJ1HUB7wMXBdutgZb1+ZqAs4CPgnNkAR8D56f7muK9LkL9usq+hwYAayK2U/59n+RrGgh0DbZPADYkI8bGdmct45aAcfdN7v5psL0XWEzoP+VRhBIKgp9XBNujgFc85BOgvZkdBVwCTHH3He6+E5gCXJrM2M2sO3AZ8HxQNuBCYHwVcZddz3hgWNB+FPC6ux9y99XACkJ/TsmMuy2hZOIFAHcvdPdd1IPPnNCgoBZm1hRoCWwiAz9zd/8A2FGhOiGfb7Cvrbt/7KFvyFciztXQ1fY77Brgz2UFMzsN6AK8k9Qoa++wr8tCa642dfcpAO6+z90PJDvgONTlz8qBHEKJQ3OgGbAlibHWRjzX5UDbYLsd5XMMpvz7Pk6HfU3uPtfdy65vIZBjZs0THWBjS9YyegmY4Nb9QGAG0MXdN0EooQOOCJpVdQ3puLYngfuA0qDcCdjl7sUxYgjHF+zfHbRPR9y9gW3AS8Et7efNrBUZ/pm7+wbgcWAdoSRtNzCH+vGZQ+I+327BdsX6xiDuPzszO5rQ3Yv3gnIT4NfAD5Mc4+E47OsC+gK7zOzN4N/zY2aWldRo43PY1+TuHwPTCP073wRMdvfFSY02fvFc1xjgm2aWT2hE9PdqcWw61OWaIl0FzHX3Q4kOsLEla3EtAZMOZtYa+BvwfXffU13TGHVeTX1SmNnlwFZ3nxNZXU0MGRF3oCmhR3S/d/eBwH5Cj+WqkhGxB328RhH6Uu8KtAJGVBNDRsQdh9rGmWnxp1Jtrv1qYLy7lwTl24FJ7r6+ivbpVJfragqcA/wAOJ3QL2M3JDrAw3DY12RmxwL9Ca180Q240MzOTUqUtRfPdV0DvOzu3Ql1c/hj8MtCpv7brcs1hU5gdjzwS+C2ZATY2JK1uJaASTUza0YoUXvV3d8MqrcEj3sIfm4N6qu6hlRf21Dgy2a2htAt4wsJ3WlrHzyiqxhDOL5gfztCj8nS8WeSD+S7+4ygPJ5Q8pbpn/lwYLW7b3P3IuBNQn1b6sNnDon7fPOD7Yr1jUFt/uyuJuIRKKE+fncG/2YfB64zs7HJCPIw1OW68gndzVgV3EH+B6F/z+lWl2v6CvBJ8Eh3H6F+mWckJcrai+e6bibUl7bsLmEOoTU1M/L/YOp2TWVdgv4OXOfuK5MSYTI6wmXqi9BvYKsI3Zko60R4fJpjMkJ9bp6sUP8Y0Z2xfxVsX0Z0Z+yZQX1HQp3POwSv1UDHFF3D+ZQPMPgr0Z3dbw+27yC6s/sbwfbxRHc4XUVqBhh8CPQLtscEn3dGf+bAEEJ9IloGsYwjdCs+Iz9zII/oAQYJ+3wJLed0BuUDDEam4u96ul/E+R0G9APWEMylGWP/DWTWAIPDvi5CncPnA7lB+SXgjnp+Tf8FvBucoxkwFfhSuq8p3usK/k3eEGz3J5T4WKq+e1J8Te2D9lclNcZ0f0hp+EMZSWjE5UrgxxkQz9mEbrd+BswLXiMJ9S2aCiwPfpb9J2XAM0H8C4BBEee6iVCHzRXAjSm8hvMpT9Z6Exqpt4JQEtE8qM8JyiuC/b0jjv9xcD1LSdGoPuAUYHbwuf+DUDKQ8Z858FNgCfA58MfgSy/jPnNCdwk2AUWEfmu9OZGfLzAo+AxWAr+jiqSkIb5ifYcBDwNfjmgzBhhbzTluIIOStbpeF3BR8G95AfAykJ3u66nLNRFKQP9AaMDZIuA36b6W2lwXodGSHxFKYuYBF0ccm/Lv+2ReE/AAoa408yJeRyQ6Pq1gICIiIpLBGlufNREREZF6RcmaiIiISAZTsiYiIiKSwZSsiYiIiGQwJWsiIiIiGUzJmoiIiEgGU7ImIiIiksGUrImIiIhksP8PfokeVBg57wEAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for param, samples in zip(['intercept', 'slope', 'precision'], trace.T):\n", " fig, axes = plt.subplots(1, 2, figsize=(10,4))\n", " axes[0].plot(samples)\n", " axes[0].set_ylabel(param)\n", " axes[1].hist(samples[int(n_iter/2):])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, with a very large proposal variance:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration 0\n", "Iteration 1000\n", "Iteration 2000\n", "Iteration 3000\n", "Iteration 4000\n", "Iteration 5000\n", "Iteration 6000\n", "Iteration 7000\n", "Iteration 8000\n", "Iteration 9000\n" ] } ], "source": [ "trace_hivar, acc = metropolis(n_iter, (1,0,1), 10)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.0426, 0.0038, 0.0086])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array(acc, float)/n_iter" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for param, samples in zip(['intercept', 'slope', 'precision'], trace_hivar.T):\n", " fig, axes = plt.subplots(1, 2, figsize=(10,4))\n", " axes[0].plot(samples)\n", " axes[0].set_ylabel(param)\n", " axes[1].hist(samples[int(n_iter/2):])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Adaptive Metropolis\n", "\n", "In order to avoid having to set the proposal variance by trial-and-error, we can add some tuning logic to the algorithm. The following implementation of Metropolis-Hastings reduces proposal variances by 10% when the acceptance rate is low, and increases it by 10% when the acceptance rate is high." