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metropolis hasting alg
{
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"id": "02c9d8b6",
"metadata": {
"ExecuteTime": {
"end_time": "2021-08-13T12:46:17.615000+09:00",
"start_time": "2021-08-13T03:46:11.728Z"
}
},
"outputs": [],
"source": [
"using StatsPlots\n",
"using Random\n",
"using Distributions"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "48de011f",
"metadata": {
"ExecuteTime": {
"end_time": "2021-08-13T12:46:34.859000+09:00",
"start_time": "2021-08-13T03:46:11.731Z"
}
},
"outputs": [
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"source": [
"c = 2.0\n",
"U = Uniform(-c, c)\n",
"S(x) = 0.5x^2\n",
"\n",
"function mcmc_mh(K)\n",
" x0 = 0.\n",
" xs = [x0]\n",
" x = xs[begin]\n",
" for k in 1:K\n",
" Δx = rand(U)\n",
" x_cand = x + Δx\n",
" r = rand()\n",
" x_next = ifelse(r < exp(S(x) - S(x_cand)), x_cand, x)\n",
" push!(xs, x_next)\n",
" x = x_next\n",
" end\n",
" xs\n",
"end\n",
"\n",
"plot(legend=false)\n",
"histogram!(mcmc_mh(100000), normalize=:pdf)\n",
"plot!(Normal(0, 1))"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "51c5ca03",
"metadata": {
"ExecuteTime": {
"end_time": "2021-08-13T12:46:35.982000+09:00",
"start_time": "2021-08-13T03:46:11.733Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" 0.217426 seconds (7.00 M allocations: 122.286 MiB, 14.08% gc time, 3.28% compilation time)\n"
]
},
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" 765.252,1400.4 765.369,1400.33 765.487,1400.26 765.604,1400.19 765.721,1400.12 765.838,1400.05 765.956,1399.98 766.073,1399.91 766.19,1399.84 766.308,1399.76 \n",
" 766.425,1399.69 766.542,1399.62 766.659,1399.55 766.777,1399.48 766.894,1399.4 767.011,1399.33 767.129,1399.26 767.246,1399.19 767.363,1399.12 767.48,1399.04 \n",
" 767.598,1398.97 767.715,1398.9 767.832,1398.82 767.949,1398.75 768.067,1398.68 768.184,1398.61 768.301,1398.53 768.419,1398.46 768.536,1398.39 768.653,1398.31 \n",
" 768.77,1398.24 768.888,1398.16 769.005,1398.09 769.122,1398.02 769.239,1397.94 769.357,1397.87 769.474,1397.79 769.591,1397.72 769.709,1397.65 769.826,1397.57 \n",
" 769.943,1397.5 770.06,1397.42 770.178,1397.35 770.295,1397.27 770.412,1397.2 770.529,1397.12 770.647,1397.05 770.764,1396.97 770.881,1396.9 770.999,1396.82 \n",
" 771.116,1396.75 771.233,1396.67 771.35,1396.59 771.468,1396.52 771.585,1396.44 771.702,1396.37 771.819,1396.29 771.937,1396.21 772.054,1396.14 772.171,1396.06 \n",
" 772.289,1395.98 772.406,1395.91 772.523,1395.83 772.64,1395.75 772.758,1395.68 772.875,1395.6 772.992,1395.52 773.109,1395.45 773.227,1395.37 773.344,1395.29 \n",
" 773.461,1395.21 773.579,1395.14 773.696,1395.06 773.813,1394.98 773.93,1394.9 774.048,1394.82 774.165,1394.75 774.282,1394.67 774.4,1394.59 774.517,1394.51 \n",
" 774.634,1394.43 774.751,1394.35 774.869,1394.27 774.986,1394.19 775.103,1394.12 775.22,1394.04 775.338,1393.96 775.455,1393.88 775.572,1393.8 775.69,1393.72 \n",
