{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Machine Learning and Statistics for Physicists" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Material for a [UC Irvine](https://uci.edu/) course offered by the [Department of Physics and Astronomy](https://www.physics.uci.edu/).\n", "\n", "Content is maintained on [github](github.com/dkirkby/MachineLearningStatistics) and distributed under a [BSD3 license](https://opensource.org/licenses/BSD-3-Clause).\n", "\n", "[Table of contents](Contents.ipynb)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns; sns.set()\n", "import numpy as np\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import scipy.stats" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from mls import StochasticProcess" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Stochastic Processes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A **stochastic process** is a black-box generator of random sequences\n", "$$\n", "x_0, x_1, x_2, \\ldots\n", "$$\n", "where, in general, the value $x_n$ depends on the history of all previous samples, so the black box has long-term memory. The values appearing at the $n$-th position of many runs of the black box sample the random variable $X_n$. In general, samples can be multi-dimensional, $\\vec{x}_i$, but this does not present any special challenges or require new concepts so we will stick with the cleaner 1D notation in the following.\n", "\n", "Here is a simple example of a general stochastic process (implemented using `mls.StochasticProcess`):" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "class StochasticExample(StochasticProcess):\n", "\n", " def initial(self, gen):\n", " return gen.uniform()\n", " \n", " def update(self, history, gen):\n", " return 0.5 * (np.mean(history) + gen.uniform())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two useful visualizations of a stochastic process are:\n", " - Plots of a few long runs output by the black box: how does it evolve in \"time\" $n$?\n", " - A pair plot of the first few random variables (from many short runs) for a more detailed look at short-range correlations." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "StochasticExample().plot(nsamples_per_run=50, nruns=3)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "StochasticExample().pairplot(nsamples_per_run=4, nruns=1000, x0cut=0.5)" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**EXERCISE:** For each panel of the pairplot above:\n", " - What distribution of random variables does each panel show?\n", " - What correlated random variables are marginalized out, if any?\n", " - What conditional probability do the two colors indicate?\n", " - Explain how the pairplot answers the question \"Are $X_3$ and $X_0$ independent?\", i.e. $P(X_3\\mid X_0) = P(X_3)$?\n", " \n", "Hint: the top-left panel shows $P(X_0\\mid X_0 \\le 0.5)$ and $P(X_0\\mid X_0 > 0.5)$, with no marginalization since $X_0$ starts the random sequence." ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "The histograms show the distributions $P(X_n)$ which are marginalized over $X_{n-1},\\ldots, X_0$. The scatter plots show the joint distributions $P(X_i, X_j)$ which are marginalized over $X_{n-1},\\ldots, X_0$ with $n = \\max(i,j)$ and excluding $X_{\\min(i,j)}$. Note that these are distributions of random variables $X_n$, not random values $x_n$.\n", "\n", "More explicitly:\n", " - $P(X_0)$ has no correlated random variables marginalized out since it starts the sequence.\n", " - $P(X_1)$ is marginalized over $X_0$.\n", " - $P(X_2)$ is marginalized over $X_1, X_0$.\n", " - $P(X_3)$ is marginalized over $X_2, X_1, X_0$.\n", " - $P(X_0, X_1)$ has no correlated random variables marginalized out.\n", " - $P(X_1, X_2)$ is marginalized over $X_0$.\n", " - $P(X_2, X_3)$ is marginalized over $X_0, X_1$.\n", " - $P(X_1, X_3)$ is marginalized over $X_0, X_2$.\n", "\n", "The two colors apply the conditions $X_0 \\le 0.5$ and $X_0 > 0.5$, so, for example:\n", " - The $(x_2, x_3)$ scatter plot shows $P(X_2, X_3\\mid X_0 \\le 0.5)$ and $P(X_2, X_3\\mid X_0 > 0.5)$.\n", " - The $x_3$ histogram shows $P(X_3\\mid X_0 \\le 0.5)$ and $P(X_3X_0 > 0.5)$.\n", "\n", "The difference between the two $x_3$ histograms demonstrates that $P(X_3\\mid X_0) \\ne P(X_3)$, therefore $X_3$ and $X_0$ are *dependent*. In other words, $X_3$ \"remembers\" $X_0$.\n", "\n", "Note that dependence nearly always implies correlation, but it is possible to construct [artificial counter-examples](https://en.wikipedia.org/wiki/Uncorrelated_random_variables#Example_of_dependence_without_correlation).\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An observer watching many different sequences generated from the same black box would need to measure all these conditional probabilities to fully describe the process:\n", "$$\n", "P(X_0) \\;,\\;\n", "P(X_1\\mid X_0) \\;,\\;\n", "P(X_2\\mid X_1, X_0) \\;,\\; \\ldots \\;,\\;\n", "P(X_n\\mid P_{n-1}, P_{n-2}\\ldots, P_0) \\; .\n", "$$\n", "The equivalent Bayesian network (up to $n=3$) is:\n", "![Stochastic process graphical model](img/Markov/stochastic_graph.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Markov Chain" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A **Markov chain** is a special type of stochastic process where $X_n$ only depends directly on $X_{n-1}$ and not on any earlier samples. In this case, we say that $X_n$ and $X_{n-2}$ are [conditionally independent](https://en.wikipedia.org/wiki/Conditional_independence).\n", "\n", "In other words, a Markov chain is a black box with very short-term memory. The samples $x_0, x_1, \\ldots$ produced by a single run of a Markov chain are referred to as a **Markov-chain Monte Carlo (MCMC)**.