diff --git a/training_bayesian/2_mcmc.ipynb b/training_bayesian/2_mcmc.ipynb index 267d46d..caf1788 100644 --- a/training_bayesian/2_mcmc.ipynb +++ b/training_bayesian/2_mcmc.ipynb @@ -1208,7 +1208,7 @@ "metadata": {}, "source": [ "## 3.1 King Markov\n", - "[statistical rethinking](http://xcelab.net/rm/statistical-rethinking/)\n", + "[statistical rethinking](http://web.stanford.edu/class/stats305a/MCMC.html)\n", "Let's take a look at an analogy to understand what is really going on.\n", "\n", "![](images/islands.png)\n", @@ -1226,18 +1226,18 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Simple algorithm\n", + "## 3.1.1 Simple algorithm\n", "* Count the number of inhabitants, stay that amount of day, then move to the next one.\n" ] }, { "cell_type": "code", - "execution_count": 92, + "execution_count": 166, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -1250,16 +1250,16 @@ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 92, + "execution_count": 166, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "
" ] @@ -1281,8 +1281,8 @@ " current_position = (current_position + 1) % len(distribution)\n", "\n", "gen = generate_path(distribution, 0)\n", + "path = np.array([next(gen) for _ in range(1200)])\n", "\n", - "path = np.array([next(gen) for _ in range(1000)])\n", "plt.plot(path)\n", "plt.show()\n", "(pd.Series(path).value_counts(normalize=1)\n", @@ -1296,29 +1296,30 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "After 1000 iterations we have visited al the islands, but the approximation is not very good." + "After 1200 iterations we have visited al the islands, but the approximation is not very good.\n", + "Below we show a plot of a situation with three islands and the approximations we get after **n** days of traveling." ] }, { "cell_type": "code", - "execution_count": 150, + "execution_count": 154, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "Text(0.5, 1.0, 'distribution ratio per island')" + "" ] }, - "execution_count": 150, + "execution_count": 154, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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\n", 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\n", 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" ] }, "metadata": { @@ -1334,33 +1335,201 @@ "n = 1000\n", "path = np.array([next(gen) for _ in range(n)])\n", "\n", + "plt.figure(figsize=(16, 6))\n", "for i in range(len(distribution)):\n", " # cumulative mean\n", " plt.plot(np.arange(n), np.cumsum(path == i) / np.arange(1, n + 1), label=f'proportion_{i}')\n", " plt.plot(np.arange(n), distribution[i] / distribution.sum() * np.ones(n), ls='--', label=f'true_proportion_{i}')\n", "\n", "plt.xlabel('days')\n", - "plt.title('distribution ratio per island')" + "plt.title('distribution ratio per island')\n", + "plt.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3.1.2 MCMC algorithm\n", + "* Pick a neighbouring island. Go with probability **P**, otherwise stay for another day.\n", + "\n", + "$$p = min(1, \\frac{\\text{#proposal}}{\\text{#current}})$$\n", + "\n", + "### Exercise\n", + "Implement the above metropolis algorithm.\n", + "* Loop, and in each loop\n", + " * Make a proposal, which is left or right\n", + " * Accept or reject the proposal based on the rejection rule\n", + " * Store all states \n", + "* Plot the distribution over the states\n", + "* Plot the path of the Markov Chain that you created" ] }, { "cell_type": "code", - "execution_count": 120, + "execution_count": 207, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "distribution = np.array([100, 200, 30, 10, 200, 50, 60, 80, 10, 1])\n", + "\n", + "def generate_path(distribution, start=0):\n", + " current_position = start\n", + " while True:\n", + " # make a proposol (left or right)\n", + " proposal = (current_position + np.random.choice([-1, 1])) % len(distribution)\n", + " \n", + " # accept or reject it based on proportions\n", + " p = min((1, distribution[proposal] / distribution[current_position]))\n", + " \n", + " if np.random.random() < p:\n", + " current_position = proposal\n", + " yield current_position\n", + "\n", + "gen = generate_path(distribution, 0)\n", + "path = np.array([next(gen) for _ in range(10000)])\n", + "\n", + "sns.distplot(path, kde=False, bins=len(distribution), norm_hist=True)\n", + "plt.show()\n", + "plt.plot(path)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Things to notice\n", + "The sample paths have become probablistic\n", + "\n", + "* The sample paths are different each time\n", + "* It is independent of absolute sizes\n", + "* We'll see much faster convergence to true distribution" + ] + }, + { + "cell_type": "code", + "execution_count": 201, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "0.34" + "" ] }, - "execution_count": 120, + "execution_count": 201, "metadata": {}, "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } ], "source": [ - "(path == 0).sum() / path.shape[0]" + "distribution = np.array([50, 100, 10])\n", + "gen = generate_path(distribution, 0)\n", + "path = np.array([next(gen) for _ in range(1000)])\n", + "\n", + "(pd.Series(path).value_counts(normalize=1)\n", + " .reindex(np.arange(len(distribution)))\n", + " .rename('approx').to_frame()\n", + " .assign(true=distribution / distribution.sum())\n", + ").plot.bar()\n", + "\n", + "plt.figure(figsize=(16, 6))\n", + "for i in range(len(distribution)):\n", + " # cumulative mean\n", + " plt.plot(np.arange(n), np.cumsum(path == i) / np.arange(1, n + 1), label=f'proportion_{i}')\n", + " plt.plot(np.arange(n), distribution[i] / distribution.sum() * np.ones(n), ls='--', label=f'true_proportion_{i}')\n", + "\n", + "plt.xlabel('days')\n", + "plt.title('distribution ratio per island')\n", + "plt.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## MCMC in discrete case\n", + "\n", + "* Multiply the likelihood with the prior to get an unnormalized posterior\n", + "* Sample a path with MCMC;\n", + " * Proposals are next or previous\n", + " * Accept according to relative density\n", + "* Count visits to each state to get proportional samples of the posterior\n", + "\n", + "## MCMC in continuous case\n", + "\n", + "* Sample a chain with MCMC\n", + " * Get proposals via a random walk in parameter space (take steps with multivariate normal distribution)\n", + " * Accept or reject according to relative density of likelihood times posterior\n", + "* These samples are proportional to the posterior distribution\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## [Let's take a walk](http://elevanth.org/blog/2017/11/28/build-a-better-markov-chain/)\n", + "\n", + "*watch different mcmc implementations at the excelent blog post Markov Chains: Why Walk When You Can Flow?*" ] } ], diff --git a/training_bayesian/images/islands.png b/training_bayesian/images/islands.png index 6342dcc..eba38bc 100644 Binary files a/training_bayesian/images/islands.png and b/training_bayesian/images/islands.png differ