" 775.807,1393.64 775.924,1393.56 776.041,1393.48 776.159,1393.4 776.276,1393.32 776.393,1393.24 776.51,1393.16 776.628,1393.08 776.745,1393 776.862,1392.92 \n",
" 776.98,1392.84 777.097,1392.76 777.214,1392.68 777.331,1392.6 777.449,1392.51 777.566,1392.43 777.683,1392.35 777.8,1392.27 777.918,1392.19 778.035,1392.11 \n",
" 778.152,1392.03 778.27,1391.94 778.387,1391.86 778.504,1391.78 778.621,1391.7 778.739,1391.62 778.856,1391.53 778.973,1391.45 779.09,1391.37 779.208,1391.29 \n",
" 779.325,1391.2 779.442,1391.12 779.56,1391.04 779.677,1390.95 779.794,1390.87 779.911,1390.79 780.029,1390.7 780.146,1390.62 780.263,1390.54 780.381,1390.45 \n",
" 780.498,1390.37 780.615,1390.29 780.732,1390.2 780.85,1390.12 780.967,1390.03 781.084,1389.95 781.201,1389.86 781.319,1389.78 781.436,1389.69 781.553,1389.61 \n",
" 781.671,1389.52 781.788,1389.44 781.905,1389.35 782.022,1389.27 782.14,1389.18 782.257,1389.1 782.374,1389.01 782.491,1388.93 782.609,1388.84 782.726,1388.76 \n",
" 782.843,1388.67 782.961,1388.58 783.078,1388.5 783.195,1388.41 783.312,1388.32 783.43,1388.24 783.547,1388.15 783.664,1388.06 783.781,1387.98 783.899,1387.89 \n",
" 784.016,1387.8 784.133,1387.72 784.251,1387.63 784.368,1387.54 784.485,1387.45 784.602,1387.37 784.72,1387.28 784.837,1387.19 784.954,1387.1 785.071,1387.02 \n",
" 785.189,1386.93 785.306,1386.84 785.423,1386.75 785.541,1386.66 785.658,1386.57 785.775,1386.48 785.892,1386.4 786.01,1386.31 786.127,1386.22 786.244,1386.13 \n",
" 786.361,1386.04 786.479,1385.95 786.596,1385.86 786.713,1385.77 786.831,1385.68 786.948,1385.59 787.065,1385.5 787.182,1385.41 787.3,1385.32 787.417,1385.23 \n",
" 787.534,1385.14 787.652,1385.05 787.769,1384.96 787.886,1384.87 788.003,1384.78 788.121,1384.69 788.238,1384.59 788.355,1384.5 788.472,1384.41 788.59,1384.32 \n",
" 788.707,1384.23 788.824,1384.14 788.942,1384.05 789.059,1383.95 789.176,1383.86 789.293,1383.77 789.411,1383.68 789.528,1383.58 789.645,1383.49 789.762,1383.4 \n",
" 789.88,1383.31 789.997,1383.21 790.114,1383.12 790.232,1383.03 790.349,1382.93 790.466,1382.84 790.583,1382.75 790.701,1382.65 790.818,1382.56 790.935,1382.47 \n",
" 791.052,1382.37 791.17,1382.28 791.287,1382.18 791.404,1382.09 791.522,1382 791.639,1381.9 791.756,1381.81 791.873,1381.71 791.991,1381.62 792.108,1381.52 \n",
" 792.225,1381.43 792.342,1381.33 792.46,1381.24 792.577,1381.14 792.694,1381.05 792.812,1380.95 792.929,1380.85 793.046,1380.76 793.163,1380.66 793.281,1380.57 \n",
" 793.398,1380.47 793.515,1380.37 793.633,1380.28 793.75,1380.18 793.867,1380.08 793.984,1379.99 794.102,1379.89 794.219,1379.79 794.336,1379.7 794.453,1379.6 \n",
" 794.571,1379.5 794.688,1379.4 794.805,1379.31 794.923,1379.21 795.04,1379.11 795.157,1379.01 795.274,1378.91 795.392,1378.82 795.509,1378.72 795.626,1378.62 \n",
" 795.743,1378.52 795.861,1378.42 795.978,1378.32 796.095,1378.22 796.213,1378.12 796.33,1378.03 796.447,1377.93 796.564,1377.83 796.682,1377.73 796.799,1377.63 \n",
" 796.916,1377.53 797.033,1377.43 797.151,1377.33 797.268,1377.23 797.385,1377.13 797.503,1377.03 797.62,1376.93 797.737,1376.83 797.854,1376.72 797.972,1376.62 \n",