\n", "\n", "Our observer now only needs to measure:\n", "$$\n", "P(X_0) \\;,\\; P(X_1\\mid X_0) \\;,\\; P(X_2\\mid X_1) \\;,\\; \\ldots \\;,\\; P(X_n\\mid X_{n-1}) \\; .\n", "$$\n", "The equivalent Bayesian network is:\n", "![Markov chain graphical model](img/Markov/markov_graph.png)\n", "Random variables without a direct connection (arrow) are conditionally independent.\n", "\n", "An important subset of Markov chains are **stationary**, which makes our observer's job even easier since they have the property that\n", "$$\n", "P(X_1\\mid X_0) = P(X_2\\mid X_1) = \\ldots = P(X_n\\mid X_{n-1}) \\; .\n", "$$\n", "In other words, a black box with very short-term memory and no sense of time. Our observer now only has two conditional probability distributions to measure, the initial probability,\n", "$$\n", "P(X_0) \\; ,\n", "$$\n", "and the update rule for $n\\ge 1$,\n", "$$\n", "P(X_n\\mid X_{n-1}) \\; .\n", "$$\n", "\n", "Here is a simple example of a stationary Markov process:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "class StationaryMarkovExample(StochasticProcess):\n", "\n", " def initial(self, gen):\n", " return gen.uniform()\n", " \n", " def update(self, history, gen):\n", " return 0.5 * (history[-1] + gen.uniform())" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "StationaryMarkovExample().pairplot(nsamples_per_run=4, nruns=1000, x0cut=0.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The pairplot above demonstrates that $X_n$ and $X_0$ are still dependent, $P(X_n\\mid X_0) \\ne P(X_n)$, even for a Markov process! Some probability calculus shows how this happens. Take $n=2$ for simplicity:\n", "$$\n", "\\begin{aligned}\n", "P(X_2\\mid X_0) &= \\int dX_1\\, P(X_2, X_1\\mid X_0) \\\\\n", "&= \\int dX_1\\, P(X_2\\mid X_1, X_0)\\, P(X_1\\mid X_0) \\\\\n", "&= \\int dX_1\\, P(X_2\\mid X_1)\\, P(X_1\\mid X_0) \\; ,\n", "\\end{aligned}\n", "$$\n", "where the first two lines are completely general, but the last assumes a Markov process, $P(X_2\\mid X_1, X_0) = P(X_2\\mid X_1)$. Compare with:\n", "$$\n", "\\begin{aligned}\n", "P(X_2) &= \\int dX_1 dX_0\\, P(X_2, X_1, X_0) \\\\\n", "&= \\int dX_1 dX_0\\, P(X_2\\mid X_1, X_0)\\, P(X_1, X_0) \\\\\n", "&= \\int dX_1\\, P(X_2\\mid X_1)\\, \\int dX_0\\, P(X_1, X_0) \\\\\n", "&= \\int dX_1\\, P(X_2\\mid X_1)\\, P(X_1) \\; .\n", "\\end{aligned}\n", "$$\n", "The comparison shows that $P(X_2\\mid X_0) = P(X_2)$ would require that $P(X_1\\mid X_0) = P(X_1)$. In other words, the direct dependence of each $X_n$ on $X_{n-1}$ is sufficient to generate long-range dependencies all the way back to $X_0$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another important property that some Markov chains have is **reversibility**,\n", "$$\n", "P(X_n\\mid X_{n-1}) = P(X_{n-1}\\mid X_n)\n", "$$\n", "which can also be defined in terms of forward conditional probabilities as\n", "$$\n", "P(X_n=x\\mid X_{n-1}=y) = P(X_{n+1}=y\\mid X_n=x) \\; ,\n", "$$\n", "and roughly corresponds to time-reversal invariance.\n", "\n", "*A reversible chain is always stationary, but not vice versa.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The update rule for a stationary Markov chain,\n", "$$\n", "P(X_n\\mid X_{n-1}) \\; .\n", "$$\n", "can be conveniently visualized with a 2D plot. For example, taking $n=1$:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "StationaryMarkovExample().plot_conditionals(which=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The blue line shows the mean $X_1$ at each $X_0$,\n", "$$\n", "\\langle X_1\\rangle = \\int dX_1\\, X_1\\, P(X_1\\mid X_0) \\; .\n", "$$\n", "Note that this is essentially the $(x_1, x_0)$ scatter plot from above, but with samples now histogrammed to yield conditional probabilities." ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**DISCUSS:**\n", " - The speckling is due to using finite statistics to estimate the probability. How would this plot look different with infinite statistics?\n", " - This plot shows $P(X_1\\mid X_0)$. Would $P(X_2\\mid X_1)$ look any different? How about $P(X_2\\mid X_0)$?\n", " - Are these conditional probabilities normalized along $X_0$? along $X_1$?\n", " - How would this plot change if we changed the definition of `initial()` in `StationaryMarkovExample`?\n", " - What condition on this plot does a reversible Markov chain satisfy? Is this example reversible?" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "With infinite statistics, the diagonal band would be a uniform color, since $P(X_1\\mid X_0)$ is uniform (within the diagonal limits shown) for each $X_0$.\n", "\n", "A plot of $P(X_2\\mid X_1)$, or any $P(X_{n+1}\\mid X_n)$ would like identical since this is the definition of a stationary Markov chain. However, $P(X_2\\mid X_0)$ involves two updates, so its plot might look different.\n", "\n", "A conditional probability $P(\\alpha\\mid \\beta)$ is normalized along $\\alpha$, with the value of $\\beta$ considered fixed. In other words, a numpy array of values `T[n,m]` tabulating $P(X_m\\mid X_n)$ on a grid satisfies:\n", "```\n", "np.sum(T, axis=1) = 1\n", "```\n", "\n", "This plot only shows the update rule and does not depend on how we chose an initial value for the Markov chain.\n", "\n", "A reversible Markov chain has $P(X_1\\mid X_0) = P(X_0\\mid X_1)$, which makes this plot symmetric under the interchange of its axes. In other words, mirroring the plot along the diagonal should not change its appearance. Since this is not true in this example, `StationaryMarkovExample` is not reversible.