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@tushuhei
Created January 29, 2017 02:53
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道具としてのベイズ統計(涌井 良幸 著)の Python での MCMC 実装例
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 道具としてのベイズ統計\n",
"涌井 良幸 著\n",
"\n",
"MCMC シミュレーションの Python による実装例"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"from matplotlib import pylab as plt\n",
"import itertools\n",
"from collections import Counter"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# § 5.6 メトロポリス法\n",
"事後分布 $\\propto \\sigma^{-n_1-3} \\exp{(-\\frac{n_1 S_1 + m_1(\\mu - \\mu_1)^2}{2\\sigma^2})}$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"mu_0 = 5\n",
"sigma_0 = 3\n",
"m_1 = 30.25\n",
"mu_1 = 5.11\n",
"n_1 = 30.02\n",
"n_1S_1 = 138.24\n",
"ma = lambda mu, sigma: sigma**(-n_1 - 3) * np.exp(-(n_1S_1 + m_1 * (mu - mu_1)**2)/(2 * sigma**2))"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(4001, 2)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"result = []\n",
"mu_t = mu_0\n",
"sigma_t = sigma_0\n",
"f_t = ma(mu_t, sigma_t)\n",
"result.append((mu_t, sigma_t))\n",
"for _ in range(5000):\n",
" mu_next = mu_t + np.random.normal(0, 0.25)\n",
" sigma_next = sigma_t + np.random.normal(0, 0.25)\n",
" f_next = ma(mu_next, sigma_next)\n",
" r = f_next / f_t\n",
" if np.random.random() < r:\n",
" mu_t = mu_next\n",
" sigma_t = sigma_next\n",
" f_t = f_next\n",
" result.append((mu_t, sigma_t))\n",
"result = np.array(result[1000:]) # burn in 廃棄\n",
"result.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"事後分布の平均のサンプリング結果"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10f5d4f60>]"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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Li97ScdY+63bsw5pte7MvR/X+1mCkCD+2IIvcURF10O0nT6qzHOo8UicKZcmG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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f4c8eb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(result.T[0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"事後分布の分散のサンプリング結果"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x10f80d3c8>]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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2ntR2nNpvzog24zVPTFsjrqRGkYwjvwE7D6rPK3ZgynJvcwB+TCM3v7rA0RPJ\nmL1VnC1z2hJNoXB6UeiyooY5/YwmLwtmLsQNBSb4vV97xdOzcswK7y7cjM8rdqb/znQ4d1qmmTA/\n7YwLr1JePXLmCivsbJwZee7exi+bXtYt0VwnK0qkNH5ru7xokxazeUm0+Eq2CSYukrOLG/O79MmZ\nuOChT7OeQo6ph43PK9PGbp6NW41fZIIEUn3q0idn4kfPWM/dGCmrlz0h79dU6vTiMJ51Wlylp9UV\nCtt4/Gw0t3HasUHfGS9KCio6p1+Baudqt3HP4bSWatb83RLmXA4zMtq6U1qP53T0l8K9EzPB2Y4c\nrbH0nJG97ZoswW9/VY6N3+GuZWz82/dXamVbp7E7t1sQylfWdGa0uRsxr5o23vdSLRR11gvTdH2v\n37yftZhPn0dx0xfdaPx2WrVbb5YcV1YXE6he0kyYmzEHHXXQ4HXvQRlTz6a9hyOLFupEQWn8Itzo\nKHYdYuXWTEzwjN6f0a7Dpqq61pV2pgtAr8JLPydzb68b7Kbv2Oz+JFv9bHdOe8x5OoXokLHxz9S8\nVGRXYcpstxf0y17UF5xemFO0zVVSVgbdxi9XsW37j6TDDMvw3UemW57buq/S8pwMfrc31K8+WCk2\nzT48pSL9WzfNOCEzuXvJE6JIN/FQUII/rCBIW/cdwZX/+tJQTvZ598Gr3NVz54FKHHf7e3hy2pqc\nJeOinPXczW6GbhB5ktiVGSSbDSY3pzG+bX+2BpUzV2FCFMfeTJeWZVrZ1oXLCky3LnvyL0fB3IjB\nKnHAQqgB+uSuno9ceT9/eb60EASAJZust0q8dUJufCY7zOPadmJdojfqbSezpsLq5WCmuKgoK28n\nYvDgzKKwBH9I+a7adsBUTvbk34qt+9PmARncPnTd/3rCvI3C3Yiy8zbY+OFg47c5p5trjm0tt1Wd\nDLKf+EcNdlXzoH9rwaaswei2LRvWE5uhjBQJ7Pg6+ivebfhdu+R7DaYh2VxFMstYJ6OiklsXztj4\nJUs8kBDHBcBauC7csCe7nS30MYupOiGyAdQyGr9UckGdONKN2gtL8IfUbrk2xtw0D364MvegBW7r\nWWSxyEqYN7KFv9d63PFWaoG1KNZRbj5yNnn91PB7P7JMA9iPx+tfnIfbtZ26ADmbvRGZ+9Fx77Lp\nDX0PVzeIhF+NwQPFKqCejpt5qgOV1ViwQf4L0AmreQwA2H/kKHY57FYmEpBTlm/FN//+eVbfWL3d\nKqig/EvIDwoOAAAgAElEQVSvysGrR6dEYnLXjp8+Owfdb4tunWthCX7BgwzC/m6WFaJn6+Zt7X5y\ny7pcy2v0snzKJ9u9VXO9NKVwmuDK8jkXZL5xt/cY/lKTf9r/IuGqR+mU1ewYjH1Hjsr3Dx8PzC5+\nkLmIjB+/c3lO/v1u+f4pnS3PDb93CgbePTnrmLmGorZcuyO1SveNec67mmXMb45JXWv8dpO7dkwK\nKLyFLIXl1SNo84xm431A5UYHzDb1AHDUUjL1cV8PWbdJvU7GVGF+PLp9uWzacxgdmjVwTOckjCqr\na3Coqhpl9cLpvjLasKwtd/eho+h75ySccZz/iLNO5bsLZ5363+mSyuqarP1yg+CxT6wnifdL2NSF\n6ytcKHhpS49Ee8nGVtJt/FGaa/xQUBq/HXLPQ5zIyjpgFMTbHSZddV6bs0EY88QOXeuWuQcGp322\nncIXTF+1AxWm+QszQXosXfToF3h2xjrHdHZRJgFgwYa96P3bDzBj9U7X9fuZRCx8PU97rx65Ab5L\n2ypRtEDQDyLlXlZI1RoWcDm9LJZvtp9TigOROcVNNxh492T86f3lUkqR0wIunRKX0TnV5G7IyAxi\nHf1hvLNwE4b84UNDHmIbv/HhyX7ird5xEL3aNwEAjO6b2TfXGOOnnRaeOF1+ulzGxyu22eafccN0\nduf80TOzcc4Dn9jmZ2fqycyR5RayfX8lpizfivcWbc46O3O18+5Msgu4xj0+w/pkANgJRVlTT5HL\nESYrD0Rt/tEy+76h89W2A4YFXJnjLQS2dzdOC2FhfgxBBDX758erpPI5KvmgZfz4jcQZmROoA6Ye\nHfNDPkZgctBl3F1vL83q8DmRJJE7aNyYcPXrG5RkPExueyMzKdW4fgkOVlajYWkxioooLcT3Hq52\nXFZvrF9uMGT32Idl1f7jnEM45Z7Mi9PLNpA6Tlqs7RyEBAcqq3M2q5Ex9chqdm5dfd2udVi8MTPp\nev8HcltjtmpUzxB2JFPgJUO64B9Ts91h44gc6YRIuM5d7yEMu8StHZWcN9End/PE0lNYGr/oLfqu\ntgTerPGLn0/q4TUxCQKr6IvG8mRte8ZrDlVV44HJK3G0phZvG/ZhPVBZjT53fIA/fpBaEavLNlHQ\nKSsIwZhp7PJIvwCdMnEw3ZgxtuWjDn75brx0RJx4xwc5gmS9Fs7XPsSupOAPaXFfy7JUcLAxD+cG\ncJMhPblrkGuil2icgv/NeRu1BXnZdRC9dGX2MTYjM2RrJE09mT0n8kPyF5bgF7S5LlDNnUXcn1MH\nG5kEv3lAZOyjmWOyA2TGqp3pst9bvAV/++gr9Px1doRGfWXjY5+sxuGqmvSLR6YMZmevGDvMglRq\n7wFDGaLUbjcf+cow7+A02RfEMLNyp7R7mX+xaqflOT/ICo5iiWBzdqQdFAzlGVesZtL5KsYXN748\nH997NHf/3slLgvGAMd67VdRO6cldF/NwQPw2/oIy9dhhfnOLBtjOA1Xo0RZoVD97kU/upiGatmR4\nerKCf8GGvRg3WCopAOAPE5elPYZkJ3cBAKSt3JUvSr9MmplrduHUHq2z2lJUnjEGUtAdPoj8rKKq\n2mX90pdfS+Xtd9MeS3zet6xLYxJNPX+ZLL9mxg7jrd386gJs2nMYD5jyfsYUO9+KdCSQBLaXiIIS\n/HZNLqPxf//xGVh73+iceC45OwAJ8jBqh8McFihtcxGrxOgFI2NX/nTl9kzIBpBr91GzhmN3/WOf\nrMb+I9Wu+nrwgj83w/cWWccLcsP2/ZXYus9fUC23lijZ9jlU5X0lrfGr0Kl/2IVeiIqwZKn5pfay\n5MtchBvPO0B+zUVYOJp6iKgzEU0loqVEtISIbhCkuZSIFhLRIiKaTkT9DOfWasfnE5FcHFaP2HVi\n8wbKVim37TuCaV/tyDpmtecnZ2n8mfObHRYo/dXFKl8jMh4DVz83F2Av8YNSmP3snQbd2ws2BbaP\nrBdEJV/z/NzA8r/8KX+Btdw+BdmmnLrCn3uoaC2KiEcc5liCJCzzmRXme5fZq8EKXfDrK96duG3C\nYudEISJj468G8Atm7g1gKIDriKi3Kc0aAGcw80kA7gbwuOn8mczcn5kH+a6xDaI+/I1+xwAA3l+c\nHefcqsP/QiI29j+mVmDz3sNZ5UWxcMONgCWPph6r+Qwr3G4+E/Tkl9Wy/KwyfaiMK7far3Nwwq2p\nZ6fkehC/ZOapkmOaeGW2WOOOqoYyezVY4dbJYJZDFNmwcbxTZt7MzHO13/sBLAPQ0ZRmOjPruy7M\nANAp6IrKIF65mzrYtonzilEAOFTl7DkzZfk2XP3c3CwNPEkr9ozunH4ndxMkF4R8KLF7UZz34FaH\n3BaB33xldQ3maJukxPm1ZibqjR3NLz23cZ+MJGRXSmlc2fiJqBzAAAB2379XATC6qTCASUTEAB5j\nZvPXgJ73eADjAaBLly5uqpVdkol3Fm5G/ZIFeH2uedbenfZsZueByiybe5I0p6M1nBpEHnpjjuAP\nWN/y00z1iovSuxa5Ic5nk0SBsHbnofTvDT7iHgVOxG1VWZ3dl2T2arDCr1tx1EgLfiJqDOB1ADcy\ns3DGh4jORErwn2Y4fBozbySitgAmE9FyZv7UfK32QngcAAYNGhToSM0V+tYCSGQWENnLN+w+jEcN\nMUdEe8cmAddePRIB6QIt0AX1SrwK/hAqI02yBYKbtSFhYzUvFdZ72xyOwe2ewkaSshG9LFKvOCIq\nRUroP8/MEyzS9AXwJICxzJyepWHmjdr/2wC8AcCFM6M73GinVilFx63y/dQQf+WEDk2ky46CVDx+\n9/ZtUQcOMgSxn5y8au5xmuFkTFFxkihTT8SyM6c/+ejnfl4acSDj1UMAngKwjJkfsEjTBcAEAJcz\n80rD8UZE1ET/DeA8AKFNZ7tzKxQnFh2eY7FptJGBXVrIFx4RXgaS+ZO1lhnn/TXnA82mUPdlyuJZ\n8CfIDJc0ophTkCVq0Sm3ml8OmZ3dkoSMqedUAJcDWERE87VjtwHoAgDM/CiA3wJoBeCfmhdDtebB\n0w7AG9qxEgAvMPP7gd6BATcPjgH85D+53qWiPH77X2cXrbC2ffSKV3dOs3Blzl5J64hDM/hpJq+u\nz7LL7vONoOPkx0HFtgOYvHQrrhnZPUtR2WTYfnPVdn+eVVaYv3b8zAV1b9PYb3UixVHwM/NncIrV\nxfxjAD8WHF8NoF/uFeHgRvgyA5MD3PwgiVqlF68e85d/8LFHvOfntY2XbYl/EVIY3OJy79ok8v3H\nvsDOg1X4wbCuWcrK8PumpH9fG+C6DCM5Gr+Prl7iM4RG1OTX94kDrjR+69ldT2UnyFQKQC4evwhz\nu7htjq93H3JO5BGvtvokmTMU2ejhPBjuQ1j7xby7li/BH3XlfZJftQ0