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "def metropolis_tuned(n_iterations, initial_values, prop_var=1, \n", " tune_for=None, tune_interval=100):\n", " \n", " n_params = len(initial_values)\n", " \n", " # Initial proposal standard deviations\n", " prop_sd = [prop_var] * n_params\n", " \n", " # Initialize trace for parameters\n", " trace = np.empty((n_iterations+1, n_params))\n", " \n", " # Set initial values\n", " trace[0] = initial_values\n", " # Initialize acceptance counts\n", " accepted = [0]*n_params\n", " \n", " # Calculate joint posterior for initial values\n", " current_log_prob = calc_posterior(*trace[0])\n", " \n", " if tune_for is None:\n", " tune_for = n_iterations/2\n", " \n", " for i in range(n_iterations):\n", " \n", " if not i%1000: print ('Iteration', i)\n", " \n", " # Grab current parameter values\n", " current_params = trace[i]\n", " \n", " for j in range(n_params):\n", " \n", " # Get current value for parameter j\n", " p = trace[i].copy()\n", " \n", " # Propose new value\n", " if j==2:\n", " # Ensure tau is positive\n", " theta = np.exp(rnorm(np.log(current_params[j]), prop_sd[j]))\n", " else:\n", " theta = rnorm(current_params[j], prop_sd[j])\n", " \n", " # Insert new value \n", " p[j] = theta\n", " \n", " # Calculate log posterior with proposed value\n", " proposed_log_prob = calc_posterior(*p)\n", " \n", " # Log-acceptance rate\n", " alpha = proposed_log_prob - current_log_prob\n", " \n", " # Sample a uniform random variate\n", " u = runif()\n", " \n", " # Test proposed value\n", " if np.log(u) < alpha:\n", " # Accept\n", " trace[i+1,j] = theta\n", " current_log_prob = proposed_log_prob\n", " accepted[j] += 1\n", " else:\n", " # Reject\n", " trace[i+1,j] = trace[i,j]\n", " \n", " # Tune every 100 iterations\n", " if (not (i+1) % tune_interval) and (i < tune_for):\n", " \n", " # Calculate aceptance rate\n", " acceptance_rate = (1.*accepted[j])/tune_interval\n", " if acceptance_rate<0.2:\n", " prop_sd[j] *= 0.9\n", " elif acceptance_rate>0.5:\n", " prop_sd[j] *= 1.1\n", " \n", " accepted[j] = 0\n", " \n", " return trace[tune_for:], accepted" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration 0\n", "Iteration 1000\n", "Iteration 2000\n", "Iteration 3000\n", "Iteration 4000\n", "Iteration 5000\n", "Iteration 6000\n", "Iteration 7000\n", "Iteration 8000\n", "Iteration 9000\n" ] } ], "source": [ "trace_tuned, acc = metropolis_tuned(n_iter, (1,0,1), prop_var=1, tune_for=9000)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.312, 0.319, 0.286])" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.array(acc, float)/(n_iter-9000)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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F7uX4g/JhFsrUkQPivN3BwGbgNhE5BlgIfInAaqYikrWaqYhcDVwNMHny5DhlMoySMZdXDQm6vAoVb1QlpUygsEKZNMIZ/FJVjUU4cdoIAHYf6Mp5Xm9i9bZ9RaX6+hMWwvs3VpdXM3A8cKOqHgfsJaJ7S1Xnqmq7qraPHj06TpkMo2RModQQb/CaPGIgE4f35+r3T490vEdTnjiLH3/w/9oPHJbzuN5GV0+S07/7JLN+9DSrtmbHmMLo8ZXrCltJM+YI1BpgjarOdz/fi6NgNrqrmBJlNVPDqBdModSQNdv3AzBuaD+e+fpZXDJzYt7ju3syixOG1QDTkAFvkDtDvqVJ+lT5lS5ff/156eZI5/gnToZZKHHO4VHVDcBqETnMbTobeIMIq5kaRj1iMZQasvuAEzQf0NYU6fhg6Y+osZcbL5vJHxetY9qogexasxPoGxaKPx6yv7Mn0jndBWIoFei3vwd+KSKtwHLgszgPer8RkSuBVcDHYr+rYVQAUyhVZO2O/azauo/jpwyjrbmJ5oQwbEALbc3RFEqwzlRbSMZR2IA3dmg/rjr9YCA9v6UvWCilWBP7u9KKJyFOBYKMiaMxJ12r6itAe8iurNVMDaPeMZdXFbni5y/wiZuf554XnPIdSdXQOEgu/E/Pg/s1h06yKzTcpZcBjnzbhsXvvoqqP6//4xsZn4+eMJRWn+LuA3rYMErGLJQq4s3C9uaHKDlKrOTAXz49rCwIwPABLXmvIX3IQunxfcdSLAsRuP+LpwHpirF9od8Mo1TMQqkinsvKm3yoqqElVjzuufqk1FwS5/x0kDnXeV8997DwHanznBPvf2VtVtmR3kJXTzKrMrHpAcOoPKZQqoinUNJFG7MXwfJz0sEjmTE+rVC6fANkLstm6qiB/PjSY/nN504O3e/d76HXNvCL51cWI37D8KH/fIbP37UwYKFEY8Kw9Boy+ZZhNgwjG3N5VRHPZeW5TZKqBScz+nffOG9Zuj3PeRcdOyHnPr9l4w9A9ybe2rCbtzbs5tHXN6ba/IqgtSlBc5OwLyTzy1+6JnyRM9MohpELs1CqxJ6ObjrdeRGeoaHkt1Agt+LI2V5ADr9l05dWIPQrgqRqzpTrQj2STBY4wDD6MKZQqsTm3emy6BRhoeQi7OnZ3ZEX/zj682dWcMmNz7JozY7ShKhT+rWEp1N39yR58q1NdCc1p+vKH3TPsySNYRghmEKpEn5XSspC0cIWSi5yWyj5r+e/X1ePsuDd7Ty3bGtJMtQruQyv+Su28dnbXwTSmXb5zs23DLNhGNmYQqkS/mGouBhKcQqn0PXCFFhXT+/y44QN+qoaabZ85jLMYTEUwzByYQqlSoQtzRvFQvF2HzVhaEb7uxGLHea6np/O7t6lULz+Pf+osUwc7mRtqUZTBlrA5WUaxTByYwqlamRPsotioXgl6CePCF+H41d/exLvm5peIbaQPRNWULKjF1koezu66Ukq/3DWIfzXZTOZ99UzAKf3o0xK9I4Y0NrEqEFtWfttYqNh5MYUSpXIqAdVhIVyzRnTefVb5/Kx9vBKxCdPH8l7xgxOfS408z4sueneBWvynlNvXHffIj4x9/ms9t+8uJoP/eQZANbtPACk+0M12hySpCqXnzyFN/7feYxwFyTzY+rEMHJj81CqREYMJZm2UAoVDBYRhvZviRy8L3TUyIFtnHbIKJ5ZuiXVtnVvZ6Rr1wu/cmuh+enqSfK13y1Kffbm2Hj94ViFESyUAkreDBTDyE1NFIqIjAB+DUwFVgIfV9XtgWOmAPcBTUAL8J+qepO7bx4wDtjvHn6uqtb1IkRhMZSkauSge0+ekayYMa61OcFdV52IqvLa2p384dV13PznFUVcoT7JigO5neLphmIslHy62yY2GkZuamWhzAaeUNU5IjLb/fz1wDHrgVNUtUNEBgGLReQBVV3n7r9MVRdUUeayCE6sA2eAi5o13NOTR6EUCiSHICIcPXEYj79Zn3p4wcptTB89iOEhbqcwggrF6+OUy4tMxdvalKCzJ8mxk4ZlnKeaP7OuD80FbQi8op1GfVCrGMpFwB3u9h3AxcEDVLVTVb3ZgG00eLwn7Ok4WcQ8lKF5qggXSnXNR8olVEe+nLU79nPJTc/xpV+/Evmczp5whQKuktXMyYyjBrUyalAbR/iKb0Lhgp3m8zKM3NRqkB6jqusB3PeDwg4SkUkisghYDdzgs04AbhORV0Tkm5InEi0iV4vIAhFZsHlz4WVgd+7r4tZnVvDUO9GWjI1KpsvLV2044i/QPmU4v/ncyZx+6Kj8BxY5T9LvEqoX9nc6kw6fXx5twuWm3Qe4d2FmYkGmknWUd6aV6H33zC+eLGA11lE3GUbdUTGFIiKPi8jikNdFUa+hqqtV9WjgEOAKERnj7rpMVY8CTndfn85zjbmq2q6q7aNHjy54zwdfW8/1f3yDK37+Qkb583IJc3ntOtAV2aIQEU6YNiL2ZWm9+zfyQDnn4bf43qNvZ7RlzngXFM1oUxTXcMlA0VCr8XPvd1a8/L/3vx6X2IbR66hYDEVVz8m1T0Q2isg4VV0vIuOAvI58VV0nIq/jKI97VXWt275bRO4GTgDujEPuju70bOrdHd0M7Z9/waqoBIPyqsqLK7dz+NjBuU8KIUzH+ZVVsZVc0haKUrR5UyGKVZAvr9rBiIGtHDxqIAve3e5ew1812AvKp9s+evxEfvdSdrp0Mkc3zP7g4TQlJG9yhGH0dWrl8noAuMLdvgK4P3iAiEwUkf7u9nDgVOBtEWkWkVFuewtwIbA4LsF6MhZlqszg8faG3dziZla9b+qIos6dOWV4VlvQvVMM6bTa+sGTJep32bGvk+MnD2OYL87Ur6UptS2S+f0e/IfTUguRZf3EOeJaIsLXzjuc6z54RESpDKPvEUmhiMh7ROQJEVnsfj5aRP6pjPvOAWaJyBJglvsZEWkXkVvcY44A5ovIq8BTwPdV9TWcAP2jbmzlFWAtcHMZsmTgVyg9Mbq8/EHihe9u518eehOAc2aMyXVKKJ//q+l59xezpLBzvPNequ58YcU2duyr3TyWPR3dbN/XxahBbRnf/YtnHZLaFiQjbbh/SxOJhDjtWTGUwnODDMMIJ6rL62bgWuBnAKq6yHU1faeUm6rqVuDskPYFwFXu9mPA0SHH7AVmlnLfKPhdGnGmiHqXvelTMzlhmmOVNDcJQ/oV51JrbQ4pzV6GXOm02uKv0tmd5OM/e46ZU4bzuy+cUoYUmURVbp+Y+zynTB8JwCEHDWL7ym0ADO3fkpm9Jc73876jZ4GIZN+rmLlBhmFkElWhDFDVFwJPv+H1vxscfyA+zrpN3pVamyW0pEc5TBs1MLVdzaHwgBtven3dzlivG1W5vbZ2J8+5mWATh/dnwUrn2wctDC+Zy/s5vT/jYF899Np6N5W7NLkNo68TNYayRUSm446LInIJzsTDXkd3pRSKN9GuAkP+1W4GEhQflPco5asecMvBN0fNfY4Z/3edOmpgKgU7GAPxYijeT+v/Dfxfe76rnC44enwFpDWM3k9UC+XvgLnA4SKyFlgBXFYxqWpIskIxlNSVYtAn00cPzJjI19KUoKVJ6Oop3l1TqgICeGmVs9Jj3E/0kZWbwoxxQzhoSBuHjx2S+u7BispODEXTSt2zUEQy7rW/q4exQ/pxWJGZd4ZhOERSKKq6HDhHRAYCCVXdXVmxaoc/hhJnklfK3RLDtZ7432dktTmDafECp+ahlPBd1+90SqkdOiZ8AL756eXc+swKnv8/WeGyaLIV6KzdHd28sX4X72yUjOOzXF6Sez0URXlmyRZ27O9k+ea99G9tCjnKMIwoRFIoIjIS+BZwGqAi8gzw/9zgeq/gkcXr+eX8VRlrYMRpoXjDWbFZWMVS8jyUMkL7C9/dzrtb9zJl5MCMdi+TrViKVW6em9Lr2yyXF27vB2MoAiu27OVTt85PHXvitOLSuA3DSBPV5XUP8DTwUffzZTjVgnNOXmw0fvTYEt7emGl4xRtDcd7rLd6bruVV/Ln+cx5ZvIHPFUhpjnzdEpVbImWhBGMobtpwSJbXy67b7lsfmsFph4xi/LD+JUptGEbUaOoIVb1eVVe4r+8Awwqe1UB0J7NXLVy1rbRldsNITdarsEYp3UIpj3qowut99WAfOBaKZmV5+X/yCcP6c+iYwQxssyWCDKNUoiqUJ0XkUhFJuK+PA72+bvRnbnuR7hiWx+3qSfLGul1AZbK83AsDxVsa6RhK8RrBf0YlrLli8SyPlqbAn7UbQwlmeflljlr12TCM3ERVKJ8D7gY63dc9wFdEZLeI7KqUcLWiyRfV7Y7h0fuGh9/iWw84RQUrNW6Vetm4LJSVW/ayfPOeMq+SSdHK1z08WEAzc9XG9Hf2x8iabPKJYZRNJIWiqoNVNaGqze4r4bYNVtUhha/QWPgHlzgevF9dsyO1Xalhq32qU+Or1Cft0mIo6ZN+u3ANZ/3gqYLHVRLvuzcHLJSkwpvrd2XFsbLWTDEMoywiO4xF5MPA+92P81T1j5URqfZMHz2IN9c7hlccrpyMzK4KDVw/+3Q7K7fsDS3Nkg+Jy0RxSSY1ax5IUqGpiO9dapd7t2gJ3GxPRzetzYmsuUB+69NcXoZRPlGLQ84BvgS84b6+5Lb1Sg4bM4h/usCpKhuHQklk6JPKDFyD2po5csLQos+LW5rgyolQfPp16VleroUSUGjHT3bzRwLVCvzLKptCMYzyiWqhnA8cq6pJABG5A3gZZy34XoeIpJ7c48he8rvQ6nXcKmceip+O7mRG6XiIRynv68xdOu5f//oogFTplaDLKyFCTzL9Db2foycjKF+2iIbR5ykmR3IYsM3dLv5RuIEQiXetdf/Tb72NW3EvAdzZnW2hFHvtsOPf3ZqZwv2VWe/hh4+9A5AqldLW7CiygYHZ7omEkFRNldXxHhb8llOlJ5wa+Zk6u9cnjfYJoiqUfwNeFpEnccbE9wPXVUyqKqKq/HbBGpZt3ptqEyT1xBrHQOsfrILxhVpTzgJbYX3z5Fub+Pj7JmW0FWuhhM3ZCV7Cb/V5m39/1iEcP2U4x03KnCKVEHh++bbUJEbvzJ6kWSiGESdRs7x+BZwE3Oe+TlbVeyopWLVQha/9blFGW0LSA3+57pqO7h6efmdz6nO9jVup9VBiMlHCYihxuLyCLjm/svEswJGD2vjwMeOZNGJAxrGe8ulwrSfv3CtPm5Z1jGEYpZNXoYjI8d4LGAesAVYD4922hkcEPnPK1Ky2uGIov3ju3cC162vgKifJKyzuEqY8iu3DMOUWbPK7EQspg2DA3SsAed35RzDcXTa43n4Xw2hECrm8fhDS5v/XPitGWWqCiDAhUL8pIX6XV3kaZU9HOph82YmTee/4+pq2U04trzC6e8KUQWkur3xkZM4V0AV+hXLEuCGpWItzrldQshgJ40NEmoAFwFpVvVBEpuFMHB4BvAR8WlVrt8ayYRRBXgtFVc9U1TOBG4GL3O0ngZ3AV6sgX1XIqv0kkhqEyrVQ/Od/88IZWRlQNaeMJYDD9IRnoTyyOL3+2u4D5S/uGbR8/OnXhVJ+/RZMcJ6Ot6eGacNfAvxlmW8AfqSqhwLbgStrIpVhlEDUWXD/pKq7ROQ0YBZwO46S6ZX4s7zK9v/Xeb2olERxWSiuBr1x3rJU228XrC7qGmFdHmwb0JZWzAMKrGGSOQ8ok/QaKtX/bURkInABcIv7WXCs/nvdQ+4ALq66YIZRIlGzvHrc9wuAm1T1fhH5dmVEqj5B/3lC0gNMnFV46zHumyuGMvfpZZwyfVTRkyW9zCn/LPSxQ6OXhH9l9Q5eXrXdkc3XHpTvo8dPZOyQfgxsa85ahyVIPmUxuF8LW/Z01mp+0L8DXwO8FcpGAjtU1TPp1gATwk4UkauBqwEmT55cYTENIxpRFcpaEfkZzvonN4hIG9Gtm7on66kV8ZU4L0+l+F1J9WmheFleme3/+tBbAKycc0HOc8N6xlMoPUmltTlBZ3cyFfiOwqVzn+NAV9hclsy79Wtp4uwjxkS6ZsY8oMBP8O0Pv5ffvLiag0fnV0pxIyIXAptUdaGInOE1hxwa+geoqnNxluWmvb29DhYPMIzoSuHjwKOuOJEuAAAdQElEQVTAeaq6AydgeG3FpKoywUEmw0KJz+NVl7Pkw2QqR4l6CiWpymB3bZEv/PKlyOeHKRPneiWLlFmpILDvr94zmp9edjwDWqu+DsqpwIdFZCVOEP4sHItlmIh4wkwE1lVbMMMolajzUPap6n2qusT9vF5V/1RZ0apHtl9dUmU8yo2hJDMUSh1qFJelm/aw+0AXAF0hi42FEdY1+7sc72hPUmkuoiLkpt0HuO6+zPlAmf1V+u+QUZuzTn4DVb1OVSeq6lTgUuB/VPUynKSXS9zDrgDur5GIhlE0vcZtVQ7B2evis1DKUSiqygsrtpYlW6Xxvvmnbp3Pmd+fh6pmpP6u2LI3/MQczH16Ofs6u1GF5kT0P695b2/mVy/kDt6Xo9ePmzy89JOrz9dx1hpaihNTubXG8hhGZEyhEB5D8bjyjgUs3VTawlFLNu3hJbfcxwVHjytVvIrif2DfsqeTdzbuyVAoZ35/Hge6ekLOzJ1qvGNfFz1anIVSKL5Ujp145WnTOGaik1xQH/ZJJqo6T1UvdLeXq+