" 798.089,1376.52 798.206,1376.42 798.323,1376.32 798.441,1376.22 798.558,1376.12 798.675,1376.02 798.793,1375.91 798.91,1375.81 799.027,1375.71 799.144,1375.61 \n",
" 799.262,1375.5 799.379,1375.4 799.496,1375.3 799.613,1375.2 799.731,1375.09 799.848,1374.99 799.965,1374.89 800.083,1374.79 800.2,1374.68 800.317,1374.58 \n",
" 800.434,1374.47 800.552,1374.37 800.669,1374.27 800.786,1374.16 800.904,1374.06 801.021,1373.96 801.138,1373.85 801.255,1373.75 801.373,1373.64 801.49,1373.54 \n",
" 801.607,1373.43 801.724,1373.33 801.842,1373.22 801.959,1373.12 802.076,1373.01 802.194,1372.91 802.311,1372.8 802.428,1372.7 802.545,1372.59 802.663,1372.48 \n",
" 802.78,1372.38 802.897,1372.27 803.014,1372.17 803.132,1372.06 803.249,1371.95 803.366,1371.85 803.484,1371.74 803.601,1371.63 803.718,1371.52 803.835,1371.42 \n",
" 803.953,1371.31 804.07,1371.2 804.187,1371.09 804.304,1370.99 804.422,1370.88 804.539,1370.77 804.656,1370.66 804.774,1370.55 804.891,1370.45 805.008,1370.34 \n",
" 805.125,1370.23 805.243,1370.12 805.36,1370.01 805.477,1369.9 805.594,1369.79 805.712,1369.68 805.829,1369.57 805.946,1369.47 806.064,1369.36 806.181,1369.25 \n",
" 806.298,1369.14 806.415,1369.03 806.533,1368.92 806.65,1368.81 806.767,1368.69 806.885,1368.58 807.002,1368.47 807.119,1368.36 807.236,1368.25 807.354,1368.14 \n",
" 807.471,1368.03 807.588,1367.92 807.705,1367.81 807.823,1367.69 807.94,1367.58 808.057,1367.47 808.175,1367.36 808.292,1367.25 808.409,1367.13 808.526,1367.02 \n",
" 808.644,1366.91 808.761,1366.8 808.878,1366.68 808.995,1366.57 809.113,1366.46 809.23,1366.34 809.347,1366.23 809.465,1366.12 809.582,1366 809.699,1365.89 \n",
" 809.816,1365.78 809.934,1365.66 810.051,1365.55 810.168,1365.43 810.285,1365.32 810.403,1365.21 810.52,1365.09 810.637,1364.98 810.755,1364.86 810.872,1364.75 \n",
" 810.989,1364.63 811.106,1364.51 811.224,1364.4 811.341,1364.28 811.458,1364.17 811.575,1364.05 811.693,1363.94 811.81,1363.82 811.927,1363.7 812.045,1363.59 \n",
" 812.162,1363.47 812.279,1363.35 812.396,1363.24 812.514,1363.12 812.631,1363 812.748,1362.89 812.866,1362.77 812.983,1362.65 813.1,1362.53 813.217,1362.42 \n",
" 813.335,1362.3 813.452,1362.18 813.569,1362.06 813.686,1361.94 813.804,1361.82 813.921,1361.71 814.038,1361.59 814.156,1361.47 814.273,1361.35 814.39,1361.23 \n",
" 814.507,1361.11 814.625,1360.99 814.742,1360.87 814.859,1360.75 814.976,1360.63 815.094,1360.51 815.211,1360.39 815.328,1360.27 815.446,1360.15 815.563,1360.03 \n",
" 815.68,1359.91 815.797,1359.79 815.915,1359.67 816.032,1359.55 816.149,1359.42 816.266,1359.3 816.384,1359.18 816.501,1359.06 816.618,1358.94 816.736,1358.82 \n",
" 816.853,1358.69 816.97,1358.57 817.087,1358.45 817.205,1358.33 817.322,1358.2 817.439,1358.08 817.556,1357.96 817.674,1357.84 817.791,1357.71 817.908,1357.59 \n",
" 818.026,1357.47 818.143,1357.34 818.26,1357.22 818.377,1357.09 818.495,1356.97 818.612,1356.85 818.729,1356.72 818.846,1356.6 818.964,1356.47 819.081,1356.35 \n",