Qq2fsdW9Rr1uuhUU6hr9L\nDducWnT1iR2bWl4vCvRlZPHG6LXvpJnhjOTZnGDgZAcgjLYxzF+QSzd775t+Vv3GQUEJflfjO2BZ\nkKQFXDpeTD3m9C/MzLUj//V/+nuu0xafsW8UhUnfOyfF4NUTXF5+Vv0aiUpJKSzBH4A7p1fsOlHH\n5g3RqF6xdYIwIEqFbHAt+J0vyDOX5USTPHUhWg4aVspH3a32Hj7qnEgSP6t+jUT1cVpQgt/NKAr6\nzZqklbs6Xjx75O7CPt8jCVoUpMgfolYorpfYf1mWwAR/ILk4U1CCX6bR/vXDU/DD4eUhaPz2OUb9\nWvBq45d5gTkN0CSavYLgdYvNOhTB4NUFOQkEFbJBmXo8INNmpcVFKC2mwD+pEinsPJl6pLK1xWo3\no3xHJnKrW9w8n66tygIvP2rO6tXW8pyTQtGuaf2AaxMcQW24ozT+kNDdHIP2T0+aqUcP2QAAO1yE\n+pUS/A6dXDYmeVQk7NF4xu/G8knA7h6c7u6U8pbBViaBKBu/B2SEOcGbt4sTMW+okwOBMHPNLsxc\nswuDfv9h3NVRABjdt4Ov6wtA7tu6r4a2TWUeEdVm7YUl+GXaTJP8QTZvg9KiRK7ctcJufEnZ+AOs\nS6Eg47V1xxjz/kXuKASN384W7rS/bf6MMO8ojd8Dsm1GAUv+1o3r2wrMOMarXZl21ZEz9biujmsi\nd3+NgLZN5TYDsiL/xb6/KJZJWyQZBkrwe0DKBx2af3uAkr+ICG/O2xhYfnEiZy4LXwTlm3YbhZki\n39pEhJ+49Und8yJIlKnHA+t3OceJWbPjYOA2/uIiSl6sHptzdgLk2NaNnPOOQP4EWUYUgykKkbz/\nSHALjuLCj9tjddIm0kyUBfCVqjR+D2za4xwOoKa2FlOWbwt0A4p8i7fSqUVDy3PfO7lzhDWxJt+2\nsguay4d2zTm2aW/+h7vw89XSTnLf7Lj47Fdn+c5DuXN6QGbFaC0Dy7fsD7Rcp8/8pNn4+xzTzPJc\nUsLLBmk6iUKLuvLU8kDz8/scxvY/JqCaBIuXkDb9OjVDg9Ii3Hphr+ArFCBB9Fi1gMsD5s2TRYSx\n0CqJi7fsBKftxK+EwI3E1BNgXlE8n5vOOx5r7xsdWH71Agr6lTS8aPxFRYRTyluieVm9EGoUHEGM\nC6Xxe+Dpz9Y4pglDCAzr3sr2/Ne7DidqEZGdGUWm7+abv3WS2l6nnsNWfaWFKvgLxIRnHEOXDukC\nIBinh8TY+ImoMxFNJaKlRLSEiG4QpCEi+hsRVRDRQiIaaDh3BRF9pf27IugbMLLRsF2bFWH42/t5\n3B2bW9vbw8J29aTEzYiSXDuyu/cKhYzombduHO/y/xvO7ml7Pikmt6Dx4tUjGrJxh6/46/cFockD\nsfUEkIcEMmpFNYBfMHNvAEMBXEdE5pUoFwDoqf0bD+ARACCilgDuADAEwGAAdxBRaLuSD+rqnHUY\noRX8KMCx2P9tz3kz9QR9H0HmJ/rKi/ujxcmW26C08NYxAN4m7Rm5X5ldWsYr+I210asWjKknITZ+\nZt7MzHO13/sBLAPQ0ZRsLID/cIoZAJoTUQcA5wOYzMy7mHk3gMkARgV6BwaKi8ixY4XxKSVjt7R6\noGH5Znu148tp/LmJgvftD3JyVyD4A8vdG7UMdGhm7aXSsEAFv5f+zsw5zytu852xeL3vBzO5G0Am\nErgyJBJROYABAGaaTnUE8LXh7w3aMavjocBw/pQc2s3eHu8FKbu4RSq/Jk8nW7GwLh5X9XrNM+78\nEjj37jjAC9XG7+W2Fm7Yi09Wbs861r9z84BqFBxBzH0lbnKXiBoDeB3Ajcwc+MapRDSeiGYT0ezt\n27c7XyCAmR03bO5zjPV+sV7x88D9avxWV3vVwKU0fqGpJ1jJH2RuIvNe3KYeJ5OjeWMPu32O84mg\nvnCDdp8NgiDubMkmb3t+u0VK8BNRKVJC/3lmniBIshGAceVPJ+2Y1fEcmPlxZh7EzIPatGkjUy1B\nHvm3233sNoccJGz8nq5yWYuQbfxxw8y2Wv+q7Qd8l9FNYhV21ATl1RN3+Aqj+VA34wZRpcufmuU/\nEwlkvHoIwFMAljHzAxbJ3gLwA827ZyiAvcy8GcAHAM4johbapO552rFQqGV2NH2E0V9kOqHV1mx+\nq2NVtNf7lLougsldtxRRanc1EUnbKwEAKhwE+6Gq7MWInm4hcUqFv1g9SaVGWz6UTzuIyajHpwK4\nHMBZRDRf+3chEV1NRFdraSYCWA2gAsATAK4FAGbeBeBuAF9q/36nHQuFWnaeFAvj4cj05bvG9hEe\nD21yF8BJHa1X6Npd55wmN9XpPb19pQXF6ntH40yL3Z0SqPBj4qItkXlwJIlC8eM3voh17d9qKMft\nOixCxqvnM2YmZu7LzP21fxOZ+VFmflRLw8x8HTN3Z+aTmHm24fqnmbmH9u9fYd4MwzlQUhj9TibL\n7wzshP8Z1ElQH782fuvr7/n2ie7z87By99QerdCjTWPXZdkR5Asxiaaen57RzVX6QlGUgxp/btuj\naYMSy3PDHRZgijC+tJ2+xoZ2S97OYXlmELeHmR29IcJYdSqbpdAN0md17Ew9Vi8Fu45KAHq0tRfi\n5lwJlEizgo5sHPc3rh0eck0ytHUIONbYJKjO693eVf4JtG4BiMfU06FZA/zy/OMtzz95xSBf+dfY\naPxr7xudzLmWuCsQJMxA26b18YNhuZENdcLodrIvE1GyIKOEypQnc83kn49wdc1nFTsC10g3u4hE\n6bT6WbaJB3QJbW2hEDvhbFzZe/voE/C/Z/aIoEbhE7WpZ9r/nYn3bxiRHgwjjmuDRy4dmJXG29qC\nzG+nOaSfjHD3dRcFBSX4F23ci2Ii/G6stYmDCGhi89nnBWmNX5CuYlv2JN8d38jdnu/n5xxnnafl\ncedKnXFcrl1e34zeDtF5t4Pn2asGo3XjYIJuTXDQ1JM4uetm5W6LsnquBaZXt9yw8Rtue8Ed52Hh\nnedJz9V1blmGZmWl6b/rlxShrH4w479cCxuhP0qrOiVxMV5BCf5urRulA6YtvPM8YRoiwjf6yYes\ntfLGycpT+jvCOV3TBqVZf9crLsIN5/R0NL8IS3MobozHzb+DcOc8rUdrD1eJcXrpiFfuiq9pEpBQ\nkEH2dXRO73bu82bn1n344gGu8/WLX1NPs4alOWNEBjL8n2Oq9FAlZuCq044FkFEsrPJxoxQ5xXAK\nioIS/FNuHokfn576rPLSObziR+M306xhdr0f+H4/ADbuoBaZ2tr4bUSO+ZrRJ8m9HNwOHiLKmei7\ne2wfTy8jYz6iSVM3gfnOP9GdLd3MNYZgdUF5c5j7RFAEvTr4W/2PwYc3nWGbJi6vHmP/NPdVK8Es\n+iLWMcYPqk1r/M5lO3F8+ybyiX1QUIJfFjdf/jJJg9P3cxnT1/7rxC5Ppw4nfGmYDok2vxBd5sVO\nar7k8mHlnsxwxrK7t879MqoRbNNg9fLr6jP4169GZdrrDx68qsLEi5eXW3q0bZy1w9t5pq+VwIKO\nWuRzskWgxoOV1anyiyhHubGqkpPSo5utMhq/O+VMRFTvxTop+IOOiOEk9PSooVHbXUV5GQWTTPCy\nMGPvi9rNywYkTlqkm12Nrj2zB1748RDXdRBh13bMwXre/GZM7tyQmUuHWDs9BIGu+dY3LKI0f1WE\nvaWmVe6z1uwGABwjcASwek7lNt44zJw2W6X9+F3U04qo9rooaMH/3FXiAeymcWWEhii7foYgUq20\nSUyvIY/tL7DKJ1ez0fO3q4e5bcLshsa8f3J6yl7qZeLNaR7GjR9/cRFheI/WrusgwlnGBSf5LxqY\nu0bEsfSA57z17IxhU3LMKjGZevSN2k/tkeuzb1UjOxMbI3Mvev8KQmZHFYqioAV//VLx7f3yPGuf\nXiOvXzPMs6mHsn67e5jPXJkbesBqkFrlvO/wUXEwNTjZ+LOR7YjeXEczF43t31FYvgyNHF4WYWy+\nI8MQm0iwY/p5m1gPlmDbRVeSjP3L3H/Mf5d6tP24nUjV3/1FRDnXugl78l3DC1Z/h6Vt/AEI7ahe\niwUt+K3Ge4tGcm6EJ3eVXHEndG/MPW3VL4YcmymHQBh5vDj0gBs6tyyz7EQXndxJK1eg/Rgu6ti8\nIdo1zZ2gDCoevzjKZ+r/7wx0jt7dqUVDfHiT85qDuLw5G9u8kDo0C3jnNZvmtxKurSQnn402ezv0\nZja2t1nBN3v1dDbNqeieMp6xaAd9EV8R5fZUNwJbjwxQRJm9P4LcID2qGJMFLfiD8N+WyULUbYya\nR1rwW1z/3I+HCAWskXY2m3aIqFdSZClYh3dvjbX3jUYXwfZ1+rCYc/s5mPTzEdKDQsbt1Q6zpnZs\nK+fVjhOuGY4ebZ29IJLgxy9qnqCqdesFvWy/uN7+2WlY+fsLso6NOK4NBnVtgak3j3TM32mdRBrB\n/eRo/OaGMF0j240sPWgsjuvmGDdzDKKk40d0w5i+HXDuCe3S92ZlSTzLInaUHV0l+n0QFLTgD3K8\nD+hivfGD6PMyy31M36HHYnSWFhdlFuxY9Mu/jRPs8WmTZ6rTutfM9exaNa4vNKE0bVAirGNREeHP\n3+tnm3duXhkbaubl6GL+RTKdcOvFiGNMvPLTYdJpLxvaxfa8+SU7fdVOW/flYiJh1FoiwrES4QRk\n20o38WTtTpVj6rHPw+8cgLWph23Pi8lN27llGf5+yUA0KyvN8eox8sa1w/FP0wphJ2bffg66Bxzz\nyorCFvwSomFAl+Z452enOab7y/f6CT0niIBFG/cIjmdJfmmskjYvq4fubXIHqZ2t086U4rZ8Gdxq\n1sbooeYBGaSOLtLI/nRR3wBLsOaNa4fjgxtHYFB5rtnQ6h5//62TbPP81oBsM5gugN752WlZWqbs\n15rT/rVuTddG04dZjjv3v3BeyA01E01pMQVmSNfvTaRYtG/WwHLf5DZN6uN+Qf+LMopnQQt+GelR\nU8s4sWOztN1b54QO2TselbdqhIsHp/aUKS0mvHp1SoMjAHPXCwS/xW8r1u08BACorglG5IlsmQDQ\n0ml+w8egcLJ1mkNPlBhsz+Z5kCC/1kRB2vp3aY5Zt53tuODILwO6tMhalPPGtcPx2tXy2r8I8+5T\n+kvzxI7NMLa//Kp0nUuG2H9hGF/KRlPJ5UOz3UNvveAEANnDzvxCdxLs0qYeizfIkeoa4fH7L+qH\nX5x7nKWfv5lmDUudv07S7pxSWaYZf3o3V9EDwqCgBb+MF58uaM0Pzzw4jW6QMsvhs2388tJ02/7K\n9G/zYiZRPsYjZxu0vSISuGYS8O0B9pOmfjQuq/aeeP3peOWnw3D92dmBxow+3vog00uX+Vqzmzw1\n8vLsr3OONW1QirZNG3gKheGHAV1apLV/kdYng9lO3b6ZP03R6YkbzxsVB12I9mrfBGvvG52ZqDVO\n7gokzC/OPQ73fkf8VePXnVE3g43p2yEr2mqbJvXxs7N7So/FK08td0ybntwV9FV7l+lg1+t4ocAF\nv7Pw0P17zej27fu+cxJaN66f8osXeuqIH3FHgyeEfl7/9Lvh7J64UxCMDQAOVB4FkIqQ+bHExJux\nc/7j0oFpDw6Rxv+NvsdIBGCTL8+MVXv3PqYpBh/bMudao62azCq/A7dd2MvWjfOikztFFvfEK2ef\n0A7/uCRlB3aKMGokxywmaPYgTWWW5sS0V4t12SLl42dn98TgY8Uec35t/Ppk/9BurSyjrcoqN47K\nncmPP+tam4uZ4986MrqIVDFgJdSz0ugav8VQGTe4C8YNzv4UNq7TI4gfcvOGuROX15zRHf07N8dp\nPVtjycbsTZV/cvqxeGLamvQg6tlOLmaHsegGpcVo26QBNu45jKKi3HrJvAiduiMzW66ulY17r1Ni\nyMdcrl1V37zuVPTrZL+7GAFoXhZOjJviIrJdFHb32D5oXuYu8mi/zs2wcc9hqbRmoVGbZVO3nnAE\nUi/E1+ZsQOP68hEjjYLSWLLummleJ2Fn43fCt1ePbiq0u1aijJVb9zumKU63tXN+ZuIW/DJ77j5N\nRNuIaLHF+V8atmRcTEQ1RNRSO7eWiBZp52aLrg+Tozb28id+kNp8wU08fOvJUgctWvu/WVkpRp3Y\nHo3rl6Q1oePapUwNaXuhRD5mWgns9qKOJeWaKtEhG9Yrxn+vOzXneO9j3G31aNT49foaS7fawKJ/\n5+ZS9aysdn7xW1EucHXVcSr58mHlodpwzaYeo36jn6ux6Pt64DFj+zk2pcV5/b1tfsnY2fh1dOWh\nXdNsN2X/O9IFw/LN+x3bJWPjdw59Yqa4iHD9WT3w6GUne6yhP2RMPc8AGGV1kpnv17dkBHArgE9M\n++qeqZ33t82NB+zivffSJtzSmpvLt7ZTp5Dp/FnntP9ktHL9pQUAlw/riqm/HIlZt52dk6/5kzbI\nPV6NISmGaStUT+7aAjNuPdvqkhxEk7s6DGDyTWeg4p5s/3M3VB71Lvjfv3EEHr1M7I5HBLx/4+l4\n93pnb7AwMC+CEmn8Ri1c+NQNB81d7uObR+Lub2UCuhmLu2J4ueG4WL3OXsAl7vudW5bhoXH9c1we\nk7Il7+Gj4kliI0XpF5/gpM196E1y03nHY5TPaLBekdlz91MAshukXwzgRV81ChC7lbe6fXiIth+m\nXGiGzBueDMdEfTtrMFl+KWQGhhsPAaP73cjj26YnKo2I3DnlNH7nNGb6HJPxgDIPXLtom00Mvudp\njT89u8soLiKUFBd53rPUz6BqUFqcVT8jBEKv9k3RR/vCadPE++Sql5dxrgkv81v/irIyu8k83/LW\njbL2UDZecp1hJzDRSwbIvidzeeYwHeZV9H52s8uuhD8lp6aWHecCMqae+BcIuiWwyV0iKkPqy+B1\nw2EGMImI5hDR+KDKCoKWjerhuauG4I4xfXLOnVJuMSkk6gcEtBH43zoNaD0rXWvIyDubODoSY0K/\nXuRN4XUVcnYdclNkHTKdnnj96ZZ5XSpwI0y/XA3HXho/TNu4xRnjphh+Y5vLiKDHLz9ZaPYKE7Op\nx9hn9HNWJkxRH9CfX7fWjdKmh2xHBnFLdNBWk990brabrozGb4VvU4/E5TIl1NSyY156W6/dcTDn\nXNLfBUF69XwDwOcmM89pzDwQwAUAriMiy8AqRDSeiGYT0ezt27cHVqlhNoGyTuvZOr0tm3HwPDRO\nvDNRWjgjezD8clRu0Dfjg7fbZN2Lxs9gdNMWc1n1TaHGL6Fd+p1zMt+rORaLkSwbf5FJ4zch6+1x\nVBN4JUFsMmI5g5j5eV6f9sJQv+6Lkm9488rdToY2Nq4mtc1RcPLsE9oKv5Ks8mlQWoy1941OB9jT\nMa4SPlRV7ZhXg9Jct16viBSHnDQSnTz1xWfv+9K2SerFVyWYS6pLgn8cTGYeZt6o/b8NwBsABltd\nzMyPM/MgZh7Upo31zjduuWJ4V+dEJqwGctaEmOF/UVwZ4+efXT8zmzjs5pqNwsFpC7uU4Ddrhrnp\n7vn2iaYVg7n5/udHg/GQFjKifVP7mEFuXhzG+pU6jHhZgVCj7brilJ8MUYZ1cGPyMb4En7nyFFx/\nVr91AJoAABFMSURBVMb8ktb4nRYCilxALS5xqwzcPvqE9O9DVc628iwlSbIsq2cT1ALA5388BM3L\n6mH6LWdZptGVRtGYtXuexhXrcRGI4CeiZgDOAPBfw7FGRNRE/w3gPABCz6BwyXSQ/p2t4+247SdG\nt3PR56nxU9uuL3tZuARYB5vSry4iuU/aS4d0zQpZIRp4I45rgzF9j8FPz+jmGOrAq6g0uz+aB66s\nCaA6HYwru2vLRPs0I3LZLCkiqU1PZDnz+LY4rUdr/N/5uTudWWFsi5HHt836urGyu+sIPdMET+1E\ng3ByErJmzurVLj3vYW5Cp8e473C1fYII6NamUXoTFruvObtYPVYK3NzfnGsbrjsqHP34iehFACMB\ntCaiDQDuAFAKAMz8qJbs2wAmMbPR2NUOwBuaVlcC4AVmfj+4qrtjePdW+Jcgzr2OTKgEw7yj4Zh4\nctfoTic8r30dZjR+F6YeFkyGmigqEpl6rNJmfluNy+IiSi/Jt8ONjdaYUjcP6IPJbNqR3ZLxwpM6\n4OEpFTlhCLxs8r3rUFXOsYo/XOg6Hzsa1S/Bcy53/LK7F91TqraW023q5WVsXBVNBPzrh6dg35HU\n4sJe7Ztg+Zb9UhFZ3U58OsUNEvHzc47DXz9cmXXMz1yZbB8uthmzVuU7hkyJCMfRxMwXS6R5Bim3\nT+Ox1QDchWsMAf0ZltUrQf0S60UrB6ucNQ09r+PaNc7SgkT2Z6PGL+pIujapX3tqj9Z46KOvMLy7\nnDaQiQWefby8VSNs3nsE9YqLct05LcaCUZBYebLI4s7Uk3vsuwM7YfbaXfj+KZ2zjl9/dk/8d/4m\nxzyPad4QC+44L+d43AtmgsQuZrt+n9W1jEcvOxkvf/m1dFgKOxF9piEcyD8vHYh56/dICWmzABR9\nPRhTlJZkzt/3nZPwxLTVWLU9d/LU+DiN9xfEU5bNI2OezW25pNv4C3rlLmB8iPZP4ufnHIePV9hP\nKhMRnv/xEPRq3wSb9x5JHxcpPjWGVTUimaN3Fl3oDj62JSruucB2UlI3AxFlXhjmTvfH7/bFZxU7\ncEKHpthuiPuj5yDCaDbyErsme+7Dftg8fPGAtKYommRr36wB/nVl7lSQ33C1cW35FwZ2LzGj+aFz\nyzLcfL54tzk7l0sz5vPd2jRGN4fnoXdL8+J5YVkWXkD6qvnyW961r2AAXD60K56dsQ6AvPIiMvV0\natEQG3YfzhH8937nJKkQ2FFR+IJf0oTSz8b+b+RUza1QF/xmG//DFw9Aq0b18MKs9cZa5OSjC2Xj\nQhFZTxQCGbZ9y76xLq3KcEmrlJmjeVkperVvgk4tyvDhsq3WGr+Wmb6qUxYiQcA6h0ETV1RCO7k/\n6ecjLLS2ZKptdpuJ6C9Vq5ASnnZK8xW4z10bWt3bQJv9MESup25XwN/9rRNxyZAuuOChaa5NPcam\n7tupGTbsPowG9bLH8sWD7SOgRk1BB2kDgvn0c8rf2E++0e8YDO/ROmvgCSfUtGODJMPEAtkvLz0W\nUI3N4tQGpcV4/8YRaRc9q8HQpEEpXrt6mOuNI36pa5NZA89VFpFRRGQZkve4dk3Qq31T4bkkIrMS\n3M0G8zpBefUYr9GroUeOHSRYI2O3Ry8ALL97lKuNbAB7Rc/qfty+pPSvyPEjuqWP/fl7/TDh2uFp\nV8+kUgc0/tT/Mo+0vFUZdh866ipfwJtXz5i+x2DrviP4wbByqfKAzD0QAf83qhdalNXDiR2dBZau\nRNlpsKKNQmSxCuKVJIqLCE//8BT0u2uS9DUJVfjtNf5ie8Gvv/wuHSLv5uznmep9bmi3Vnjqh2Ln\nCrs9egFYbmhiW67rKzLxg9xMwK69b3TW32X1SjDQIipokih8jV9C6Om88tNh0vFX9FjyNcxCwT+m\nb4f0b5FLWHERYfyI7p46NSG1UcwD3++PsnrO7243Lz83iFeBZtpi9u3nBFyid4qI0htly5LUpfh2\ngrhrqzL07tAUd43NXZEOpOZQ1t43Om2yBICRx6dMfGP6dRBe42Y/CTPpuSybl9WPT89ozPpYOucE\n+/1qrark54uzZ7smuHtsHzx8sXgBZyFR8Bq/jswQNse7sUPXDqprWKiljO3fEaNObI/3F2/BOSe0\nk87XDq8257AXImXZWLX/65cUhbKVnGjvWDs6Nm+IjXsOo1Xjeq49e7yYS8JEvxciYFSf9jizV+6c\nTP2SYky8wTpMhogebZvkaK5GvMyLpyd3tf+NAfnM3HJBLzz6ySoAxglTufwBL18k1ldc7uILPJ8p\neMFv3DUrSHQBVMtsqRHVLynOWc4eB0GtZrTMX3AsDPfJm849ztWcCJCauH3s09W4bGhX1wIsaRr/\nhGuHY+mmfSAiPHp5dOF8g9D4ZfuD034CsiR1Yj4pFLzgR0hmjozgjy6UrNHG7wYZTwcviAaXceVw\n0FzvYUetRvVLcoKIyWI3cR4H7Zo2yIlfn1xSPUHvInamHiN633bztTW8e8Zs5fbr9skfRB4tPhEU\nvODXu0HQGoDR5BDZ4qD0LbgrT2Zy1wu6V4Nx71y9jIYScw9J59QemcV0z1x5CsoFMZmCRF8RWwjo\nzg360JBdOW0XBsGIfrpBaVE6Zg4AtNL24LDbj1mvSr/OzXFO72DMsH549ephaOsjtLcX8n90OqBH\nhwzKzq7TUJuUvWJY1+gEv8diwrLxf3dgJ8xdtztrlW2TBqX45fnxbTARJF0Ngn