oJqnqIqn5MVTtqLZ9hRMUUCmQFEhIC/d35Iiu27OXZZVtKuqx//sVPP1mfhQWC5fT3dXbT0ZOpQPyTM8P40DHjATj1kJEAHOjqcVxeRaS1BVftDVL2xEv3N64Tj5dh9EpMoRA+N+GMww7ie5ccDUBXyOzvXkPgy+/v6uG0G57MbOvMYaG43dKS8NYhcf6cNuw8QDKp2Wu756GQwohrzfpKrUdjGIYpFCAsy0tobU5w/lGOm6orpOBhKdetR4Ii7trflVWCftPu/F4Xz7XlTTD85C3zWbfzQFEur0JZXOXqkwb4KQyj4TGFQvZT63i3tpf3hN1dqkIpT6yqECwF401IHD24LdW2YeeBvNeY7Fb3Pfe9Y/jIcel5eMUE5cMskMwcr/I0Skq5N8KPYhgNStWT7+sRb7CZOnIA93/xNIb2dybieWuT92aX16wZY/iPTxzHG+t2cdNTy1LzSJqLWGXy0ydNZfLIgZz33rEM7d/CfS+vBbLXds9HwQKSMVkopk8Mo3LUzEIRkREi8piILHHfc+Z2isgQEVkrIj/xtc0UkddEZKmI/IeUMcHAO3FAa3NKmbj3oCkhdEeclxGkEdRQv5YmPnzMeM44bDSQVp5+d1Wh+EX/Vucarc2JjGyt4iyUaPu/eeEMHvny6ZGvG6QR3JCG0ajU0uU1G3jCrar6BPnXp78eeCrQdiNOLaND3dd5pQriDTJhPv/mhKTSaA909dD+nce57S8rIl03rpLw1cBTBD2u8mzxKYNc3yPMqvArlLaW8lxeGfdy1fPRE4dy+NjilwColwmNhtGbqaVCuQinmirkqaoqIjOBMcCffG3jgCGq+pw6o9qduc6PghdDCUtzbU5Iyg20+0A3W/Z08N1H3o503bhWQawG3lf3LBR/uZJC38I/VvvP69ccvVR/1KB8qWoh7fIyxWIYlaKWCmWMqq4Hp5QLcFDwABFJ4CzyFawbNgGnEqtHzqqskUhZKNndkRBJDXbeU3RSlb8s3cJPn1ya97KNo07ST/CpGEqT30JRHlm8gbvnr8o4J0xf+pVLvyIslELKN73OfGkKwTvNDBXDqBwVDcqLyOPA2JBd34h4iWuAh1R1dWAgiVyVNUqZb+9iYRaKSFqReIOtCFx2y3wA/u7MQ3IKX26l4mriffXukKC8Knz+roUAfPJEpw+ffmczP3jsHSDzx2jy/U7FLCYW2le+Cz/2xganqUyFYAolGlNnP1hrEYwGpKIKRVXPybVPRDaKyDhVXe+6sDaFHHYycLqIXAMMAlpFZA/wY5xKrB45q7JGKfPtlRbZH1JipCkhGZYJZMYJVJVdB7ppaZKsirUNpE9S38lLkfbHk8JSdq+999Xw6/gUUTHzUL79hzfy7r/recc6Kt3lZZrEMCpNLV1eD+BUU4UcVVVV9TJVnexWZP0qcKeqznZdZLtF5CQ3u+vysPOj4g38R4UsJuW4vFyFkky3eSzbvJdj/vlPnB6YXQ7lz52oJimF4nZGoaD8xl3pyY5+69HfN2celuXFLJuSg+uey8sUi2FUjFoqlDnALBFZgrOs8BwAEWkXkVsinP8FnKVTlwLLgIdLFSTM8vAQXwylR9MuryH9HGtk295OALa6734aKCafcgV5GW3+rgh+jx37sr+rhz8o70/Bjop/YmQY5aoDc3kZRuWo2cRGVd0KnB3SvgC4KqT9dpy17P3HHRmHLPlcU02JtH/fi6EkRBjcr5ldB7r514fezHluIymUtIXimGHHTxnO/BXbgOzgVGeeygH+MFRbEVleHn9/9qGpiZFhlGmgGIZRQWymPOkMozALxe/yUp+FMnF4f9Zs388rq3fkvG5cBQ2rgefh8lxe44b2S+0r9D38vVbqPBSPpgIao7vEwJRZJkajUWpiRL5luyuN1fIibUmEVVtPhLi8EiIM6VfYndM46iStCDx3Vqs/hTr4RfJ8sQyF0lyCQvEF8sN0gLescLF4sROb4GgYlcMsFNJP4GFjjUi2y0t821Gue/dVJ8YjaAXxJiF6qyYO9A3cweSC4Df395tXcRiKSxtOyxGuhIYNaGHqyIEcOmZw0df0Y+rEMCqHKRTSA2SYyysjbdgNHYgI3UmlpUkyCkc++fYmJgzrz3u8Qc/dNaDEp+pqMmlEf265vJ3t+zoZ0NrMiQePSO0rxnM3ddRA7vybExjY1pxp5RTg2EnDGNyvOefKjc0J4b3jiy+54mETGw2j8tT/SFcF0hZKrhiKs71jf6d7nHNOS1OCLt/qhp+97UUg7cNMXbdikseHiHDOjDGpz7sPdKW2szxegYZgv73/PU6hyZ37uoiKutfxKxT/dZNaeJngfJgiMYzKYzEU8sdQRNKxk+eWbQVg5MBWunsKL3Gbvm7jjWb+SsGlJhdIgb+u55dv5f5X3IwuVUfx5uiqpGro7xNZFi+GUvolDMMogFkopGMkYeN+k0gqu8tTIHs7uxncr7ngErf5YjP1TlOg9IqfqBM2CynSS+c+D8BFx05wLZRMpT5yYGtqO5nUWALqFpQ3jMphFgq+woMhz68JETbsPMBra3amLJXV2/bz4srtGaVF/CscZl23Acew5jzVhqMaLMVYFI4FIhkD/oTh/TPuGYfLqwF/CsNoGEyhAK1uZlFYddyhA1p4adUOLv6vv7D7QHfGPr9baHC/bGMvNW+lAYexREL4z08c53wo0eVVjAJQdQb7XEqoXJeXYRiVxxQK8JHjJ3Dp+ybx8fZJWftu/nQ715wxnZ6ksiegUPxL3IalEXtNRSxcWFecMn0kUNQ0lAyKViiSW/kmNbPwZLF4lk8jWouG0ShYDAU4aHA/5nz06NB9Qwe0MHXUQCC7GrE/hhKmUN7dug8obincesIbhG/5c+YKlVEXDos6/v9x0TpStlyOGmJJ1ZiUgWkUw6gUjTnSVRlvxndQoTTnUSjJpHLDI285xzWor8aTetW2fSWdH9VC+eLdL7N9b6cblA8/p+wYivfemD+FYTQEplAi4E3QO5BloaRHp2CNqR7f43VToyqUgNgj3KyrqCGVYgbvzp4kEjjHn02W9NKKS8QUiWFUHnN5RcBzbe3vyqyy67c8ghaKf9AtZqGpeiKYYlvsfJRcKbo/fXIpa7ZnWj09Sc1voRDPfJ7G/CUMozEwhRIBLwusI2ChHDx6EC+tcqoNdwdKuid7oYVSavHkMUMyU6q/9+jbWcf0JBUJhOSDMZTyJja67435UxhGQ2Aurwh4CiXo8vrHWe9Jbe8KZID5KVSSvV4JSp0u4x/9GidMG8E0N6khH56FEtZVPUl1s8BiyPIyG8UwKoZZKBFoDQnKNyUk7xOzf9Bt1NnZWXIrzP7dIu55cXVR14migHrUUyjpez67bCu/XbCamVOGA/kX9ipEY/4ChtFYmIUSAS8ov78zrVASeeZMQGZAubdYKLs7unnk9Q1FXyOKQZN0XV5Brr13ER3djiI5asLQou4dKk9j/hSG0RCYQomAN4Pe79ZyKuPmPseL0b93/BCGDih+bfV6ICwIHqwWUAgR2LW/i64C1kV3UlMa7KZPHZ+R8OAplEK10wrJ4X83DCN+TKFEYNqoQXzp7EO5/OQpqbaEkNeP4k3+u/jYCRWWrnKElaKJsrCYny17Onlrw27+5vYXs/YF5+d4n847chyHHDQo1e4lQ7SUlS1nMRTDqDQWQ4lAU0JSAfg7n3vXaRPJGxto5MKQHiLCuKH9WL/zQMnX8JYU/vOSLVn7WpoSdCfTbsSX3t0eeo04LRTTJ4ZROcxCKZGESM6n9YdfW8+Z35sHNG5A3qPcuR/5LJpgkH2dT3H5lfWz7jo05SgUwzAqj/2HlohI7sHyD4vWsXWvu7pjNYWqAOWWIcunUPLt8yc1eJbL5BEDSpbDDBTDqDymUEpERFKlSD56/MSMff515hvcQCnbQiky5JIiOKnxqAlDGTu0X8lypIPyDf6DGEYdYzGUMhjY1szKOReweO1OfvfSmlS7f9Z8Iy7/66d8hVKaRvGf1RNDpeFLZk4iqfCR4xo3ScIw6h1TKCXiH+CCg66/UGSD65OyF7UKurXu8ylecPqnkM6JY/nfWTPGMGvGmLKuETciMgm4ExgLJIG5qvpjERkB/BqYCqwEPq6q4RkLhlFHmMurSA4enV1GJBhn8Gc0Nbg+YdnmvUD4ipRRCFooi9bszPicq7S/f82V7mR5lYbrmG7gf6vqEcBJwN+JyAxgNvCEqh4KPOF+Noy6xxRKkdx42UwgU1EEZ8IfMW5I+kOjmyguYatZRiG7CnPm5zFDwuMi/gmUXp2v3oaqrlfVl9zt3cCbwATgIuAO97A7gItrI6FhFIcplCIJG9iC7phzfa6VBi00nMXZhx9U0nnBoHzw83vHDyGMS0+Y7Dun11ooKURkKnAcMB8Yo6rrwVE6QGmdbxhVxhRKkaTLoKeHuKDS8LtxesvM7FJL8A/tn1l2pidgofj75/Cxg1PbI90MOnAslEZPbsiHiAwCfgd8WVV3RTznahFZICILNm/eXFkBDSMiplCKJGxcCw62Tb4SIb1lHCxVoXz/Y8cAcKhbSkVVM0qo+ONPv/+7U0OvsWzzXlZvL20Z4npHRFpwlMkvVfU+t3mjiIxz948DNgXPU9W5qtququ2jR4+unsCGkYeaKBQRGSEij4nIEvd9eJ5jh4jIWhH5ia9tnoi8LSKvuK8qugSyB9bg03OmhdI7KFWhzJoxhrMPPyi1BEAyCW3NTan9fkuvX0u6PXi7jbs6Srp/PSPOl78VeFNVf+jb9QBwhbt9BXB/tWUzjFKolYVSTBbL9cBTIe2Xqeqx7ivrCa5SpCbIhbR5NPkeu3uLq6a5jCnz4qt7llRlUFs6Yyxn//SSfivAqcCngbN8D0fnA3OAWSKyBJjlfjaMuqdW81AuAs5wt+8A5gFfDx4kIjOBMcAjQHuVZMtL2DAXfHrPSIXtJeOi/zuOH9ovo+5WIUTS6cNJda41ZeQA3t26r9ckLZSCqj5D7r+Qs6spi2HEQa0slIJZLCKSAH4AXJvjGre5T3TflCrW00gtJZtnYmNTL3J5feGM6Vx87PhMhTKsf1HXyFwnXkkk0ouW5bJQ+rKiMYxGpWIWiog8jjMDOMg3Il7iGuAhVV0doi8uU9W1IjIYJ6D5aZwZx2FyXA1cDTB58uSwQ4oibJzLG0NpcNfN1887HIClm/ak2kYPbivqGv7Z8D3qZGy1uWut5Oqd3pIdZxh9iYopFFU9J9c+EdkoIuNUdX2uLBbgZOB0EbkGGAS0isgeVZ2tqmvde+wWkbuBE8ihUFR1LjAXoL29vcRShX7ZU1uptuDTdCKRe1+jkqkkiztXkFT14KQ6E0G9mEyjK1zDMNLUyuVVMItFVS9T1cmqOhX4KnCnqs4WkWYRGQWplMsLgcXVETv8yTnL5SWlD771SlMZc2tEYM32/fzXvKXs6+hGJF3KJZfC7S39Zhh9iVoplNAsFhFpF5FbCpzbBjwqIouAV4C1wM2VFNZP2NrkicCo6E+I6i2um6YyEg1EYF9nD9995G1eWLGNhAjHTXYyxXOZjL2j1wyjb1GTLC9V3UpIFouqLgCuCmm/Hbjd3d4LzKyshIXxj69ZLi8RDh87mOWb9zJlZOmLQtUT5cyt8SvVjp4kCZHUevW5FtkyC8UwGg8rX18k3vrmA1pzz6UQER758vurKlelaSon0cB3eGd3EpF0lldXYBng9CmmUQyj0bDSK0XS0d0DwPAB6RpVwXkovSUQ78c/sbF4CyWThEhq5nx3Tw6nVy/sQ8Po7ZiFUiRHjB3CNWdM5/KTp6bagg/svWV2vJ9y6pMFLZr1O/enLJTuXC6v4m5hGEYdYAqlSBIJ4Wvu3AyP4HoovdFCychcK/Lc4PGnTB9FS0qhJLnpUzMZF1gvfuaUnOXdDMOoU8zlFQPZFknv0yi5YihRBv5g9/RraeKwsYM5aHAb5x81jvOOHMsxk4ZlHHPw6EGsnHMBE4qclW8YRu0wCyUGggOmv/hhbyEsy+v7HzuGS2ZOLHhumHo9csJQXvhGzrmvhmGUyNTZD5Z03so5F5R9b7NQYsD/xP6lsw/llOkjayhNZfDm2hwzcWhKQwSX881FObPhe2E4yjB6LaZQYmLUIKe+1dETh2ZNdOwtvPzNWdxz9ckpF1/UOjbl9IYpFMNoHHqfb6ZGeANfb8zw8hjuLsvrfcOoFko5GsXmo5RHqe4PwygFs1BiphfrkxSlFIcs914//eTxJV/DMIzqYAolZnqzheLhKYjIBkqgSzSysyxt3Ew/aGDkcwzDqA2mUGLCG/j6hEJxv2KOOYlZBBXPR48vnBnm4fWnub4Mo/4xhRIzvTQen0GxOrM7ma7XddeVJ3LqIaOKuFlp9zQMo/pYUD4m0mXt+8LI52V5RTNRLj52Atv3dfG1DxzGkROGlnCn3jhV1DB6H6ZQYqYvWCjnHTmW37+8lmMmDit8MHDm4Qdx5uEHlXQvKTJF2TCM2mEKJSY8H39vnYPi56/eM5rX//kDVfmu6RTlit/KMIwysRhKzPR+deJQLcXpeRCLyQwzDKM2mEKJib4VQ6kexaYoG4ZRO0yhxEQ6bbimYvQ6UhaKKRTDqHtMocRMX5iHUk08iy9pGsUw6h5TKDFxyJjBAKmFo4x4MPVsGI2DZXnFxL995CieW7aVw8cOrrUovQpzeRlG42AKJSYmDOsfabEpozgsy8swGgfzzxh1jWV5GUbjYArFqGvSFophGPWOKRSjrkmVXjETxTDqHlMoRl0zoKUJsAmjhtEIWFDeqGv+/dJj+eXz73LMxOKqFBuGUX1MoRh1zZgh/fjKuYfVWgzDMCJgLi/DMAwjFkyhGIZhGLFQE4UiIiNE5DERWeK+D89xXI+IvOK+HvC1TxOR+e75vxaR1upJbxiGYYRRKwtlNvCEqh4KPOF+DmO/qh7rvj7sa78B+JF7/nbgysqKaxiGYRSiVgrlIuAOd/sO4OKoJ4qTP3oWcG8p5xtGIyAi54nI2yKyVERyPXAZRl1RK4UyRlXXA7jvuRYc7yciC0TkeRHxlMZIYIeqdruf1wATKiuuYVQPEWkCfgp8EJgBfEJEZtRWKsMoTMXShkXkcWBsyK5vFHGZyaq6TkQOBv5HRF4DdoUcl3MatYhcDVwNMHny5CJubRg14wRgqaouBxCRe3Cs+jdqKpVhFKBiCkVVz8m1T0Q2isg4VV0vIuOATTmusc59Xy4i84DjgN8Bw0Sk2bVSJgLr8sgxF5gL0N7ebvU7jEZgArDa93kNcGKNZDGMyNRqYuMDwBXAHPf9/uABbubXPlXtEJFRwKnAd1VVReRJ4BLgnlznh7Fw4cItIvJujt2jgC1Ff5P4qRc5wGQJI58cU2K6R1idmYyHIb/lDewRka155KomjfA7VZOGkUNuyHt+pL9tqUXRPREZCfwGmAysAj6mqttEpB34vKpeJSKnAD8Dkjixnn9X1Vvd8w/GUSYjgJeBT6lqR5kyLVDV9nKuEQf1IgeYLLWSQ0ROBr6tqh9wP18HoKr/Vku5omBy9G05amKhqOpW4OyQ9gXAVe72s8BROc5fjuNnNozeyIvAoSIyDVgLXAp8srYiGUZhrJaXYdQZqtotIl8EHgWagJ+r6us1FsswCmIKJc3cWgvgUi9ygMkSRlXkUNWHgIeKOKVP9U8ETI5MqiJHTWIohmEYRu/DikMahmEYsdDnFUq1S1yIyCQReVJE3hSR10XkS277t0Vkra8Y5vm+c65z5XtbRD4QoywrReQ1934L3LbQwp3i8B+uHItE5PgY5TjM971fEZFdIvLlavWJiPxcRDaJyGJfW9H9ICJXuMcvEZErypEph5x1UVQ1qhzusUPc3/AnvrZ57u/myZirUkal5Zjp/v0vdX/TkpYFjSKHiEwRkYXu931dRD7v21e1/iggR/n9oap99oUT8FwGHAy0Aq8CMyp8z3HA8e72YOAdnPIa3wa+GnL8DFeuNmCaK29TTLKsBEYF2r4LzHa3ZwM3uNvnAw/jzJE4CZhfwd9kA07ee1X6BHg/cDywuNR+wElhX+6+D3e3h8fcN6EyhRy3J0f7b4BL3e2bgC9UUg53/4+Bu4Gf+NrmAe3V6o88crwAnOz+lg8DH6yUHO740uZuD3L/98ZXuz8KyFF2f/R1CyVV4kJVO3HmtlxUyRuq6npVfcnd3g28Sf5aZBcB96hqh6quAJZS2ZTpXIU7LwLuVIfncaoVjKvA/c8Glqlqrgmoniyx9YmqPg1sC7lHMf3wAeAxVd2mqtuBx4DzSpUpB/VSVDWSHCIyExgD/KnE+1RMDvc3G6Kqz6kzmt6Z6/w45FDVTk3PlWujMt6hkuWIqz/6ukIJK3FRtUKTIjIVp5zMfLfpi64b5ec+c7WSMirwJ9cE9mZd5yrcWa2+uhT4le9ztfvEo9h+qKVMQSpdVLWgHCKSAH4AXJvjGre5bpdvlupqKlOOCTh94FHR/nBlmSQii3D+Tm5Qt7SUS1X6I48csfRHX08bLljiomI3FhmEU5fsy6q6S0RuBK537389zj/B31RYxlPVKb55EPCYiLyVT+QKyuHcwPHpfxi4zm2qRZ8UIte9Y5FJ6qeoarlyXAM8pKqrQ8bHy1R1rYgMxvkf+DTOE3E15Sjq94rjd1HV1cDRIjIe+L2I3KuqG6luf4TKQUx/v31doawBJvk+5y00GRci0oLzh/NLVb0PwP3D8vbfDPyx0jJquvjmJhH5bxy3Ua7CndXoqw8CL3l9UYs+8VFsP6wBzgi0zyv2plo/RVXLleNk4HQRuQbHV98qIntUdbaqrnXvsVtE7sb5uwsdQCslB05MZaLvuEr3h/9a60TkdeB04N4q90cuOf5CEf2Ri77u8kqVuHCfji/FKVxZMVxz9lbgTVX9oa/dH4/4a8DLOHoAuFRE2sQpxXEoTvCsXDkGuk9EiMhA4Fz3nl7hTsgsvPkAcLk4nATs9MzrGPkEPndXtfskQLH98ChwrogMd11z57pt1ZAphXv/NnfbK6r6husX94qq5jw/LjlU9TJVnayqU4Gv4sSdZotIsyuX92B1IenftWpyuL/ZbhE5yf2fvDzs/LjkEJGJItLf3R6O87u8Xe3+yCVHbP1RbBS/t71wsnbewckU+kYV7ncajim5CHjFfZ0P/AJ4zW1/ABjnO+cbrnxvU2ImSogcB+NkSr0KvO59dxxf+xPAEvd9hNsuOIs+LXPlLDsrJSDPAGArMNTXVpU+wVFi64EuHEvjylL6Accdt9R9fbYCfzu5ZGoHbnG3T3HletV9vzLwm7/gyvdb3GyfSsgROP4zuNlVwEBgofubvo5jKZSUoVeOHL7jFru/5U9wJ3pX6HeZ5X7nV933q2vRH7nkiKs/bKa8YRiGEQt93eVlGIZhxIQpFMMwDCMWTKEYhmEYsWAKxTAMw4gFUyiGYRhGLJhCMQzDMGLBFIphGIYRC6ZQDMMwjFj4/4ALG0+t1LwYAAAAAElFTkSuQmCC\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for param, samples in zip(['intercept', 'slope', 