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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Loading required package: ggplot2\n",
"Loading required package: StanHeaders\n",
"rstan (Version 2.18.2, GitRev: 2e1f913d3ca3)\n",
"For execution on a local, multicore CPU with excess RAM we recommend calling\n",
"options(mc.cores = parallel::detectCores()).\n",
"To avoid recompilation of unchanged Stan programs, we recommend calling\n",
"rstan_options(auto_write = TRUE)\n"
]
}
],
"source": [
"library(tictoc)\n",
"library(rstan)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"stancode <- '\n",
"data {\n",
" int<lower=1> N;\n",
" real x[N];\n",
" vector[N] y;\n",
"}\n",
"transformed data {\n",
" vector[N] mu = rep_vector(0, N);\n",
"}\n",
"parameters {\n",
" real<lower=0> length;\n",
" real<lower=0> alpha;\n",
" real<lower=0> noise;\n",
"}\n",
"model {\n",
" matrix[N, N] L_K;\n",
" matrix[N, N] K = cov_exp_quad(x, alpha, length);\n",
"\n",
" // diagonal elements\n",
" for (n in 1:N)\n",
" K[n, n] = K[n, n] + noise;\n",
"\n",
" L_K = cholesky_decompose(K);\n",
"\n",
" alpha ~ lognormal(0, 10); // square root of variance\n",
" length ~ lognormal(0, 10);\n",
" noise ~ lognormal(0, 10);\n",
"\n",
" y ~ multi_normal_cholesky(mu, L_K);\n",
"}\n",
"'"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"N <- 400\n",
"x <- c( -1. , -0.99498747, -0.98997494, -0.98496241, -0.97994987,\n",
" -0.97493734, -0.96992481, -0.96491228, -0.95989975, -0.95488722,\n",
" -0.94987469, -0.94486216, -0.93984962, -0.93483709, -0.92982456,\n",
" -0.92481203, -0.9197995 , -0.91478697, -0.90977444, -0.9047619 ,\n",
" -0.89974937, -0.89473684, -0.88972431, -0.88471178, -0.87969925,\n",
" -0.87468672, -0.86967419, -0.86466165, -0.85964912, -0.85463659,\n",
" -0.84962406, -0.84461153, -0.839599 , -0.83458647, -0.82957393,\n",
" -0.8245614 , -0.81954887, -0.81453634, -0.80952381, -0.80451128,\n",
" -0.79949875, -0.79448622, -0.78947368, -0.78446115, -0.77944862,\n",
" -0.77443609, -0.76942356, -0.76441103, -0.7593985 , -0.75438596,\n",
" -0.74937343, -0.7443609 , -0.73934837, -0.73433584, -0.72932331,\n",
" -0.72431078, -0.71929825, -0.71428571, -0.70927318, -0.70426065,\n",
" -0.69924812, -0.69423559, -0.68922306, -0.68421053, -0.67919799,\n",
" -0.67418546, -0.66917293, -0.6641604 , -0.65914787, -0.65413534,\n",
" -0.64912281, -0.64411028, -0.63909774, -0.63408521, -0.62907268,\n",
" -0.62406015, -0.61904762, -0.61403509, -0.60902256, -0.60401003,\n",
" -0.59899749, -0.59398496, -0.58897243, -0.5839599 , -0.57894737,\n",
" -0.57393484, -0.56892231, -0.56390977, -0.55889724, -0.55388471,\n",
" -0.54887218, -0.54385965, -0.53884712, -0.53383459, -0.52882206,\n",
" -0.52380952, -0.51879699, -0.51378446, -0.50877193, -0.5037594 ,\n",
" -0.49874687, -0.49373434, -0.4887218 , -0.48370927, -0.47869674,\n",
" -0.47368421, -0.46867168, -0.46365915, -0.45864662, -0.45363409,\n",
" -0.44862155, -0.44360902, -0.43859649, -0.43358396, -0.42857143,\n",
" -0.4235589 , -0.41854637, -0.41353383, -0.4085213 , -0.40350877,\n",
" -0.39849624, -0.39348371, -0.38847118, -0.38345865, -0.37844612,\n",
" -0.37343358, -0.36842105, -0.36340852, -0.35839599, -0.35338346,\n",
" -0.34837093, -0.3433584 , -0.33834586, -0.33333333, -0.3283208 ,\n",
" -0.32330827, -0.31829574, -0.31328321, -0.30827068, -0.30325815,\n",
" -0.29824561, -0.29323308, -0.28822055, -0.28320802, -0.27819549,\n",
" -0.27318296, -0.26817043, -0.26315789, -0.25814536, -0.25313283,\n",
" -0.2481203 , -0.24310777, -0.23809524, -0.23308271, -0.22807018,\n",
" -0.22305764, -0.21804511, -0.21303258, -0.20802005, -0.20300752,\n",
" -0.19799499, -0.19298246, -0.18796992, -0.18295739, -0.17794486,\n",
" -0.17293233, -0.1679198 , -0.16290727, -0.15789474, -0.15288221,\n",
" -0.14786967, -0.14285714, -0.13784461, -0.13283208, -0.12781955,\n",
" -0.12280702, -0.11779449, -0.11278195, -0.10776942, -0.10275689,\n",