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Equilibrium Distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Repeated use of the (same) update rule associated with a stationary Markov chain reveals a useful feature. These plots show 1, 2, 4, and 8 iterations of the same rule:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "StationaryMarkovExample().plot_conditionals(which=(1, 2, 4, 8))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**A stationary Markov chain eventually reaches an equilibrium $P(X_n\\mid X_0) \\rightarrow \\tilde{P}(X_n)$ that does not depend on $X_0$.**\n", "\n", "We saw earlier how, in general, $X_n$ and $X_0$ are dependent, but we now learn that stationarity tames this behavior and guarantees that $X_n$ and $X_0$ are independent for sufficiently large $n$.\n", "\n", "We will not prove this result, but here is a less trivial example to help build the case:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "class StationaryMarkovExample2(StochasticProcess):\n", "\n", " def initial(self, gen):\n", " return gen.uniform()\n", " \n", " def update(self, history, gen):\n", " return np.abs(np.fmod(np.cos(2 * np.pi * history[-1]) + 0.1 * gen.normal(), 1))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "StationaryMarkovExample2().plot_conditionals(which=(1, 2, 3, 8))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For practical applications, there are two issues to deal with:\n", " - There is no way to know in advance how big $n$ needs to be to achieve equilibrium.\n", " - Given some stationary Markov chain, we can generate samples from *some* equilibrium distribution $\\tilde{P}(X_n)$, but how do we build a chain to sample a specific distribution?\n", "\n", "The second issue requires solving an [inverse problem](https://en.wikipedia.org/wiki/Inverse_problem), which is generally challenging. However, there is a general class of solutions that we will look at below." ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**EXERCISE:** Define your own Markov chain, following the `StationaryMarkovExample` above, and make similar plots. Is your chain stationary? For a challenge, try to build a reversible chain." ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "The test for a stationary chain is whether it only uses `history[-1]` in its `update()` method. The test for a reversible chain is whether its plot of $P(X_1\\mid X_0)$ is symmetric about the diagonal.\n", "\n", "Here is an example of a reversible (and therefore stationary) Markov chain:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "solution2": "hidden" }, "outputs": [], "source": [ "class ReversibleMarkovExample(StochasticProcess):\n", "\n", " def initial(self, gen):\n", " return gen.uniform()\n", " \n", " def update(self, history, gen):\n", " return np.fmod(history[-1] + 0.2 * gen.normal() + 1, 1)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "solution2": "hidden" }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ReversibleMarkovExample().plot_conditionals(which=(1, 2, 4, 8))" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "Note that we can use the diagonal symmetry of the first plot to confirm that this is a reversible chain.\n", "\n", "---" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "# Your solution here..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Custom Markov Chains" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Metropolis-Hastings-Green (MHG) algorithm is a general approach to designing a custom Markov chain that has a specified target probability density, $\\tilde{P}(X_n)$. All practical algorithms are special cases of MHG:\n", " - Metropolis-Hastings-Green\n", " - Metropolis-Hastings\n", " - Metropolis\n", " - Gibbs\n", " - Hamiltonian\n", " \n", "The simpler Metropolis-Hastings (MH) algorithm contains the essential ideas so we will focus on that.\n", "\n", "The history of using Markov chains for practical inference is intimately connected with physics: many of the pioneers were physicists motivated by physics problems, including [Metropolis](https://en.wikipedia.org/wiki/Nicholas_Metropolis) and [Gibbs](https://en.wikipedia.org/wiki/Josiah_Willard_Gibbs), and the Hamiltonian method derives from classical mechanics.\n", "\n", "See this [blog post](http://twiecki.github.io/blog/2014/01/02/visualizing-mcmc/) for helpful animations comparing some of these methods." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Metropolis-Hastings Updates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The MH algorithm relies on a **proposal distribution** $Q(X_{n+1}\\mid X_n)$ that is easier to sample than $\\tilde{P}(X_{n+1}\\mid X_n)$. (If you knew how to sample $P$ directly, you would not need MCMC!)\n", "\n", "We often use a multivariate Gaussian for $Q$ since it is easy (and efficient) to sample from. Any proposal distribution is valid, but choosing a $Q$ \"closer\" to $P$ generally reaches the desired equilibrium faster.\n", "\n", "The proposal distribution can either be used to update to the current state (\"random walk\") or to generate a new state:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def sample_proposal(x0, gen, mu, C, mode):\n", " sample = gen.multivariate_normal(mu, C)\n", " return x0 + sample if mode == 'random_walk' else