7k8faTjUHw9s9O\nS5R5qUOzBlkLFd2gh0DR53kaS4bcSJt6HL629CFndsO9bGhX1NQyvtnfer1I0jzPTvHhUeeVghf8\n3ds0xqxfny2Mme+H0uIizPr12WhZVs/V9o1+eOIHg/DsF+sstyS0Iqz3UrumDfDkFbkuesbNOhTy\nlAYRSjpAJlw7HEs27vN07QUntserczbg16NPwEkdm2FUHzlFQMYLCEi5eL74k6E4oUP2ngvNGpY6\nmgT1l9FQiw3fzQzo0hzz1u+RSpsvFLzgBxDaYgo931qOxhjcvU1j3PlNsZueHUUhT+4qCpMOzRqi\nQzNvew3cckEvjO3fEa0b18ePTjvWMf0/Lx2Izyt2pL15ZJSVYZJxrcx0blmGqTePROcWcvf23FVD\n0OeODzyVlVTqhOAPm+SHgdEnd5Xkn3DtcDRr6C8QXVT845KBaN8sWttvULRqXB+n9ZSv+4UndcCF\nJ3XAJytT8bJkJ4O94iZuTiOb+YJ8pfDuKAaSHvkxbHfOfCIfVlXqjO4rXlBVyJzavRUuG9pFmQtD\nRgn+AEi43He1raMim2YNSzHAJkCYIlhKiovw+2+d5Pq6164eJrXbl1eevWowDlaGl3/UKMEfAH4W\nuERB2qVVmXpc8/HNI9HQZagHRfT4iTUlw+k9g9sONgkowV8H0DfuSKLG/8GNI5AwZ5YsWiRkxySF\nIkiU4K8DpMNWxFwPEce3b+KcSKFQBIqjrkVETxPRNiISbpRORCOJaC8Rzdf+/dZwbhQRrSCiCiK6\nJciKK1yQbEuUQqGIGJmP7GcAjHJIM42Z+2v/fgcARFQM4B8ALgDQG8DFRNTbT2UV3kh7HSVR5Vco\nFJHjKPiZ+VMAuzzkPRhABTOvZuYqAC8BGOshH4VPGmmTk9097KerUCgKj6Bs/MOIaAGATQBuZuYl\nADoC+NqQZgOAIVYZENF4AOMBoEuXZO1Pme8M7NICL/xkCPp2Um6JCoUimB245gLoysz9ADwM4E0v\nmTDz48w8iJkHtWlTWK5TcVNURBjevbVtxEKFQlF38C34mXkfMx/Qfk8EUEpErQFsBNDZkLSTdkyh\nUCgUMeJb8BNRe9JWMBHRYC3PnQC+BNCTiI4lonoAxgF4y295CoVCofCH47c/Eb0IYCSA1kS0AcAd\nAEoBgJkfBXARgGuIqBrAYQDjOLUbRzUR/S+ADwAUA3has/0rFAqFIkYoiXtTDho0iGfPnh13NVzx\nwsz1OKFDEwzIoyBgCoWicCCiOcwstZekmu0LiEuGKE8khUKRHyQ4SopCoVAowkAJfoVCoahjKMGv\nUCgUdQwl+BUKhaKOoQS/QqFQ1DGU4FcoFIo6hhL8CoVCUcdQgl+hUCjqGIlcuUtE2wGs83h5awA7\nAqxOUKh6uUPVyx2qXu4oxHp1ZWap0MaJFPx+IKLZssuWo0TVyx2qXu5Q9XJHXa+XMvUoFApFHUMJ\nfoVCoahjFKLgfzzuClig6uUOVS93qHq5o07Xq+Bs/AqFQqGwpxA1foVCoVDYUDCCn4hGEdEKIqog\noltiKH8tES0iovlENFs71pKIJhPRV9r/LbTjRER/0+q6kIgGBliPp4loGxEtNhxzXQ8iukJL/xUR\nXRFSve4koo1am80nogsN527V6rWCiM43HA/0ORNRZyKaSkRLiWgJEd2gHY+1zWzqFWubEVEDIppF\nRAu0et2lHT+WiGZqZbysbbcKIqqv/V2hnS93qm/A9XqGiNYY2qu/djyyvq/lWUxE84joHe3vWNsL\nzJz3/5Da2nEVgG4A6gFYAKB3xHVYC6C16difANyi/b4FwB+13xcCeA8AARgKYGaA9RgBYCCAxV7r\nAaAlgNXa/y203y1CqNedAG4WpO2tPcP6AI7Vnm1xGM8ZQAcAA7XfTQCs1MqPtc1s6hVrm2n33Vj7\nXQpgptYOryC17SoAPArgGu33tQAe1X6PA/CyXX1DqNczAC4SpI+s72v53gTgBQDvaH/H2l6FovEP\nBlDBzKuZuQrASwDGxlwnIFWHf2u//w3gW4bj/+EUMwA0J6IOQRTIzJ8C2OWzHucDmMzMu5h5N4DJ\nAEaFUC8rxgJ4iZkrmXkNgAqknnHgz5mZNzPzXO33fgDLAHREzG1mUy8rImkz7b4PaH+Wav8YwFkA\nXtOOm9tLb8fXAJxNRGRT36DrZUVkfZ+IOgEYDeBJ7W9CzO1VKIK/I4CvDX9vgP0gCQMGMImI5hDR\neO1YO2berP3eAqCd9jvq+rqtR5T1+1/tU/tp3ZwSV720z+oBSGmLiWkzU72AmNtMM1vMB7ANKcG4\nCsAeZq4WlJEuXzu/F0CrKOrFzHp73aO111+JqL65Xqbyw3iODwL4PwC12t+tEHN7FYrgTwKnMfNA\nABcAuI6IRhhPcup7LXYXqqTUQ+MRAN0B9AewGcBf4qoIETUG8DqAG5l5n/FcnG0mqFfsbcbMNczc\nH0AnpLTOXlHXQYS5XkR0IoBbkarfKUiZb34VZZ2IaAyAbcw8J8pynSgUwb8RQGfD3520Y5HBzBu1\n/7cBeAOpAbFVN+Fo/2/TkkddX7f1iKR+zLxVG6y1AJ5A5tM10noRUSlSwvV5Zp6gHY69zUT1Skqb\naXXZA2AqgGFImUpKBGWky9fONwOwM6J6jdJMZszMlQD+hejb61QA3ySitUiZ2c4C8BDibi+vkwNJ\n+gegBKlJmGORmcDqE2H5jQA0MfyejpRd8H5kTxD+Sfs9GtkTS7MCrk85sidRXdUDKc1oDVKTWy20\n3y1DqFcHw++fI2XDBIA+yJ7IWo3UJGXgz1m79/8AeNB0PNY2s6lXrG0GoA2A5trvhgCmARgD4FVk\nT1Zeq/2+DtmTla/Y1TeEenUwtOeDAO6Lo+9reY9EZnI33vYK4oaS8A+pWfqVSNkbfx1x2d20h7IA\nwBK9fKRscx8B+ArAh3oH0jrbP7S6LgIwKMC6vIiUCeAoUnbAq7zUA8CPkJpAqgBwZUj1elYrdyGA\nt5At1H6t1WsFgAvCes4ATkPKjLMQwHzt34Vxt5lNvWJtMwB9AczTyl8M4LeGMTBLu/dXAdTXjjfQ\n/q7Qzndzqm/A9ZqitddiAM8h4/kTWd835DsSGcEfa3uplbsKhUJRxygUG79CoVAoJFGCX6FQKOoY\nSvArFApFHUMJfoVCoahjKMGvUCgUdQwl+BUKhaKOoQS/QqFQ1DGU4FcoFIo6xv8D5cmFTGbhxLoA\nAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f61a3c8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(result.T[1])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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cB5Zla7YUOY7De97zHmSzWQiCgI9+9KN49NFHC16TzWZx33334fXXX8fAwACe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\n1gAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10f736978>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from mpl_toolkits.mplot3d import Axes3D\n",
