diff --git a/exercises/Chapter7.ipynb b/exercises/Chapter7.ipynb new file mode 100644 index 0000000..32b8c5b --- /dev/null +++ b/exercises/Chapter7.ipynb @@ -0,0 +1,887 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7 Exercises" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import pymc3 as pm\n", + "import numpy as np\n", + "from scipy import stats\n", + "import arviz as az\n", + "import pandas as pd\n", + "from scipy.special import expit as logistic\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 1" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def exp_quad_kernel(x, knots, ℓ=1):\n", + " \"\"\"exponentiated quadratic kernel\"\"\"\n", + " return np.array([np.exp(-(x-k)**2 / (2*ℓ**2)) for k in knots])" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "data = np.array([-1, 0, 1, 2])\n", + "\n", + "def plot_covariance(data):\n", + " \"\"\"Functionalize the code block from the chapter to try different data\"\"\"\n", + " cov = exp_quad_kernel(data, data, 1)\n", + "\n", + " _, ax = plt.subplots(1, 2, figsize=(12, 5))\n", + " ax = np.ravel(ax)\n", + "\n", + " ax[0].plot(data, np.zeros_like(data), 'ko')\n", + " ax[0].set_yticks([])\n", + " for idx, i in enumerate(data):\n", + " ax[0].text(i, 0+0.005, idx)\n", + " ax[0].set_xticks(data)\n", + " ax[0].set_xticklabels(np.round(data, 2))\n", + " #ax[0].set_xticklabels(np.round(data, 2), rotation=70)\n", + "\n", + " ax[1].grid(False)\n", + " im = ax[1].imshow(cov)\n", + " colors = ['w', 'k']\n", + " for i in range(len(cov)):\n", + " for j in range(len(cov)):\n", + " ax[1].text(j, i, round(cov[i, j], 2),\n", + " color=colors[int(im.norm(cov[i, j]) > 0.5)],\n", + " ha='center', va='center', fontdict={'size': 16})\n", + " ax[1].set_xticks(range(len(data)))\n", + " ax[1].set_yticks(range(len(data)))\n", + " ax[1].xaxis.tick_top()\n", + "plot_covariance(data)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "data = np.random.normal(size=4)\n", + "plot_covariance(data)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "data = np.array([0, 0, 0,1])\n", + "plot_covariance(data)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "data = np.array([0, 0, 0,10])\n", + "plot_covariance(data)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "data = np.array([0, 1, 10,11])\n", + "plot_covariance(data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can validate the kernel value between the points 10 and 11 by using the calculation below. This should match the value in the image" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.6065306597126334" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.exp(-(11-10)**2 / (2*1**2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 2\n", + "Rerun the code generating Figure 7.3 and increase the number of samples obtained from the GP-prior to around 200. In the original figure the number of\n", + "samples is 2. Which is the range of the generated Y values?" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def exp_quad_kernel(x, knots, ℓ=1):\n", + " \"\"\"exponentiated quadratic kernel\"\"\"\n", + " return np.array([np.exp(-(x-k)**2 / (2*ℓ**2)) for k in knots])" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(-0.03, 0.5, 'f(x)')" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(24)\n", + "test_points = np.linspace(0, 10, 200)\n", + "fig, ax = plt.subplots(2, 2, figsize=(12, 6), sharex=True, sharey=True, constrained_layout=True)\n", + "ax = np.ravel(ax)\n", + "\n", + "for idx, ℓ in enumerate((0.2, 1, 2, 10)):\n", + " cov = exp_quad_kernel(test_points, test_points, ℓ)\n", + " vals = stats.multivariate_normal.rvs(cov=cov, size=200).T\n", + " ax[idx].plot(test_points, vals, alpha=.1, c='b')\n", + " ax[idx].set_title(f'ℓ ={ℓ}')\n", + "fig.text(0.51, -0.03, 'x', fontsize=16)\n", + "fig.text(-0.03, 0.5, 'f(x)', fontsize=16)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The range of Y looks to range from -3 to 3 " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 3\n", + "\n", + "For the generated plot in the previous exercise. Compute the standard deviation\n", + "for the values of Y at each point. Do this in the following form:\n", + "* Visually, just observing the plots\n", + "* Directly from the values generated from stats.multivariate_normal.rvs\n", + "* By inspecting the covariance matrix (if you have doubts go back to Exercise 1)\n", + "\n", + "Did the values you get from these 3 methods agree?" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0069400954007475" + ] + }, + "execution_count": 105, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cov = exp_quad_kernel(test_points, test_points, 10)\n", + "vals = stats.multivariate_normal.rvs(cov=cov, size=1000)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "First we'll calculate the variance of all y values at X=0 to see that we get a variance of 1" + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0139283557256664" + ] + }, + "execution_count": 106, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.var(vals.T[1,:])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we'll inspect the covariance matrix for the covariance for (x=0, x=0), again seeing that the covariance for the same x location is 1" + ] + }, + { + "cell_type": "code", + "execution_count": 108, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0" + ] + }, + "execution_count": 108, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cov[0][0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally visually inspecting the plot it looks like the range of the y values is mostly around -3 to 3. We can simulate a gaussian distribution with a variance of 1 to double check our estimation of the range." + ] + }, + { + "cell_type": "code", + "execution_count": 113, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 113, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_kde(stats.norm(0, scale=np.sqrt(1)).rvs(10000))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 4\n", + "Re-run the model model_reg and get new plots but using as `test_points X_new np.linspace(np.floor(x.min()), 20, 100)[:,None]` . What did you observed How is this related to the specification of the GP-prior?" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/canyon/miniconda3/envs/pymc4/lib/python3.6/site-packages/theano/tensor/basic.py:6592: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "/home/canyon/miniconda3/envs/pymc4/lib/python3.6/site-packages/theano/tensor/basic.py:6592: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/home/canyon/miniconda3/envs/pymc4/lib/python3.6/site-packages/theano/tensor/basic.py:6592: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/home/canyon/miniconda3/envs/pymc4/lib/python3.6/site-packages/theano/tensor/basic.py:6592: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "/home/canyon/miniconda3/envs/pymc4/lib/python3.6/site-packages/theano/tensor/basic.py:6592: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " result[diagonal_slice] = x\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [ϵ, ℓ]\n", + "Sampling 4 chains: 0%| | 0/10000 [00:00" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "X_new = np.linspace(np.floor(x.min()), 20, 100)[:,None]\n", + "\n", + "with model_reg:\n", + " # conditional distribution evaluated over new input locations\n", + " f_pred = gp.conditional(\"f_pred\", X_new)\n", + " # samples from the posterior predictive distribution evaluated at the X_new values\n", + " pred_samples = pm.sample_posterior_predictive(trace_reg, vars=[f_pred])\n", + "\n", + "_, ax = plt.subplots(figsize=(12,5))\n", + "ax.plot(X_new, pred_samples[\"f_pred\"].T, \"C1-\", alpha=0.3)\n", + "ax.plot(X, y, \"ko\");\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[,\n", + " ],\n", + " [,\n", + " ]],\n", + " dtype=object)" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_trace(trace_reg)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exercise 5\n", + "Go back to exercise 1, but this time use a linear kernel (see the accompanying code for a linear kernel)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "data = np.array([-1, 0, 1, 2])\n", + "\n", + "def linear_kernel(x, knots):\n", + " \"\"\" linear kernel \"\"\"\n", + " return np.array([(x - 2) * (k - 2) for k in knots])\n", + "\n", + "def plot_covariance(data):\n", + " \"\"\"Functionalize the code block from the chapter to try different data\"\"\"\n", + " cov = linear_kernel(data, data)\n", + "\n", + " _, ax = plt.subplots(1, 2, figsize=(12, 5))\n", + " ax = np.ravel(ax)\n", + "\n", + " ax[0].plot(data, np.zeros_like(data), 'ko')\n", + " ax[0].set_yticks([])\n", + " for idx, i in enumerate(data):\n", + " ax[0].text(i, 0+0.005, idx)\n", + " ax[0].set_xticks(data)\n", + " ax[0].set_xticklabels(np.round(data, 2))\n", + " #ax[0].set_xticklabels(np.round(data, 2), rotation=70)\n", + "\n", + " ax[1].grid(False)\n", + " im = ax[1].imshow(cov)\n", + " colors = ['w', 'k']\n", + " for i in range(len(cov)):\n", + " for j in range(len(cov)):\n", + " ax[1].text(j, i, round(cov[i, j], 2),\n", + " color=colors[int(im.norm(cov[i, j]) > 0.5)],\n", + " ha='center', va='center', fontdict={'size': 16})\n", + " ax[1].set_xticks(range(len(data)))\n", + " ax[1].set_yticks(range(len(data)))\n", + " ax[1].xaxis.tick_top()\n", + "plot_covariance(data)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "data = np.random.normal(size=4)\n", + "plot_covariance(data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Exercise 7\n", + "Run a logistic regression model for the space_flu data. What do you see? Can you explain the result?" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "df_sf = pd.read_csv('../code/data/space_flu.csv')\n", + "age = df_sf.age.values\n", + "space_flu = df_sf.space_flu.values" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [ϵ, β, α]\n", + "Sampling 4 chains: 100%|██████████| 18000/18000 [00:04<00:00, 3888.38draws/s]\n", + "100%|██████████| 1000/1000 [00:00<00:00, 3894.51it/s]\n" + ] + } + ], + "source": [ + "# Linear Model\n", + "with pm.Model() as space_flu_model:\n", + " α = pm.Normal(\"α\", 0,1)\n", + " β = pm.Normal(\"β\", 0,1)\n", + " \n", + " μ = α + pm.math.dot(age, β)\n", + " θ = pm.Deterministic(\"θ\", pm.math.sigmoid(μ))\n", + " \n", + " bd = pm.Deterministic('bd', -α/β)\n", + " \n", + " y = pm.Bernoulli(\"y\", p=θ, observed=space_flu)\n", + " flu_logistic_trace = pm.sample(4000)\n", + " flu_logistic_samples = pm.sample_posterior_predictive(flu_logistic_trace, vars=[θ,y], samples=1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'θ')" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plot decision boundary\n", + "plt.vlines(flu_logistic_trace['bd'].mean(), 0, 1, color='k')\n", + "bd_hpd = az.hpd(flu_logistic_trace['bd'])\n", + "plt.fill_betweenx([0, 1], bd_hpd[0], bd_hpd[1], color='k', alpha=0.5)\n", + "\n", + "# Plot observed value\n", + "plt.scatter(age, np.random.normal(space_flu, 0.02), marker='.', color=[f'C{x}' for x in space_flu])\n", + "\n", + "# Plot mean of parameter estimate\n", + "theta = flu_logistic_trace['θ'].mean(axis=0)\n", + "idx = np.argsort(age)\n", + "plt.plot(age[idx], theta[idx], color='C2', lw=3)\n", + "\n", + "# Plot confidence of parameter estimate\n", + "az.plot_hpd(age, flu_logistic_trace['θ'], color='C2')\n", + "\n", + "plt.ylabel('θ', rotation=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 8\n", + "Change the logistic regression model in order to fit the data. Tip, use an order two polynomial." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "df_sf = pd.read_csv('../code/data/space_flu.csv')\n", + "age = df_sf.age.values\n", + "space_flu = df_sf.space_flu.values\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [ϵ, β, α]\n", + "Sampling 4 chains: 100%|██████████| 18000/18000 [00:12<00:00, 1474.98draws/s]\n", + "The acceptance probability does not match the target. It is 0.8979909354540494, but should be close to 0.8. Try to increase the number of tuning steps.\n", + "The acceptance probability does not match the target. It is 0.8789797304019081, but should be close to 0.8. Try to increase the number of tuning steps.\n", + "The acceptance probability does not match the target. It is 0.9055478985631059, but should be close to 0.8. Try to increase the number of tuning steps.\n", + "The acceptance probability does not match the target. It is 0.9182246730128105, but should be close to 0.8. Try to increase the number of tuning steps.\n", + "100%|██████████| 1000/1000 [00:00<00:00, 3940.01it/s]\n" + ] + } + ], + "source": [ + "# Quadratic Model\n", + "with pm.Model() as space_flu_model:\n", + " α = pm.Normal(\"α\", 0,1)\n", + " β = pm.Normal(\"β\", 0,1, shape=2)\n", + " \n", + " # Quadratic Parmetarization is in this line\n", + " μ = α + pm.math.dot(age, β[0]) + pm.math.dot(age**2, β[1])\n", + " θ = pm.Deterministic(\"θ\", pm.math.sigmoid(μ))\n", + " \n", + " # bd = pm.Deterministic('bd', -α/β)\n", + " \n", + " y = pm.Bernoulli(\"y\", p=θ, observed=space_flu)\n", + " flu_logistic_trace = pm.sample(4000)\n", + " flu_logistic_samples = pm.sample_posterior_predictive(flu_logistic_trace, vars=[θ,y], samples=1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'θ')" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plot observed value\n", + "plt.scatter(age, np.random.normal(space_flu, 0.02), marker='.', color=[f'C{x}' for x in space_flu])\n", + "\n", + "# Plot mean of parameter estimate\n", + "theta = flu_logistic_trace['θ'].mean(axis=0)\n", + "idx = np.argsort(age)\n", + "plt.plot(age[idx], theta[idx], color='C2', lw=3)\n", + "\n", + "# Plot confidence of parameter estimate\n", + "az.plot_hpd(age, flu_logistic_trace['θ'], color='C2')\n", + "\n", + "plt.ylabel('θ', rotation=0)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise 9\n", + "Compare the model for the coal mining disaster with the one from the PyMC3\n", + "documentation ( https://docs.pymc.io/notebooks/getting_started.html#Case-study-2:-Coal-mining-disasters). Describe the differences between both models in terms of model-specification and results." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Question:\n", + "The model in the book and the model from PyMC3 docs answer different questions\n", + "\n", + "PyMC3 docs answer question: When did rate of coal mining diaster change, specifically done by estimating three things, rate prior to change event, and rate post change event, and change event time\n", + "Book estimates what is rate of coal mining disasters at any point in time. It does not answer the question of when was an event that led to change in rate\n", + "\n", + "Is my understanding correct" + ] + } + ], + "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 +}