sample" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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qiVulE775XX/dW/+voRPNuZUcCIwxvwf8LXA2cBJwjTHmhJzTTgM+Zq09KfO/75ZeVJHiBZ0tlC8X0OwLlxNLJLKPJxLMueyS8hY2Qs7oP2Vyt7Bc+VoLXscrPc/f7zp+m9I04vqCMC2C84BHrbW7rbXDwE+Bj+accxrwOWPMJmPMPxpjpoe4n0jRgs4WSpy+HFqzK3snF1D3mYs54vKVky2D1lm9HHH5Sg5f+m7f+45uXc/Q6hvYd9tKhlbfwOjW9eH+kCZ0kbnAd1pmMUncKp3wLV/a6kret5rCjBEcBWx3/b4d1/7ExphO4L+AG4FfAauALwCfD3FPkaIEmS0EhXMBdZ+5eMrCs30vPsHQf9w75fz9T97NxMuPTZ4XpU1oilFoWqZX6og9I3u5ad1Xs86rdMI3v+sX2qymkZSca8gY83lgurX2C5nfrwZOtdZe53P+ycBd1tog0yzmAr8uqWAiLr99/Am2ffdWkiMjk8fibW3Mu/66vG/0hex78Ql2PXgrqfFD1421ttF54rnse/ZfPb/T2j2bOZ/8Qcn3jJonX9vIjzf9M7v2757yWaIlwbWnX8I5x56Rde7A/t30dszi4hMvmPysnGXJvX6l7xtCUbmGwgSCK4BzrLVXZX7/AhCz1n4l8/sc4Dxr7V2Z308BbrXWBnlKc1HSubrQDM+lHDmGcq/R2X+Q9s7hqSfG4pBKTj2e0XXNqiJL35jK+e+m3Enfaq3Zks79O/BlY0wfMAwsB65xfX4AuNkY81imQNcD/xTifiIl8erWKYbXgrK9eyE1Fzpm55ycJwhEYROaSohC0rdaKzkQWGvfzHQPPQYkgDustRuNMQ8BX7TW/tIYcy3w88znvwBuKUehRSopd4Xxzl+OTJl5RBL2veERCPK0CKKyCU25RSHpW62FWlBmrV0NrM459gHXz2sAZfWShuG1wnhi0PvcZE5soDVBy/wlTGxdN2VxWsvC92QNFCsldnCNvvtXI9DKYhEXrxXG8YRHpQ9M6+ki1pmYMmtotH9+3p3IlBK7OFFI+lZrCgQiLl4rjLuOht+9Crh6fGKJBHOvvNIz6Vxi/uK800TzLXJTIPBWraRvzZI7qFjaj0DExWtAt2M29CyYUdSCsnzCpsSWynByCjnjEU7uoHLtk1DP1CIQcUmcvjxrjACA1gQ9H7qEw8u0GCzoIjeprnw5i5q9VaAWgYhLYv5i2s5ZOdkyiHX20nbOyrKuCPbLXeSkxJbaiPI0VbUIJNL8Zu9UMhWEMw6gWUP1JcrTVBUIpCkVmp45uGE9v/3JapJDQ5PHSpm9s//Ju5nY8nh67UAsTsuCpXScc0XB74Vd5CblF+VpqiWnmKiwuSjFRF1oxOeSOz0TgJZWYtPbSA0PE5sxg9TBEZgY975AIgHj45BMQjxO97uX0n/pocrdHWTiifSsIvfCspaF7wkUDPzK3gwthUb8dwPVmTXUbCkmROqS1/RMJsZJDacr/tSwR44gN/d3k0kG/zOdSbT/0iumBJnkaGZqKYeCwcSWx6GEQKD1BbXX7HsT+9FgsTSdSkzDHHziccAnyCThd6/A28/B/l3kzTeUT9BNdETKTS0CaTp+0zNDSSZ55bM35L3uZOsgBl15LpWby8hZeaz1BVIrahFI0/GanlkOgSrkJAztaPP92Mll5KxgdjatGd263ncdgdYXSKUpEEjTyd1aMt7ZCS0tVbv/xPCI72cj6++bksuI8VFGn17jHcDi0Nl/UFtdSkWpa0iaUu70zNzZODP69sHY6JQcQuXQ0hZndOv6KWsRRreuhxHvgerU0ACxTbdx2O/PYN9rMSaGRyZnJLV3DmurS6koBQKJhNzAsO/uP4eR9Jv5vje8s4sW0tLVSXJkNHuANw6J7iSvf/s2kiO3ZU0BHX268KBve+cw7Ys8Psi0GhQIpBIUCKTp5Q7Oxo85EUbSC8k6Zh+a9rl9Y3HXndg3lO52mhglNZFOV912GBwYYLKV4Z4CGvPIbOq2f9ehoOS1PsErM6pIOSgQSN0Ls8jKc6OZlx/zPNdv34F8kkNDEIfD3pGutN9+jildTc4U0MNP6vWtzPfvyk517bU+QVtdSqWECgTGmBXATcA04NvW2u/mfH4ScAfQDTwBXGet9VnOKTJV2EVWzkYzhd62IX1s8LU4qYkiBw1c21b6BZLx3QMkTr9mambTjH1vMHWswr0dZmtCW11KxZQ8a8gY83vA3wJnAycB1xhjTsg57V7gz621xwMx4OpS7yfRFHaRVWpoYPJt26mknbft/buyz+2YDYeZduIlzDx1ru333dZZvZ6ZTVsWvgdaE74BJDlamQyoIm5hWgTnAY9aa3cDGGN+CnwU+Erm92OBdmvthsz5q4D/BXw/xD0lYsIusop19rLvuYH8b9sZ6VbDcEkDx04A8NvNzEkx7bV72Wj/fFqeuYOJkaktkdZZvXSuuKX4AokUIUwgOArY7vp9O3BGgc+PDnE/iaCwm7jEjzmR5Kj3mIC7ws/toy9KPB0AJsVcH3V2cvjHVuTtxkrMX0zfZUxJlBdLJJg+53C2XX8lEyNJWtrizPzjpcz6cGkJ7UT8hAkEccCdGjRG9n9GhT4vKJNFr2r6+vIlBoiuWj6X1MpL2fbdW0mOHFqkFW9r47iVlwYq1+tvvuA7COzuxvHso/cQa4WUa5TLPd7gFUxSIwcZfWo1+zbdTmt3LzPfcwld75y6xWXfh95HV3c7r//oPkZ2DdA2u5cZxx3Jnl++MJm6aGIkycBDj9HenmDOpdcULmyN6b8nf/X2bMIEgjeAc1y/9wNv5Xx+ZJ7PC1Ia6tqr9XOJnXAyh192xZRZQ7ETTg5UrvHBXZ7dNcRh1nvfQ2z/JlJDA4G7g9xBgFj2oLNXMEmNjbN36xBHnJQuy84Hv8/g4AHP/v7YCSdz7NdOnvx92/VXTslfl0rCm//8r4y/9q9ZeYrqTa3/3dSzKqWhLkqYQPDvwJeNMX3AMLAcmHxNsda+Zow5aIxZYq1dB1wGPBzifhJRzmIwZxrpjjtuY9faNVOmkXolc4t19tJBumvJPWuo+/dnZHWx7PxV/oRynlIw+PqhQJBvwHeSa2FYoWmxXmMG7us5eYpAK44lnJJnDVlr3wQ+DzwGPAesttZuNMY8ZIw5LXPaJcC3jDFbgE7gO2ELLNE0uGE9O35452RlPb57gB0/vJPBDekcPLnJ3IZfHeD1b9/GW48O8Pbz6WsccRIceQYccVp6M3q3UhPV5XYT+ZlMUU26Anemxbr/nrfvWTX59wDE22Jel8q+TyawiIQRah2BtXY1sDrn2AdcPz9P9gCySEne/vF9MDGRfXBigrd/fN+h9A2Z+flTFmeNwOCr6Z9nzPXuTuk+czH7f7U1ve9AsrTkQ55dUBnuBWIz5vayM8+0WKdV0DU3we+2jkzp0urKmXKhFccSlrKPSkPw21XMOe6uDD376pMwvDc9FdOrG2Vww3r2rV9XfBBwJTXtmA2HHQct3T59tJkpq4nTlweaFttx2AiHzT3UAogn4LC5UxfCacWxhKUUE1IXwu7VG+s8lL4h3+peP547j7mvnzNbyHHYse6TWug4qp2O3iHfvEVO2YJMi3XGN3Ir/lxacSxhqUUgNReov7zT+y3bOZ44fTm0pl+d863u9ZMvSMQTmSDQkg4IzrWOueh9zJibuWbbDIjFJpPZ+ZUhnsB37wH3wrPcv8lPy8L3aKBYQlOLQGouXxoJp1Vw+MdWsOOHd8GE67W8pZXDP7YCODRrZvTpNXQdPcDgq9lbB+dWsrnybW852cKYgFQmwdwRn7slMw3wYgB++83rGfzV+OSspNwspMBk/35qaGDy78rXCnL/TamhAWjrBFIwMlzXU0el8SgQSM0F6S8PWnEm5i+mE2gvsqtp9oXLp6zs9ZSEoTfjHOE6NLhhPXu3DGdlDj0wAO29MPK7qYnunD793D0SvHilpBApNwUCqbmgaSSCVJylnOucD9mBxi9A5c7v37V2jWcuo5Hfpaesuu3f08LQlhHeenRlSWMhIpWgQNCkntq8g7WPb2NgcITe7jYuXDqPsxb117pYnrzexgt15fgJM+icGzxe+az3IrPcAFWwSykjPa11ApJDk98rJqW2SKUoEDShpzbv4O6HtzA6nn5NHRgc4e6HtwCULRiUM9AE6fYJIsjeBfkCRe7K5J7FJzLwb+sKBii/1kN6QVgqPZA8NsK+N8Z9N60pJRCEnWkl4lAgaEJrH982GQQco+NJ1j6+rSyBoBKBptiuHC+FBp3zBYrpvUzZyWzawXX0vncJe9dvylvZ+rVoDr9sJV1nLmZo9Q2kRvzTWxed2oLwG/aIuCkQNKGBwZGijher0oGmVPkGnUe3rmfnj+4gNZpd7kPbSDJ157DxURL7N/GOm/PvB1CoReOsb8i3FebghvUFK3B3i2Xn83Hfv0WBQIqlQNCEervbPCv93u62sly/0oEmV9AuEL8umpbuTkaeXOWbxG189wCpIe97B03f4G7RuJPjtc7qpbN/Bu2dw+kUFK94f79QBZ6793K+v0WkWFpQ1oQuXDqPRGv2/2sTrXEuXDqvLNf3CyjlCjRuQRabOfwWaXUdnYLx0bwLzfzSNBSbvsGrvL/77xH272nJu0K4UAXuzqUEpS2aE/GjQNCEzlrUzxXnL5ismHu727ji/AVl67apdKBxK2bP4u4zF3PE5SsnK8PWWb0ccflK2jvT+Yi6jmbKv3hn8NdzFW8JG8Z7lnd8nKG324l19pZcgee2TPL9LSLFUtdQkzprUX/F+uud61ZjemqxexZ7DToPvZLuV3feyAdfd+UNmjYNmLqKt9SVu75rDwaH6Fzxjxz+jvUlTZV151KCQ4nnht6MMzGS1KwhCUWBoMlUa/1AJQONW9g9iyGdsydrRpB7K8nh4azZNk7FP7hhPW/cvobx3bcVVckWKm+pU2Vz/waAjv4EMy9aqZXHEpoCQROpxvqBaivHYjP32/6+5wYKzuUPMzUzSHlLmSpbrhaLiJeSA4ExZg5wL3A4YIFLrLVDOeccC7wIbMscetta+75S79mIqrnCt16ndYZRrsVmTs6e5KMrPT93v8UHSYJX6fJ6Ud4hqZQwLYLvAd+z1v7EGPMF4AvAX+WccxrpLSyvDXGfhlXtN/RqT+uslnIsNnME6WoqdlwiV/eZi5ne63p7f2UNo73F7yuslcNSLSXNGjLGTAPeDfw0c2gVcJHHqacD7zTGPGeMedQY866SStmg8r2hV0I1p3U2qiD7APiNPwQdl8jdP9nZZH5069Qpr36KmTYrElap00dnA4PWWmfuxXbgaI/zDpLuPjoF+HvgAWNM8TuEN6hqvaE/tXkHN35vned1KzWts1H5TTF1v2kHCRb55M75B4reZL6YabMiYRXsGjLGXAR8K+fwViCVc2zKUkdr7Zddvz5kjPkasBB4Pkjhent99n6tkL6+rvJeb2Y7O/cc8Dxernv95zO/4Z5HLCNjE1M+65vZzuXnL+TcU48JdY9yP5da6/vQ+5j3If+hqr4PvY+u7nZe/9F9jOwaoG12L3Muu4TDl7576rkez2bf0G7P66aGdgd+lv+9x/sa43uCX6PWGqWctVBvz6ZgILDW3g/c7z6W6RoaMMa0WGsngCOBt3K/a4z5JOkxAqdzNQaMBS3cwMAQyWRuvKmM9G5T+8p6zQ+ffVzWGAGk39A/fPZxZbvXqn/Z7BkEervb+Ma1ZwGEulclnksjiJ1wMsd+7eSsY7nPwe/ZxDpneaamiHXOCvwsW2fO8h7LmBn8GrUU1X83QVTy2cTjsZJeoEsaLLbWjhljngT+DFgNXA487HHqUqAduNkYsxRoAbaUcs9GVI2FV806QFys3BTS1ZxamXvv+DEnMrF1XXb3UJGrlMu5R4NIIWFmDX0CuNsYcxPwOnAxgDHmOuAoa+0XgU8Bq4wxlwMHgIuttd7ZsppUpRdeVTrBXCPITcjmDM5C8TN1ynHvia3raJm/hORvNmUFh9Gn1zDy2G2BAlUlp6GK5Co5EFhrXwPO9Th+q+vnN4E/LvUejaJSawWCXPfCpfM8u5+iNECcb3C24oHA597J32yic0U6fXWpgarYabO1bBVJY9PK4pDKvVbAXfnPacB9AAAPfklEQVS7+V03bPdTI21p6ccvVXTQFNKVvnc1AlUtW0XS+CITCMpd4flV2FB4Na9fWXKDStDrltr91CwpKXITsrmP18O9qxGoatkqksYXiTTUToXnVNpOhffU5h1luZ4Xv8/ylcVrAVrQ65ai2gveKqVcKaQrde9y7XWQTy1bRdL4IhEIyl3hBamw/QZr85UlSCVfzkHgZplxlJi/mLZzVk5WrLHOXtrOqU5WziD3rkagqkawkeYVia6hcld4hb6Xb7A2X1n8ZgAFuW4pmmnGUS0TshW6dzUyh3qlqa5Wq0gaXyRaBOXOwZPvezOmt5CYFuf2n7/Ejd9bN6X7KV9ZvHb+cn9ezl3GAE6c5/22ODA44ll2KV1i/mI6V9xC1zWr6FxxS9mDVi1bRdL4ItEiKPcUS7/rLXlXP+te2MHoeHqlr9fga6GyTGuNMZrJ4NTZ3srF5x1fkYHbpzbvYN0L/hW9U/buruksmtNT9vtL+SlNtZQqEi2Ccu/h63e9TdsGCo5F+H0X4O6HtzB88FC6iNGxyq29CzLOMTqe5J6HX65YGUSkPkSiRQDlX+Hrdb3bf/6S57lOP3zutNGrP3TC5DVu/N66qm4qE3R8ZJdH0rxmpQVZElWRaBFUS77+/0JTWKs9gyfo+Mjsme0VuX+9KcceAiKNSoGgjLwGe53+/0JTWKu9qUy+gWlHojXO5ecvrMj960059hAQaVSR6RqqhnzpHgp1G1UiZ1C+1dReZT1xXi+btg1knX/uqccUTJmrNBUijU2BoMz8xiIKzdl3vvO5z1zL2HiSsz7y16Eq1CDpI8oxbqI0FSKNT11DZeJsF3nl1x/1nIOfr9vIcdaift5xVDdmTg9/94kloSrSaqWPUJoKkcanFkGRvLpBgEBv31DZTWrcqjX43ExpKqCyq39F6pUCQRH8ukHSi8AKT/2s9CY1bpVKH5EbCGdMb8la+1Cu+9SCFmRJVKlrqAh+3SBeFSHU9q04SFdUsbymwI6MJWmJZZ8XtY1xRBpd6BaBMeZvgAlr7Zc9PksAdwKnkd6qcoW1tmH3LC62Yq/lW3EluqK8AuH4RIrO9lbaprU09KwhkSgrORAYYw4Dvkl6r+KbfU77C2DYWrvQGPNuYBVwZqn3rDW/7pbO9lZGx5IV3S6ylCma5e6K8guEQwfG+c6n3l22+4hIdYXpGroA2ArckuecPwHuA7DWPgH0GWPmhLhnTfl1t1x83vFT8gcteVc/ax/f5juLqBjl3linVNVe9NYoRreuZ2j1Dey7bSVDq2/QamRpOGE2r78HwBjz5TynHQVsd/2+HTgaeL3U+9ZSoe4W5//6DSr/6o293PXtv2JsPMm01jize6bT3ZE9ZfGZZ54G4OMfv2zy2CtvDTKW0yVz/B992jcPUaUWeFVi0Vuj017B0gwKBgJjzEXAt3IOb7HWnhfg+nEg5fo9BgROqdnb2xn01LLo6+sqeM6yc7tYdu78vOc88IunPAeVH/uvtyYr9LHxJG/vPkBrS5yerulTrmFf38u0aXH6Z3VMCQKO3YMjU8r8n8/8hnsesYyMHUqFfc8jlu6u6Zx76jEF/z4vzj2WndtFd9d07nn4ZXbtOcDsme1cfv7Ckq/bDCaeWeuZmmLimbX0LX5fbQpVJ4L89xRV9fZsCgYCa+39wP0lXv8N4EjAWV3UD7wV9MsDA0Mkk6nCJ5ZBX19XwVQKQe3Mk7Hz+D/6dNbvvd1t/N0nlgDpN/kXt11NKnXovERrnNmtMc+ZSbO626aUedW/bJ4MAo6RsQlW/cvmkvYVyH0ui+b08I1rz8o6p1zPrdH09XUxPrjL87PxwV2RfS5Q3v+emk0ln008HivpBbrS00cfAi4HMMacDRy01jZkt1Axiukzdw/Arn18G6mcuDc6niQWiwWeCtosC7wahfYKlmZQ9kBgjLnOGPOVzK//ALQZYzYD3wEu8/9meRRK9VANQTJ7OtxBI9+snCXv6ieema8fj8GSd/nnNCp0HykfpaaQZhB6HUHu+gFr7a2unw8CV4S9R1D1kgDNa1D58JntvPza3qzzct/q/SrrGdNbWPfCDpxesmQK1r2wg98/umfK36UB3epSagppBk2VYiJfArRqL3Byz+F3AlSu3Lf6C5fOY8MDZHUPJVrjxGKxyX2QHX5/V7VzGolSU0jja6pAUK/94377A2/alp32+KxF/fT3drBr70GAyUq80F4GuaqZ00hEGl9TBYJKJVpzlDo/v5gA1d2RoLsjwZ1//YeTx5x75irH39UMm8qISDhNFQhK7R9/avMOHvjFU+zcc8C3Mgwz/hA2QJWr3z+30j9xXi/rXthR8zEVEamtWCp3vmJ9mAv8upR1BMW+4eZW8JCuZK84f0HW92783jrfytxZBxD2HuX8u4KUwc+M6S1MT7QyMDhC38x2Pnz2cQoMHjRX3p+ejb8qrSM4Dng16PeaqkUAxfePBx1gDjP+kG8AN2gF7/xdzvm3//wl1j6+LXBA8Bun8DJ8cGJyAdvOPQfUShBpck0XCIoVtIIP273jFaCK7W4K0z0VZsC8VjOvRKQ6Ir8xTdAFWJXY6KXY/X7D7A8cdmC51jOvRKRyIh8IiqngE9MOnTdjektRffxeiu1uCtM9lS9gOSuWe7vb6Gz3biRqZbJI84p815BTkT/wi1/7zhryGmgdGy99kN3p5/eTr5VSiWmkyRTclZmu6jewrZXJIs0r8oEA0sFg2bnzfUfyy7liudDsnXyVbpjpsV4rmx3uQJI7sK1ZQyLNT4EggGK7ZPLNBMo3e6fQtNBS00fku6dXIHEPbGsaoEjzUyAIoJgumUIze/L15xdaj+Bco9i383z3DDvOISKNT4EggGK6ZAp1I5XSzx9mMVm+NNy93W0KAiKiQBCEV5fMifN6Jxd2uSvnQt1Ixfbzh02tnW9QWgPAIgIKBIF5pZX2qpwLvfEX289fykC1uwVR6G8SEQkdCIwxfwNM5G5Qk/nsWOBFDu1Z/La1tuF39M5XOQd54y+mn7+UgeogOYW0LkBEHCUHAmPMYcA3gYuBm31OOw1Yba29ttT71KN8lbMTJOKx9Pz8sKmdO9tbGTow7nncS5CcQloXICJuYVoEFwBbgVvynHM68E5jzHPAbuBT1toXQtyzLvh1/8ChIJFMHapww3TB+GWH9TteqDtIew6ISK6SU0xYa++x1n4dmMhz2kHgXuAU4O+BB4wxiTznN4Sgm9MHzQOUj5MFNOjxfKuS7/rrP+TvPrFEQUBEshRsERhjLgK+lXN4i7X2vELfzRk3eMgY8zVgIfB8kMJl8mpXTV9fV6Dzlp3bRXfXdO55+GV27TnA7Jnt7NxzwPPcgcGRwNf1LJPPtftmtnted+UHF/GP9z/PyNihQNE2rYWVH1xUcjnClL/Z6dn407PxV2/PpmAgsNbeD9xfysWNMZ8kPUbgbM4bA8aCfr+UjWlKVewK2kVzevjGtWdN/n7VNx7Fq6jxGKFW5n747OM8B58/fPZxntddNKeHy99vpsxKWjSnp6RyaGWxPz0bf3o2/qq0MU1RKj19dCnQDtxsjFkKtAD+SW8amF+8ChvHSkkroc3rRaQYZQ8ExpjrgKOstV8EPgWsMsZcDhwALrbWBtsmq8FUKjMoqGIXkcoKHQhy1w9Ya291/fwm8Mdh79EIyrXBvIhItWllcZmUmhlURKTWFAjKSF04ItKIIr9VpYhI1CkQiIhEnAKBiEjEKRCIiEScAoGISMQpEIiIRJwCgYhIxCkQiIhEnAKBiEjEKRCIiEScUkzUyFObdygvkYjUBQWCGnhq846sTKUDgyPc/XB6mwYFAxGpNnUN1cDax7dlpauG8uxvLCJSCgWCGvDawCbfcRGRSlIgqAG/XcvKsZuZiEixSh4jMMYsAb4FJIAB4Epr7Ws55ySAO4HTSG9VucJa25R7FhdDu5mJSD0J0yK4D7jKWntS5ufveJzzF8CwtXYh8JfAqhD3axpnLernivMXTLYAervbuOL8BRooFpGaKKlFYIxpA26y1m7KHNoEfNLj1D8BvghgrX3CGNNnjJljrX29pNI2Ee1mJiL1oqRAYK0dAe4FMMbEgS8DD3icehSw3fX7duBoIPKBQESkXhQMBMaYi0iPBbhtsdaelxkDuDtzna96fD0OpFy/x4Ckx3meens7g55aFn19XVW9X6PQc/GnZ+NPz8ZfvT2bgoHAWns/cH/ucWNMJ/Az0gPFF1hrxzy+/gZwJOBMkO8H3gpauIGBIZLJVOETy6Cvr4udO/dV5V6NRM/Fn56NPz0bf5V8NvF4rKQX6DCDxfcCvwL+LNNV5OUh4HIAY8zZwEGND4iI1JdSB4tPBi4AXgKeNcYAvGWt/YAx5jrgKGvtF4F/AH5gjNkMjACXBbxFC6SjWzVV+36NQs/Fn56NPz0bf5V6Nq7rthTzvVgqVZ2ulyKdDTxZ60KIiDSoc4BfBD25XgNBG3A66VlGEzUui4hIo2ghPS77NOlemEDqNRCIiEiVKNeQiEjEKRCIiEScAoGISMQpEIiIRJwCgYhIxCkQiIhEnAKBiEjElbxDWbPKpM/YYK3VvpEZQXajixpjzArgJmAa8G1r7XdrXKS6YIz5EvCnmV8ftNZ+tpblqUfGmL8HZltrV9a6LA61CFyMMR2k8yMlal2WOhNkN7rIMMb8HvC3pFOhnARcY4w5obalqj1jzHnAe4GTST+XU40xH6ltqeqLMeaPgCtqXY5cCgTZbgG+XetC1BOf3ejm1LBI9eA84FFr7W5r7TDwU+CjNS5TPdgO3GCtHc2kpX8Z/VuZZIyZRfoFwmvvlppS11CGMWYZ0GGt/Wkmm6pQ1G50UeK1894ZNSpL3bDWbnZ+NsbMJ91FtKR2Jao7PwA+DxxT64Lkilwg8NtxDegm/aYXWSF3o4uSUDvvNTtjzCLgQeBGa+3WWpenHhhjrgJ+Y639D2PMylqXJ5eSzjH5/6T/CTjbBv0P4HngHGtt5LdZytmN7tI8GxFFgjHmCtL/Nq7K/P4FIGat/UptS1Z7mYkFa4C/tNb+pNblqRfGmP9LOivoODAL6ATuttZ+uqYFy1Ag8GCMSVlrtatGhjHmAeC3wHXW2si/+WYGi39BujtoGFgPXGOt3VjTgtWYMeYY4FnSuxY+Wuvy1KtMi+Dcepo1FLmuISlOvt3oalqwGrLWvmmM+TzwGOkZZndEPQhkfAaYDnzTNc52q7X21toVSYJQi0BEJOI0fVREJOIUCEREIk6BQEQk4hQIREQiToFARCTiFAhERCJOgUBEJOIUCEREIu7/A/blbDjCZngeAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_proposals(n=50, seed=123):\n", " gen = np.random.RandomState(seed=seed)\n", " mu = np.zeros(2)\n", " C = np.diag((.3, .1))\n", " for xy0 in np.array([-3, -1]), np.array([3, 1]):\n", " xy = np.array([sample_proposal(xy0, gen, mu, C, 'random_walk') for i in range(n)])\n", " plt.scatter(*xy.T, label='random_walk')\n", " xy = np.array([sample_proposal(xy0, gen, mu, C, 'independent') for i in range(n)])\n", " plt.scatter(*xy.T, label='independent')\n", " plt.scatter(*xy0, marker='+', s=300, c='k')\n", " \n", "plot_proposals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "During each update we evaluate a proposed move to $x_{n+1}$ by calculating the **Hastings ratio**,\n", "$$\n", "r(x_{n+1}, x_n) = \\frac{\\tilde{P}(x_{n+1})}{\\tilde{P}(x_n)}\\, \\frac{Q(x_n\\mid x_{n+1})}{Q(x_{n+1}\\mid x_n)} \\; ,\n", "$$\n", "where $\\tilde{P}$ is the desired equilibrium distribution. Since $\\tilde{P}$ only appears in a ratio, it does not need to be normalized: we saw earlier how this freedom is very useful for performing Bayesian inference, where the normalization is generally not calculable.