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devmotion/emcee.ipynb

Created May 27, 2020 15:00
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emcee.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"import emcee\n",
"import scipy\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Constrained space"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"def logprior(theta):\n",
" s = theta[0]\n",
" if s <= 0:\n",
" return -np.inf\n",
" else:\n",
" m = theta[1]\n",
" return scipy.stats.invgamma.logpdf(s, 2, scale=3) + scipy.stats.norm.logpdf(m, scale=np.sqrt(s))\n",
" \n",
"def loglik(theta):\n",
" sqrts = np.sqrt(theta[0])\n",
" m = theta[1]\n",
" return np.sum(scipy.stats.norm.logpdf([1.5, 2], loc=m, scale=sqrts))\n",
"\n",
"def logprob(theta):\n",
" lp = logprior(theta)\n",
" if not np.isfinite(lp):\n",
" return lp\n",
" else:\n",
" return lp + loglik(theta)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"State([[ 2.97363097 2.03379989]\n",
" [ 0.76484226 1.59296986]\n",
" [ 2.08804361 1.34183598]\n",
" ...\n",
" [ 1.44487003 1.9794192 ]\n",
" [ 1.0427938 -0.0082669 ]\n",
" [ 3.78338425 2.89900957]], log_prob=[ -7.21609273 -5.0484125 -5.85023644 -5.64431234 -6.64877049\n",
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" 3793074643, 1092872364, 1309677685, 453182616, 2447988448,\n",
" 3284141499, 2638784441, 87001326, 3269282429, 3718888549,\n",
" 367375689, 1949121885, 2806462726, 1452968790, 2170981319,\n",
" 3969009723, 3871039373, 4232213578, 3265086603, 2991703903,\n",
" 4195667936, 378689420, 3982993351, 2374169512, 2558669238,\n",
" 3871380929, 556348435, 4029442965, 1200381164, 2761725919,\n",
" 3902128736, 2380511184, 1744639910, 470404620], dtype=uint32), 475, 0, 0.0))"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sampler = emcee.EnsembleSampler(1_000, 2, logprob)\n",
"p0 = np.random.rand(1_000, 2)\n",
"state = sampler.run_mcmc(p0, 100)\n",
"sampler.reset()\n",
"sampler.run_mcmc(state, 1000)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"samples = sampler.get_chain(flat=True)\n",
"\n",
"plt.hist(samples[:, 0], 100, histtype=\"step\", density=True)\n",
"plt.xlabel(\"s\")\n",
"plt.ylabel(\"density\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"samples = sampler.get_chain(flat=True)\n",
"\n",
"plt.hist(samples[:, 1], 100, histtype=\"step\", density=True)\n",
"plt.xlabel(\"m\")\n",
"plt.ylabel(\"density\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x504 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(2, figsize=(10, 7), sharex=True)\n",
"samples = sampler.get_chain()\n",
"labels = [\"s\", \"m\"]\n",
"for i in range(2):\n",
" ax = axes[i]\n",
" ax.plot(samples[:, :, i], \"k\", alpha=0.3)\n",
" ax.set_xlim(0, len(samples))\n",
" ax.set_ylabel(labels[i])\n",
" ax.yaxis.set_label_coords(-0.1, 0.5)\n",
"\n",
"axes[-1].set_xlabel(\"step number\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"s:\n",
" mean (estimated): 2.0020708564462035\n",
"\n",
" mean (true): 2.0416666666666665\n"
]
}
],
"source": [
"print(\"s:\\n mean (estimated): \", np.mean(samples[:, :, 0]))\n",
"print(\"\\n mean (true): \", 49/24)"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"s:\n",
" mean (estimated): 1.163463086357075\n",
"\n",
" mean (true): 1.1666666666666667\n"
]
}
],
"source": [
"print(\"s:\\n mean (estimated): \", np.mean(samples[:, :, 1]))\n",