"\n",
"mus = np.arange(1, 10, 0.1)\n",
"vars_ = np.arange(1, 10, 0.1)\n",
"X, Y = np.meshgrid(mus, vars_)\n",
"Z = ma(X, np.sqrt(Y))\n",
"\n",
"fig = plt.figure()\n",
"ax = Axes3D(fig)\n",
"ax.plot_wireframe(X,Y,Z)\n",
"ax.set_xlabel('mu')\n",
"ax.set_ylabel('var')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# § 6.6 階層ベイズモデル\n",
"事前分布 = $\\prod_{i=1}^{20}f(\\beta, \\sigma, \\gamma_{i} \\mid x_i)\\frac{1}{10\\sqrt{2\\pi}}\\exp{(\\frac{-\\beta^2}{200})}$\n",
"\n",
"ここで $f(\\beta, \\sigma, \\gamma_i \\mid x_i) = {}_{10}C_{x_i} q_{i}^{x_i}(1-q_{i})^{10-x_i}\\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp(\\frac{-\\gamma_{i}^2}{2\\sigma^2})$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"20\n"
]
},
{
"data": {
"text/plain": [
"(array([ 2., 3., 1., 0., 2., 1., 1., 1., 1., 8.]),\n",
" array([ 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10.]),\n",
" <a list of 10 Patch objects>)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x10fa6a710>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data = [1, 0, 10, 4, 10, 10, 10, 6, 4, 10, 1, 9, 0, 5, 10, 7, 1, 9, 2, 8]\n",
"print(len(data))\n",
"plt.hist(data)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def q(beta, gamma):\n",
" return 1. / (1. + np.exp(-beta - gamma))\n",
"\n",
"def f(beta, sigma, gamma, x):\n",
" gamma_term = np.exp((-1. * gamma**2) / (2. * sigma**2)) / np.abs(sigma)\n",
" result = (q(beta, gamma) ** x) * ((1 - q(beta, gamma)) ** (10 - x)) * gamma_term\n",
" return result\n",
"\n",
"def rprop(beta, sigma, gammas, beta_next, sigma_next, gammas_next, data):\n",
" p = np.array([\n",
" f(beta, sigma, gammas[i], d) for i, d in enumerate(data)\n",
" ])\n",
" p_next = np.array([\n",
" f(beta_next, sigma_next, gammas_next[i], d) for i, d in enumerate(data)\n",
" ])\n",
" r = np.product(p_next / p) * np.exp((beta**2 - beta_next**2) / 200.)\n",
" return r"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"result_gammas = []\n",
"result_beta = []\n",
"result_sigma = []\n",
"sigma = 5.\n",
"beta = 1.\n",
"gammas = [0. for _ in data]\n",
"\n",
"result_beta.append(beta)\n",
"result_sigma.append(sigma)\n",
"result_gammas.append(gammas)\n",
"\n",
"for _ in range(10000):\n",
" beta_next = beta + np.random.normal(0, .2)\n",
" sigma_next = sigma + np.random.normal(0, .5)\n",
" gammas_next = [g + np.random.normal(0, .3) for g in gammas]\n",
" r = rprop(beta, sigma, gammas, beta_next, sigma_next, gammas_next, data)\n",
" if np.random.random() < r:\n",
" beta = beta_next\n",
" sigma = sigma_next\n",
" gammas = gammas_next\n",
"\n",
" result_beta.append(beta)\n",
" result_sigma.append(sigma)\n",
" result_gammas.append(gammas)\n",
"\n",
"result_beta = np.array(result_beta[1000:])\n",
"result_sigma = np.array(result_sigma[1000:])\n",