\n", "\n", "In general, the Hastings ratio is $\\ge 0$ but it can otherwise be arbitrarily large. We always accept a proposed move when $r(x_{n+1}, x_n) \\ge 1$. Otherwise, we accept it with a probability of $0\\le r(x_{n+1}, x_n) < 1$. When a proposed move is rejected, the update returns the original value (so repetitions are possible and quite normal).\n", "\n", "In practice, we work with\n", "$$\n", "\\log r(x_{n+1}, x_n) = \\log \\tilde{P}(x_{n+1}) - \\log \\tilde{P}(x_n)\n", "+ \\log Q(x_n\\mid x_{n+1}) - \\log Q(x_{n+1}\\mid x_n)\n", "$$\n", "rather than $r(x_{n+1}, x_n)$ in order to minimize the effects of round-off errors.\n", "\n", "We can now build a simple custom Markov chain for an arbitrary target equilibrium distribution:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "class MetropolisHastings(StochasticProcess):\n", "\n", " def __init__(self, x0, Qrms, logP, mode, seed=123):\n", " super().__init__(seed)\n", " self.x0 = np.asarray(x0)\n", " self.Q = scipy.stats.multivariate_normal(\n", " mean=np.zeros_like(x0), cov=np.diag(Qrms ** 2 * np.ones_like(x0)))\n", " self.logP = logP\n", " self.mode = mode\n", " \n", " def initial(self, gen):\n", " # Start from the origin.\n", " return self.x0\n", " \n", " def update(self, history, gen):\n", " x0 = history[-1]\n", " # Sample the proposal distribution Q to generate x1 and calculate\n", " # the log of the proposal ratio.\n", " sample = self.Q.rvs(random_state=gen)\n", " if self.mode == 'random_walk':\n", " x1 = x0 + sample\n", " log_Q_ratio = 0. # self.Q.logpdf(x0-x1) - self.Q.logpdf(x1-x0)\n", " else:\n", " x1 = sample\n", " log_Q_ratio = self.Q.logpdf(x0) - self.Q.logpdf(x1)\n", " # Calculate log of the Hastings ratio.\n", " log_ratio = self.logP(x1) - self.logP(x0) + log_Q_ratio\n", " # Accept x1 or keep x0?\n", " if log_ratio >= 0:\n", " return x1\n", " else:\n", " accept_prob = np.exp(log_ratio)\n", " return x1 if gen.uniform() < accept_prob else x0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define the un-normalized PDF for samples that are uniformly distributed within a (hyper)cube spanning $[-1,+1]$ along each axis:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def logP(x):\n", " return 1. if np.max(np.abs(x)) < 1 else -np.inf" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generate samples in 2D using a 2D Gaussian with zero mean and unit variance for the proposal distribution $Q$. Use the following utiliity function to make a scatter plot of the results using:\n", " - color to indicate the last position $n$ in the chain,\n", " - a superimposed plus ($+$) to indicate samples repeated twice,\n", " - a superimposed asterisk ($\\ast$) to indicate samples repeated three or more times,\n", " - a larger circle to indicate the initial position, and\n", " - a dashed box showing the boundary of the target (square) distribution." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def plot_square(xy):\n", " _, ax = plt.subplots(figsize=(8, 8))\n", " xy_unique, xy_counts = np.unique(xy, axis=0, return_counts=True)\n", " repeated = xy_counts > np.arange(3).reshape(-1, 1)\n", " ax.scatter(*xy.T, s=100, c=np.arange(len(xy)), cmap='gist_rainbow', lw=0)\n", " ax.scatter(*xy[0], s=400, marker='o', edgecolors='k', facecolors='none', lw=2)\n", " ax.scatter(*xy_unique[repeated[1]].T, marker='+', s=30, c='w', lw=1, zorder=10)\n", " ax.scatter(*xy_unique[repeated[2]].T, marker='x', s=30, c='w', lw=1, zorder=10)\n", " ax.set_title('Chain has {} / {} unique samples with {} repeated'\n", " .format(len(xy_unique), len(xy), np.count_nonzero(repeated[1])), fontsize='x-large')\n", " ax.set_xlim(-1.1, 1.1); ax.set_ylim(-1.1, 1.1)\n", " ax.add_artist(plt.Rectangle([-1,-1], 2, 2, fc='none', ec='k', ls='--', lw=1))" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_square(MetropolisHastings([0,0], 1., logP, 'random_walk').run(500))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the unique points in the sample do cover the square uniformly and there is no obvious imprint of the Gaussian proposal distribution. However, there are also many repetitions and, more generally, successive points are highly correlated with each other.\n", "\n", "The example above worked out reasonably well, but there are many pitfalls with the MH algorithm, some obvious and others more subtle:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_square(MetropolisHastings([0,0], 0.3, logP, 'independent').run(500))" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_square(MetropolisHastings([1, 1], 0.05, logP, 'random_walk').run(500))" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden", "solution2_first": true }, "source": [ "**EXERCISE:** Study the two examples above and describe how and why they are failing to sample the desired target distribution. Do the locations of repeated samples make sense?" ] }, { "cell_type": "markdown", "metadata": { "solution2": "hidden" }, "source": [ "The first example uses independent updates with a proposal distribution that is too narrow ($\\sigma = 0.3$) to sample the edges of the box efficiently. As a result, points far from the initial point (the origin) are repeated often and the chain would need to be much longer to populate the corners. Note that, although the density of samples is higher close to the origin, when weighted by the number of repetitions, the generated chain correctly samples the target (flat) distribution.