'precision'], trace_tuned.T):\n", " fig, axes = plt.subplots(1, 2)\n", " axes[0].plot(samples)\n", " axes[0].set_ylabel(param)\n", " axes[1].hist(samples[int(len(samples)/2):])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "50 random regression lines drawn from the posterior:" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,6))\n", "plt.plot(age, price, 'bo')\n", "plt.xlabel('age (years)'); plt.ylabel('price ($1000\\'s)')\n", "xvals = np.linspace(age.min(), age.max())\n", "for i in range(50):\n", " b0,b1,tau = trace_tuned[np.random.randint(0, 1000)]\n", " plt.plot(xvals, b0 + b1*xvals, 'r-', alpha=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise: Bioassay analysis\n", "\n", "Gelman et al. (2003) present an example of an acute toxicity test, commonly performed on animals to estimate the toxicity of various compounds.\n", "\n", "In this dataset `log_dose` includes 4 levels of dosage, on the log scale, each administered to 5 rats during the experiment. The response variable is `death`, the number of positive responses to the dosage.\n", "\n", "The number of deaths can be modeled as a binomial response, with the probability of death being a linear function of dose:\n", "\n", "
\n", "$$\\begin{aligned}\n", "y_i &\\sim \\text{Bin}(n_i, p_i) \\\\\n", "\\text{logit}(p_i) &= a + b x_i\n", "\\end{aligned}$$\n", "
\n", "\n", "The common statistic of interest in such experiments is the **LD50**, the dosage at which the probability of death is 50%.\n", "\n", "Use Metropolis-Hastings sampling to fit a Bayesian model to analyze this bioassay data, and to estimate LD50." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "# Log dose in each group\n", "log_dose = np.array([-.86, -.3, -.05, .73])\n", "\n", "# Sample size in each group\n", "n = 5\n", "\n", "# Outcomes\n", "deaths = [0, 1, 3, 5]" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "from scipy.stats import distributions\n", "dbin = distributions.binom.logpmf\n", "dnorm = distributions.norm.logpdf\n", "\n", "invlogit = lambda x: 1./(1 + np.exp(-x))\n", "\n", "def calc_posterior(a, b, y=deaths, x=log_dose):\n", "\n", " # Priors on a,b\n", " logp = dnorm(a, 0, 10000) + dnorm(b, 0, 10000)\n", " # Calculate p\n", " p = invlogit(a + b*x)\n", " # Data likelihood\n", " logp += sum([dbin(yi, n, pi) for yi,pi in zip(y,p)])\n", " \n", " return logp" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Iteration 0\n", "Iteration 1000\n", "Iteration 2000\n", "Iteration 3000\n", "Iteration 4000\n", "Iteration 5000\n", "Iteration 6000\n", "Iteration 7000\n", "Iteration 8000\n", "Iteration 9000\n" ] } ], "source": [ "trace_tuned, acc = metropolis_tuned(n_iter, (1,0), prop_var=1, tune_for=9000)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for param, samples in zip(['intercept', 'slope'], trace_tuned.T):\n", " fig, axes = plt.subplots(1, 2)\n", " axes[0].plot(samples)\n", " axes[0].set_ylabel(param)\n", " axes[1].hist(samples[int(len(samples)/2):])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open(\"styles/custom.css\", \"r\").read()\n", " return HTML(styles)\n", "css_styling()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.2" } }, "nbformat": 4, "nbformat_minor": 1 }