" 819.198,1356.22 819.316,1356.1 819.433,1355.97 819.55,1355.85 819.667,1355.72 819.785,1355.6 819.902,1355.47 820.019,1355.34 820.137,1355.22 820.254,1355.09 \n",
" 820.371,1354.97 820.488,1354.84 820.606,1354.71 820.723,1354.59 820.84,1354.46 820.957,1354.33 821.075,1354.2 821.192,1354.08 821.309,1353.95 821.427,1353.82 \n",
" 821.544,1353.69 821.661,1353.57 821.778,1353.44 821.896,1353.31 822.013,1353.18 822.13,1353.05 822.247,1352.92 822.365,1352.8 822.482,1352.67 822.599,1352.54 \n",
" 822.717,1352.41 822.834,1352.28 822.951,1352.15 823.068,1352.02 823.186,1351.89 823.303,1351.76 823.42,1351.63 823.537,1351.5 823.655,1351.37 823.772,1351.24 \n",
" 823.889,1351.11 824.007,1350.98 824.124,1350.85 824.241,1350.71 824.358,1350.58 824.476,1350.45 824.593,1350.32 824.71,1350.19 824.827,1350.06 824.945,1349.92 \n",
" 825.062,1349.79 825.179,1349.66 825.297,1349.53 825.414,1349.39 825.531,1349.26 825.648,1349.13 825.766,1349 825.883,1348.86 826,1348.73 826.118,1348.6 \n",
" 826.235,1348.46 826.352,1348.33 826.469,1348.19 826.587,1348.06 826.704,1347.93 826.821,1347.79 826.938,1347.66 827.056,1347.52 827.173,1347.39 827.29,1347.25 \n",
" 827.408,1347.12 827.525,1346.98 827.642,1346.85 827.759,1346.71 827.877,1346.58 827.994,1346.44 828.111,1346.3 828.228,1346.17 828.346,1346.03 828.463,1345.89 \n",
" 828.58,1345.76 828.698,1345.62 828.815,1345.48 828.932,1345.35 829.049,1345.21 829.167,1345.07 829.284,1344.93 829.401,1344.8 829.518,1344.66 829.636,1344.52 \n",
" 829.753,1344.38 829.87,1344.24 829.988,1344.11 830.105,1343.97 830.222,1343.83 830.339,1343.69 830.457,1343.55 830.574,1343.41 830.691,1343.27 830.808,1343.13 \n",
" 830.926,1342.99 831.043,1342.85 831.16,1342.71 831.278,1342.57 831.395,1342.43 831.512,1342.29 831.629,1342.15 831.747,1342.01 831.864,1341.87 831.981,1341.73 \n",
" 832.098,1341.59 832.216,1341.45 832.333,1341.3 832.45,1341.16 832.568,1341.02 832.685,1340.88 832.802,1340.74 832.919,1340.59 833.037,1340.45 833.154,1340.31 \n",
" 833.271,1340.17 833.389,1340.02 833.506,1339.88 833.623,1339.74 833.74,1339.59 833.858,1339.45 833.975,1339.31 834.092,1339.16 834.209,1339.02 834.327,1338.87 \n",
" 834.444,1338.73 834.561,1338.58 834.679,1338.44 834.796,1338.3 834.913,1338.15 835.03,1338.01 835.148,1337.86 835.265,1337.71 835.382,1337.57 835.499,1337.42 \n",
" 835.617,1337.28 835.734,1337.13 835.851,1336.98 835.969,1336.84 836.086,1336.69 836.203,1336.55 836.32,1336.4 836.438,1336.25 836.555,1336.1 836.672,1335.96 \n",
" 836.789,1335.81 836.907,1335.66 837.024,1335.51 837.141,1335.37 837.259,1335.22 837.376,1335.07 837.493,1334.92 837.61,1334.77 837.728,1334.62 837.845,1334.47 \n",
" 837.962,1334.33 838.079,1334.18 838.197,1334.03 838.314,1333.88 838.431,1333.73 838.549,1333.58 838.666,1333.43 838.783,1333.28 838.9,1333.13 839.018,1332.98 \n",
" 839.135,1332.83 839.252,1332.67 839.37,1332.52 839.487,1332.37 839.604,1332.22 839.721,1332.07 839.839,1331.92 839.956,1331.77 840.073,1331.61 840.19,1331.46 \n",