"print(\"\\n mean (true): \", 7/6)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Unconstrained space"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [],
"source": [
"def logprior(theta):\n",
" s = np.exp(theta[0])\n",
" m = theta[1]\n",
" return scipy.stats.invgamma.logpdf(s, 2, scale=3) + scipy.stats.norm.logpdf(m, scale=np.sqrt(s)) + theta[0]\n",
" \n",
"def loglik(theta):\n",
" sqrts = np.exp(theta[0] / 2)\n",
" m = theta[1]\n",
" return np.sum(scipy.stats.norm.logpdf([1.5, 2], loc=m, scale=sqrts))\n",
"\n",
"def logprob(theta):\n",
" return logprior(theta) + loglik(theta)"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"State([[-0.19351632 1.45906584]\n",
" [ 0.55572187 1.585888 ]\n",
" [ 0.77917216 1.6299971 ]\n",
" ...\n",
" [-0.51275513 0.91550155]\n",
" [ 0.73726995 -0.13775847]\n",
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" 671769253, 625987283, 2105293248, 4254260970, 4174225286,\n",
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" 2003038784, 3533442723, 711753792, 2904500810, 3080770361,\n",
" 3905834874, 3737096162, 323919774, 2193206176, 3874778105,\n",
" 4967298, 1276953058, 1402158303, 1967088926, 2735218174,\n",
" 788189982, 2203062931, 3295205731, 2724154205, 1701981919,\n",
" 327864089, 2386584526, 3401726448, 2998543483, 398671604,\n",
" 3877492069, 2468665607, 4020280386, 2644481605, 3599166748,\n",
" 276106163, 3666768609, 3935523775, 868948319], dtype=uint32), 57, 0, 0.0))"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sampler = emcee.EnsembleSampler(1_000, 2, logprob)\n",
"p0 = np.random.randn(1_000, 2)\n",
"state = sampler.run_mcmc(p0, 100)\n",
"sampler.reset()\n",
"sampler.run_mcmc(state, 1000)"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"samples = sampler.get_chain(flat=True)\n",
"\n",
"plt.hist(np.exp(samples[:, 0]), 100, histtype=\"step\", density=True)\n",
"plt.xlabel(\"s\")\n",
"plt.ylabel(\"density\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"samples = sampler.get_chain(flat=True)\n",
"\n",
"plt.hist(samples[:, 1], 100, histtype=\"step\", density=True)\n",
"plt.xlabel(\"m\")\n",
"plt.ylabel(\"density\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x504 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, axes = plt.subplots(2, figsize=(10, 7), sharex=True)\n",
"samples = sampler.get_chain()\n",
"labels = [\"s\", \"m\"]\n",
"for i in range(2):\n",
" ax = axes[i]\n",
" if i == 0:\n",
" ax.plot(np.exp(samples[:, :, i]), \"k\", alpha=0.3)\n",
" else:\n",
" ax.plot(samples[:, :, i], \"k\", alpha=0.3)\n",
" ax.set_xlim(0, len(samples))\n",
" ax.set_ylabel(labels[i])\n",
" ax.yaxis.set_label_coords(-0.1, 0.5)\n",
"\n",
"axes[-1].set_xlabel(\"step number\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"s:\n",
" mean (estimated): 2.029339351120266\n",
"\n",
" mean (true): 2.0416666666666665\n"
]
}
],
"source": [
"print(\"s:\\n mean (estimated): \", np.mean(np.exp(samples[:, :, 0])))\n",
"print(\"\\n mean (true): \", 49/24)"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"s:\n",
" mean (estimated): 1.1695912260905177\n",
"\n",
" mean (true): 1.1666666666666667\n"
]
}
],
"source": [
"print(\"s:\\n mean (estimated): \", np.mean(samples[:, :, 1]))\n",
"print(\"\\n mean (true): \", 7/6)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python [conda env:.conda-emcee] *",
"language": "python",
"name": "conda-env-.conda-emcee-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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