\n", "\n", "The second example use random-walk updates with a proposal distribution that is much narrower than the target ($\\sigma = 0.05$) so tends to explore the target space slowly with long range correlations between samples. We have effectively simulated the [Brownian motion](https://en.wikipedia.org/wiki/Brownian_motion) of a particle in a 2D fluid. With a long enough chain, our particle will explore the full square, spending about the same amount of time in each part of it, but this is not true of shorter sections of the chain. Note how repeated samples occur only at the edges of square, where there is a high probability of a proposed sample falling outside the square and therefore being rejected.\n", "\n", "Both of these examples are \"correct\" implementations of MH updates, but also have peculiar features that you might care about when using MCMC for pratical work. The lesson is that you should generally not assume that an MCMC chain has any desirable properties beyond its minimum guarantee of asymptotically sampling $\\tilde{P}(X_n)$.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When the proposal distribution $Q$ is reversible, it cancels in the Hastings ratio,\n", "$$\n", "r(x_{n+1}, x_n) = \\frac{\\tilde{P}(x_{n+1})}{\\tilde{P}(x_n)}\\, \\frac{Q(x_n\\mid x_{n+1})}{Q(x_{n+1}\\mid x_n)} \\;\\rightarrow\\; \\frac{\\tilde{P}(x_{n+1})}{\\tilde{P}(x_n)} \\; .\n", "$$\n", "The resulting **Metropolis updates** are a special case of MH updates and eliminate the need to evaluate $Q$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Gibbs Sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When sampling a multidimensional target distribution $\\tilde{P}$, some additional constraints on $\\tilde{P}$, allow us to exploit a different special case of MH updates and are the basis of **Gibbs sampling**.\n", "\n", "For example, suppose we want to sample in 3D from $\\tilde{P}(x, y, z)$, then Gibbs updates require that we can sample from each of the 1D conditional distributions:\n", "$$\n", "\\tilde{P}(x\\mid y, z) \\quad ,\\quad\n", "\\tilde{P}(y\\mid x, z) \\quad ,\\quad\n", "\\tilde{P}(z\\mid x, y) \\; .\n", "$$\n", "This condition is trivially satisfied when the random variables are mutually independent,\n", "$$\n", "\\tilde{P}(x,y,z) = P_X(x) P_Y(y) P_Z(z) \\; ,\n", "$$\n", "but is more useful in cases where this is not true and simpler alternative methods are not available.\n", "\n", "The rules for a single Gibbs update starting from sample $(x_{n-1}, y_{n-1}, z_{n-1})$ are:\n", " - Sample $x_n$ from $\\tilde{P}(x\\mid y_{n-1}, z_{n-1})$\n", " - Sample $y_n$ from $\\tilde{P}(y\\mid x_n, z_{n-1})$\n", " - Sample $z_n$ from $\\tilde{P}(z\\mid x_n, y_n)$\n", " - Accept the new sample $(x_n, y_n, z_n)$ with probability one (!)\n", " \n", "We will not prove the correctness of this approach, but the key insight is that each sub-step samples from a conditional PDF that is proportional to the full joint PDF, for example:\n", "$$\n", "\\tilde{P}(y\\mid x, z) = \\frac{\\tilde{P}(x, y, z)}{\\tilde{P}(x, z)} \\propto \\tilde{P}(x, y, z) \\; .\n", "$$\n", "The 3D example above generalizes in the obvious way to higher dimensions.\n", "\n", "[Gibbs sampling](https://en.wikipedia.org/wiki/Gibbs_sampling) places extra conditions on $\\tilde{P}$, so is not a general-purpose algorithm, but is efficient and eliminates repeated samples when its conditions are met. Gibbs sampling is often a good fit to target distributions that can be expressed using a graphical model with few dependencies." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hamiltonian Sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another special case of MH sampling requires that we can calculate all partial derivatives of our target $\\log\\tilde{P}$,\n", "$$\n", "\\frac{\\partial}{\\partial z_i}\\, \\log\\tilde{P}(\\vec{x}) \\; .\n", "$$\n", "The resulting **Hamiltonian sampling** method relies on a nifty physics analogy.\n", "\n", "[Recall](https://en.wikipedia.org/wiki/Hamiltonian_mechanics) that the equations of motion for a classical system of particles with Hamiltonian $H$ are:\n", "$$\n", "\\frac{dq_i}{dt} = + \\frac{\\partial H}{\\partial p_i} \\quad , \\quad\n", "\\frac{dp_i}{dt} = - \\frac{\\partial H}{\\partial q_i} \\; ,\n", "$$\n", "where $q_i$ and $p_i$ are (generalized) position and momentum coordinates for particle $i$.\n", "\n", "We identify $H$ with the total energy of the system and can often split it into separate kinetic and potential terms,\n", "$$\n", "H(q,p) = K(p) + U(q) \\; ,\n", "$$\n", "where, generically,\n", "$$\n", "K(p) = \\sum_i\\, \\frac{p_i^2}{2 m_i} \\; ,\n", "$$\n", "with particle \"masses\" $m_i$, and $U(q)$ encapsulates all the specifics of a particular system. Using this split, we can simplify the equations of motion to:\n", "$$\n", "\\frac{dq_i}{dt} = +\\frac{p_i}{m_i} \\quad ,\\quad \\frac{dp_i}{dt} = -\\frac{\\partial U}{\\partial q_i} \\; .\n", "$$\n", "\n", "We turn Hamiltonian dynamics into a stationary Markov chain with the following recipe:\n", " - Identify positions $q_i$ with the random variables we wish to sample.\n", " - Create new random variables $p_i$ for the corresponding momenta. We will treat these are nuisance parameters, but this does not look promising since we just doubled the dimension of our sampling space!\n", " - Assign fixed (arbitrary) masses $m_i$ to each \"particle\".\n", " - Use $U(q) = -\\log\\tilde{P}(q)$ for our \"potential energy\".\n", " \n", "Plugging $U(q) = -\\log\\tilde{P}(q)$ into the $dp_i/dt$ equation of motion above reveals why we need to be able to calculate partial derivatives of $\\log\\tilde{P}$.