"result_gammas = np.array(result_gammas[1000:])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\beta$のサンプリング結果"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x110b4a4e0>]"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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tkX7q9nTDK1fPfwP4BkBPItpBRDcR0a1EdKu0yXgAa4loFYDnAVwlojjj4cTE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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x110605da0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(result_beta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\sigma$のサンプリング結果"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x110b14c50>]"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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48o9Y5bLo79crdsbUvnj6YQuDoBLZ1nrYZ1dGWQC1b5ZvuD6F5Tk27KrCGz+a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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x110aee828>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(result_sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$\\gamma$のサンプリング結果"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x110972630>,\n",
" <matplotlib.lines.Line2D at 0x1109727f0>,\n",
" <matplotlib.lines.Line2D at 0x1109729e8>,\n",
" <matplotlib.lines.Line2D at 0x110972be0>,\n",
" <matplotlib.lines.Line2D at 0x110972dd8>,\n",
" <matplotlib.lines.Line2D at 0x110972fd0>,\n",
" <matplotlib.lines.Line2D at 0x110977208>,\n",
" <matplotlib.lines.Line2D at 0x110977400>,\n",
" <matplotlib.lines.Line2D at 0x1109775f8>,\n",
" <matplotlib.lines.Line2D at 0x1109777f0>,\n",
" <matplotlib.lines.Line2D at 0x110931908>,\n",
" <matplotlib.lines.Line2D at 0x110977ba8>,\n",
" <matplotlib.lines.Line2D at 0x110977da0>,\n",
" <matplotlib.lines.Line2D at 0x110977f98>,\n",
" <matplotlib.lines.Line2D at 0x11097f1d0>,\n",
" <matplotlib.lines.Line2D at 0x11097f3c8>,\n",
" <matplotlib.lines.Line2D at 0x11097f5c0>,\n",
" <matplotlib.lines.Line2D at 0x11097f7b8>,\n",
" <matplotlib.lines.Line2D at 0x11097f9b0>,\n",
" <matplotlib.lines.Line2D at 0x11097fba8>]"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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BKPp0Anna2ZrAP/szEzFhdj7Ovn4iZl/EVkWfhmIh2ZF8vLCy4hCur2DasDuJ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pv6PVr7BfxXmMd8tjlg1d79HWu+Sd+CX1Lguf+U3/2fysdC4XuduZMo4QvVF3hO7VvpbT/FfHzM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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x110909320>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(result_gammas)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1111b4ba8>"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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AvYJva2NUn8dsd2UdmT7t1d7G0ocWyYfmSgwZtn0/2jznhaU6evt/blVWuAQO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\nEkB8nQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x110cec4e0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mean_beta = np.mean(result_beta)\n",
"estimated = []\n",
"for i, d in enumerate(data):\n",
" gamma_mean = np.mean(result_gammas.T[i])\n",
" estimated.append(round(10. * q(mean_beta, gamma_mean)))\n",
"plt.plot(estimated, label='estimated')\n",
"plt.plot(data, label='actual')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1112b7fd0>"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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DQGAobgAIDMUNAIGhuAEgMBQ3AASG4gaAwFDcABAYihsAAkNxA0BgKG4ACAzFDQCBobgB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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1111d5320>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.scatter(*zip(*Counter(estimated).items()), marker='o', label='estimated')\n",
"plt.scatter(*zip(*Counter(data).items()), marker='.', label='actual')\n",
"plt.legend()"
]
}
],
"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": "3.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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