{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import pymc3 as pm\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import warnings\n", "warnings.filterwarnings(\"ignore\", category=FutureWarning)\n", "\n", "from matplotlib import gridspec\n", "from IPython.display import Image\n", "import theano.tensor as tt\n", "\n", "%matplotlib inline\n", "plt.style.use('seaborn-white')\n", "\n", "color = '#87ceeb'\n", "\n", "f_dict = {'size':16}" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "RangeIndex: 300 entries, 0 to 299\n", "Data columns (total 3 columns):\n", " # Column Non-Null Count Dtype \n", "--- ------ -------------- ----- \n", " 0 male 300 non-null int64 \n", " 1 height 300 non-null float64\n", " 2 weight 300 non-null float64\n", "dtypes: float64(2), int64(1)\n", "memory usage: 7.2 KB\n" ] } ], "source": [ "df = pd.read_csv('data/HtWtData300.csv')\n", "#df = pd.read_csv('data/HtWtData30.csv')\n", "df.info()" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [], "source": [ "# Standardize the data\n", "zheight = ( (df['height']-df['height'].mean()) / df['height'].std() ).to_numpy()\n", "zweight = ( (df['weight']-df['weight'].mean()) / df['weight'].std() ).to_numpy()" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [], "source": [ "with pm.Model() as model:\n", " \n", " beta0 = pm.Normal('beta0', mu=0, tau=1/10**2)\n", " beta1 = pm.Normal('beta1', mu=0, tau=1/10**2)\n", " mu = beta0 + beta1*zheight\n", "\n", " sigma = pm.Uniform('sigma', 10**-3, 10**3)\n", " nu = pm.Exponential('nu', 1/29.)\n", " \n", " likelihood = pm.StudentT('likelihood', nu, mu=mu, sd=sigma, observed=zweight)" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [nu, sigma, beta1, beta0]\n", "Sampling 2 chains, 0 divergences: 100%|██████████| 7000/7000 [00:08<00:00, 804.64draws/s] \n" ] } ], "source": [ "with model:\n", " trace = pm.sample(3000, cores=2, nuts_kwargs={'target_accept': 0.95})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Posterior Predictive Checks" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 6000/6000 [00:06<00:00, 930.76it/s]\n" ] } ], "source": [ "ppc_trace = pm.sample_posterior_predictive(trace, model=model)" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(6000, 300)" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ppc_trace['likelihood'].shape" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-3.0133562481781397, 6.622338999068915)" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plain vanilla PPC\n", "# we'll plot the weights we observed for each individual\n", "# against the mean \"predicted\" weight for those same individuals\n", "plt.scatter(np.mean(ppc_trace['likelihood'], axis=0), zweight, facecolor='none', edgecolor='k')\n", "mn = -1 + np.min([np.mean(ppc_trace['likelihood'], axis=0), zweight])\n", "mx = 1 + np.max([np.mean(ppc_trace['likelihood'], axis=0), zweight])\n", "#plt.plot([mn,mx],[mn,mx], c='k')\n", "plt.plot([0,0],[mn,mx], c='k')\n", "plt.plot([mn, mx],[0,0], c='k')\n", "plt.xlim(mn,mx)\n", "plt.ylim(mn,mx)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This looks ok. The handful of weights are far greater than the predicted values. These data points are likely to have been outliers in the original dataset itself. For this reason, the discrepancy between the model and the predictions is not too overly concerning (although one would certainly want to follow this up to confirm the suspicion that these were empirical outliers).\n", "\n", "Let's move on to composite variables generated using the set of predicted weights. We can begin with inspecting some basic measures of central tendency. Let's check to see whether our predictions about the mean weight are consistent with the mean of the weights observed in our sample." ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist([np.mean(weight) for weight in ppc_trace['likelihood']], bins=100);\n", "plt.axvline(np.mean(zweight), c='k')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hm. That doesn't look quite right. The observed mean is at 0.0, which makes sense because we are working with the standardized version of our weights. But our predictions about the mean seem to be biased in the negative direction. In other words, our posterior seems to suggest a smaller mean weight in our sample than we actually observed.\n", "\n", "This seems like bad news, but it is important to remember that we modeled our data so as to be robust to outlying data points (outlying weights, specifically). So perhaps we observed a few extremely large weights that are dragging the observed mean \"upward\". If that explanation is correct, we would expect our posterior prediction about the _median_ weight to be more closely aligned with the observed median than the predicted _mean_ weight was. Let's check." ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist([np.median(weight) for weight in ppc_trace['likelihood']], bins=100);\n", "plt.axvline(np.median(zweight), c='k')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Great. Our prediction about the median is pretty good. We can do similar things for the standard deviation." ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.hist([np.std(weight) for weight in ppc_trace['likelihood']], bins=100);\n", "plt.axvline(np.std(zweight), c='k')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This also looks pretty good, although it is clear that we think the standard deviation could have credibly been substantialy larger than was actually observed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Extensions\n", "\n", "Above, we have confined ourselves to posterior predictions about the weights our posterior \"predicts\" for each of the heights we observed in our sample. However, there is no particular reason that we need to confine ourselves to the set of observed heights. We can explore our predictions about a wide variety of heights. We can also calculate a variety of composite variables that are based on the height and (predicted) weight variables.\n", "\n", "Let's begin by visualizing credible regression lines. We'll do so by sampling by going back to the trace generate during the sampling step we performed early inference (the sampling done for inference, not the set of posterior predictive samples). We can use these credible parameter values, the intercept (`beta0`) and slope (`beta1`) in particular. We can then take these credible intercept-slope pairs and generate a credible regression line for each one." ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create some synthetic heights\n", "heights = np.linspace(df['height'].min()*.9, df['height'].max()*1.1, num=10)\n", "\n", "sd_h = df['height'].std()\n", "mean_h = df['height'].mean()\n", "sd_w = df['weight'].std()\n", "mean_w = df['weight'].mean()\n", "\n", "# plot original data\n", "plt.scatter(df['height'], df['weight'], s=40, linewidths=1, facecolor='none', edgecolor='k', zorder=1)\n", "plt.xlabel('height')\n", "plt.ylabel('weight')\n", "\n", "# sample 50 steps (sets of parameter values)\n", "for i in range(50):\n", " step = np.random.choice(trace)\n", " # unstandardize the parameter values so we can plot in the native scale\n", " beta0 = (step['beta0']*sd_w)+ mean_w - (step['beta1']*mean_h*sd_w/sd_h)\n", " beta1 = step['beta1']*(sd_w/sd_h)\n", " weights = beta0 + (beta1 * heights)\n", " plt.plot(heights, weights, c='#87ceeb', alpha=.5, zorder=2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we squint, we can sort of make out a credible band of weights for each height. This mimics an interval-valued function, in which each height is mapped to an interval of credible weights. If we wish, we can simply calculate such intervals themselves." ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "There is a 95% probabilty of someone of height 50 having a weight between 69.30 and 97.16\n", "There is a 95% probabilty of someone of height 60 having a weight between 121.55 and 134.06\n", "There is a 95% probabilty of someone of height 70 having a weight between 168.16 and 176.56\n", "There is a 95% probabilty of someone of height 80 having a weight between 205.44 and 228.16\n" ] } ], "source": [ "# figure out the 95% credible interval\n", "beta0 = (trace['beta0']*sd_w)+ mean_w - (trace['beta1']*mean_h*sd_w/sd_h)\n", "beta1 = trace['beta1']*(sd_w/sd_h)\n", "\n", "hpi_x = (50, 60,70,80)\n", "hpi_y = np.zeros((len(hpi_x),2))\n", "\n", "\n", "for i in range(len(hpi_x)):\n", " hpi_y[i,0] = np.percentile(beta0 + (beta1 * hpi_x[i]), 2.5)\n", " hpi_y[i,1] = np.percentile(beta0 + (beta1 * hpi_x[i]), 97.5)\n", " print(f'There is a 95% probabilty of someone of height {hpi_x[i]}'\n", " f' having a weight between {hpi_y[i,0]:.2f} and {hpi_y[i,1]:.2f}')" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot original data\n", "plt.scatter(df['height'], df['weight'], s=40, linewidths=1, facecolor='none', edgecolor='k', zorder=1)\n", "plt.xlabel('height')\n", "plt.ylabel('weight')\n", "\n", "# sample 50 steps (sets of parameter values)\n", "for i in range(50):\n", " step = np.random.choice(trace)\n", " # unstandardize the parameter values so we can plot in the native scale\n", " beta0 = (step['beta0']*sd_w)+ mean_w - (step['beta1']*mean_h*sd_w/sd_h)\n", " beta1 = step['beta1']*(sd_w/sd_h)\n", " weights = beta0 + (beta1 * heights)\n", " #plt.plot(heights, weights, c='#87ceeb', alpha=.5, zorder=2)\n", "\n", "for x,y in zip(hpi_x, hpi_y):\n", " plt.plot([x, x], y, lw=5, c='r', zorder=3);" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "beta0 = (trace['beta0']*sd_w)+ mean_w - (trace['beta1']*mean_h*sd_w/sd_h)\n", "beta1 = trace['beta1']*(sd_w/sd_h)\n", "\n", "# plot original data\n", "plt.scatter(df['height'], df['weight'], s=40, linewidths=1, facecolor='none', edgecolor='k', zorder=1)\n", "plt.xlabel('height')\n", "plt.ylabel('weight')\n", "\n", "# create some new synthetic heights\n", "heights = np.linspace(df['height'].min()*.75, df['height'].max()*1.25, num=305)\n", "\n", "hpi_x = (heights)\n", "hpi_y = np.zeros((len(hpi_x),2))\n", "\n", "for i in range(len(hpi_x)):\n", " hpi_y[i,0] = np.percentile(beta0 + (beta1 * hpi_x[i]), 2.5)\n", " hpi_y[i,1] = np.percentile(beta0 + (beta1 * hpi_x[i]), 97.5)\n", "\n", "for x,y in zip(hpi_x, hpi_y):\n", " plt.plot([x, x], y, lw=1, c='#87ceeb', alpha=.5, zorder=3)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.6" } }, "nbformat": 4, "nbformat_minor": 4 }