\n", "\n", "A single Hamiltonian Monte Carlo (HMC) update then consists of:\n", " - Pick a random starting point in $(q, p)$ space, to specify the initial conditions for our \"particles\".\n", " - Follow the evolution of our \"particles\" for some fixed time interval using Hamiltonian dynamics.\n", " - Use the final positions of our \"particles\" as a new sample added to the chain.\n", "\n", "How does this sample the target $\\tilde{P}(q)$? The answer comes from statistical mechanics, which tells us that the probability that our system of particles is in a state with positions $q$ is given by the [canonical distribution](https://en.wikipedia.org/wiki/Canonical_ensemble):\n", "$$\n", "P(q) \\propto \\exp\\left( -\\frac{U(q)}{k_B T} \\right) \\; ,\n", "$$\n", "where $k_B$ is Boltzmann's constant and $T$ is the system's absolute temperature.\n", "\n", "In practice, you can usually set $k_B T = 1$ and all masses $m_i = 1$ and this works surprisingly well! The disadvantages of this approach are that:\n", " - It is relatively complex to implement, compared with the much simpler (and general purpose) MH sampling, so let someone else do this work for you.\n", " - It requires that you can evaluate all the necessary partial derivatives of your target $\\tilde{P}$.\n", "\n", "However, the main advantage is that HMC can often explore the target space much more efficiently than other methods, since it uses the additional information provided by the derivatives. We will soon discuss computational graphs, which are a general-purpose framework for automating the necessary derivate calculations.\n", "\n", "See this [blog post](http://arogozhnikov.github.io/2016/12/19/markov_chain_monte_carlo.html) for a more detailed explanation of HMC with some helpful interactive visualizations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Practical Advice" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is tempting to assume that MCMC samples have desirable properties beyond their minimum guarantees, since this is often true, but avoid this temptation.\n", "\n", "In particular, MCMC samples are only guaranteed to sample your target $\\tilde{P}(X_n)$ for $n$ sufficiently large. Therefore:\n", " - There is no way to know how big $n$ needs to be for a particular $\\tilde{P}$.\n", " - **Burn-in?** Should I throw away the first $B$ samples to ensure that my chain is independent of its initial starting point?\n", " - **No:** There is no practical way to know how big $B$ should be. Instead, ensure that your starting point is reasonably probable (according to $\\tilde{P}$) and use all samples. If you do not know how to chose a reasonably probably starting point, you need to solve a separate optimization problem before you are ready to use MCMC (which is notoriously inefficient at discovering new regions of high probability).\n", " - There are no useful guarantees about $\\tilde{P}(X_n, X_m)$ and, in general, you should assume that the consecutive samples in any stretch of the chain are highly correlated.\n", " - **Thinning?** Should I just keep every $T$-th sample so that my chain is uncorrelated?\n", " - **No:** There is no practical way to know in advance how big $T$ should be, and you can never get a better answer (for a fixed amount of computation) by throwing away valid information. Just accept that samples are correlated.\n", "\n", "How long should your chain be? You should ideally use empirical measurements to determine $k$ such that the [autocorrelation](https://en.wikipedia.org/wiki/Autocorrelation)\n", "$$\n", "\\frac{\\langle (X_{n+k} - \\mu) (X_n - \\mu)\\rangle}{\\sigma^2} \\simeq 0 \\; ,\n", "$$\n", "where $\\mu$ and $\\sigma$ are the long-term mean and standard deviation of $\\tilde{P}(X_n)$, then generate a chain whose length is at least 10-100 times this [autocorrelation](https://en.wikipedia.org/wiki/Autocorrelation) length $k$.\n", "\n", "Which update rule should you use?\n", " - Determine which special cases apply to your target $\\tilde{P}$, so you know which algorithms are possible.\n", " - Can you sample from a complete set of conditional distributions? If so, add Gibbs sampling to your list.\n", " - Can you compute all partial derivatives? If so, add HMC to your list.\n", " - There is no \"best\" algorithm, so you will need to benchmark your problem against the available methods. \n", "\n", "Although it is instructive (and fun!) to implement simple update rules yourself, for serious work you should generally let someone else do the hard work for you by using an existing package.\n", "\n", "Which package should you use?\n", " - For initial exploratory work, start with [emcee](http://dfm.io/emcee/), which implements [ensemble sampling](http://dx.doi.org/10.2140/camcos.2010.5.65) where many independent \"walkers\" simultaneously crawl around your target space, and has a nice [affine invariance](https://en.wikipedia.org/wiki/Affine_geometry) property, where the efficiency is not affected by any linear (aka \"affine\") transformation of your target space.\n", " - Look into [PyMC3](http://docs.pymc.io/notebooks/getting_started.html), [Edward](http://edwardlib.org/) (based on tensorflow) or [Pyro](http://docs.pyro.ai/en/0.2.1-release/index.html) (based on PyTorch) to explore HMC and other more advanced updating rules. These are generally more complex to use and have rigid rules for specifying your target $\\tilde{P}$.\n", " - Consider an alternative approximate method for Bayesian inference, such as [variational inference](https://en.wikipedia.org/wiki/Variational_Bayesian_methods), with different tradeoffs.\n", " \n", "This [blog post](http://twiecki.github.io/blog/2013/09/23/emcee-pymc/) compares emcee and PyMC3." ] } ], "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": "3.6.7" } }, "nbformat": 4, "nbformat_minor": 2 }