" -0.09774436, -0.09273183, -0.0877193 , -0.08270677, -0.07769424,\n",
" -0.0726817 , -0.06766917, -0.06265664, -0.05764411, -0.05263158,\n",
" -0.04761905, -0.04260652, -0.03759398, -0.03258145, -0.02756892,\n",
" -0.02255639, -0.01754386, -0.01253133, -0.0075188 , -0.00250627,\n",
" 0.00250627, 0.0075188 , 0.01253133, 0.01754386, 0.02255639,\n",
" 0.02756892, 0.03258145, 0.03759398, 0.04260652, 0.04761905,\n",
" 0.05263158, 0.05764411, 0.06265664, 0.06766917, 0.0726817 ,\n",
" 0.07769424, 0.08270677, 0.0877193 , 0.09273183, 0.09774436,\n",
" 0.10275689, 0.10776942, 0.11278195, 0.11779449, 0.12280702,\n",
" 0.12781955, 0.13283208, 0.13784461, 0.14285714, 0.14786967,\n",
" 0.15288221, 0.15789474, 0.16290727, 0.1679198 , 0.17293233,\n",
" 0.17794486, 0.18295739, 0.18796992, 0.19298246, 0.19799499,\n",
" 0.20300752, 0.20802005, 0.21303258, 0.21804511, 0.22305764,\n",
" 0.22807018, 0.23308271, 0.23809524, 0.24310777, 0.2481203 ,\n",
" 0.25313283, 0.25814536, 0.26315789, 0.26817043, 0.27318296,\n",
" 0.27819549, 0.28320802, 0.28822055, 0.29323308, 0.29824561,\n",
" 0.30325815, 0.30827068, 0.31328321, 0.31829574, 0.32330827,\n",
" 0.3283208 , 0.33333333, 0.33834586, 0.3433584 , 0.34837093,\n",
" 0.35338346, 0.35839599, 0.36340852, 0.36842105, 0.37343358,\n",
" 0.37844612, 0.38345865, 0.38847118, 0.39348371, 0.39849624,\n",
" 0.40350877, 0.4085213 , 0.41353383, 0.41854637, 0.4235589 ,\n",
" 0.42857143, 0.43358396, 0.43859649, 0.44360902, 0.44862155,\n",
" 0.45363409, 0.45864662, 0.46365915, 0.46867168, 0.47368421,\n",
" 0.47869674, 0.48370927, 0.4887218 , 0.49373434, 0.49874687,\n",
" 0.5037594 , 0.50877193, 0.51378446, 0.51879699, 0.52380952,\n",
" 0.52882206, 0.53383459, 0.53884712, 0.54385965, 0.54887218,\n",
" 0.55388471, 0.55889724, 0.56390977, 0.56892231, 0.57393484,\n",
" 0.57894737, 0.5839599 , 0.58897243, 0.59398496, 0.59899749,\n",
" 0.60401003, 0.60902256, 0.61403509, 0.61904762, 0.62406015,\n",
" 0.62907268, 0.63408521, 0.63909774, 0.64411028, 0.64912281,\n",
" 0.65413534, 0.65914787, 0.6641604 , 0.66917293, 0.67418546,\n",
" 0.67919799, 0.68421053, 0.68922306, 0.69423559, 0.69924812,\n",
" 0.70426065, 0.70927318, 0.71428571, 0.71929825, 0.72431078,\n",
" 0.72932331, 0.73433584, 0.73934837, 0.7443609 , 0.74937343,\n",
" 0.75438596, 0.7593985 , 0.76441103, 0.76942356, 0.77443609,\n",
" 0.77944862, 0.78446115, 0.78947368, 0.79448622, 0.79949875,\n",
" 0.80451128, 0.80952381, 0.81453634, 0.81954887, 0.8245614 ,\n",
" 0.82957393, 0.83458647, 0.839599 , 0.84461153, 0.84962406,\n",
" 0.85463659, 0.85964912, 0.86466165, 0.86967419, 0.87468672,\n",
" 0.87969925, 0.88471178, 0.88972431, 0.89473684, 0.89974937,\n",
" 0.9047619 , 0.90977444, 0.91478697, 0.9197995 , 0.92481203,\n",
" 0.92982456, 0.93483709, 0.93984962, 0.94486216, 0.94987469,\n",
" 0.95488722, 0.95989975, 0.96491228, 0.96992481, 0.97493734,\n",
" 0.97994987, 0.98496241, 0.98997494, 0.99498747, 1. )\n",
"y <- c( -1.29620278e+00, -1.58648443e+00, -1.45403159e+00, -1.17279458e+00,\n",
" -1.24742830e+00, -1.85985684e+00, -1.43375599e+00, -1.66672242e+00,\n",
" -1.64948285e+00, -1.53086114e+00, -1.58201170e+00, -1.28998518e+00,\n",
" -1.43388820e+00, -1.56601584e+00, -1.48884463e+00, -1.50570905e+00,\n",
" -1.24602008e+00, -1.60856843e+00, -1.48851013e+00, -1.73515499e+00,\n",
" -2.09745121e+00, -1.39218676e+00, -1.33878314e+00, -1.68081105e+00,\n",
" -1.01772809e+00, -1.82043099e+00, -1.48620892e+00, -1.52906179e+00,\n",
" -1.14687514e+00, -1.15271306e+00, -1.43072045e+00, -1.37405932e+00,\n",
" -1.64139771e+00, -1.87104213e+00, -1.50743723e+00, -1.38937593e+00,\n",
" -1.14728653e+00, -1.14491701e+00, -1.48235786e+00, -1.45530057e+00,\n",
" -1.60908520e+00, -1.68125880e+00, -1.73483777e+00, -9.30254757e-01,\n",
" -1.45686328e+00, -1.43242824e+00, -1.60081744e+00, -1.15005338e+00,\n",
" -1.66145957e+00, -1.34751952e+00, -1.48702061e+00, -1.19885540e+00,\n",
" -1.38506794e+00, -1.52165818e+00, -1.26166701e+00, -1.15309179e+00,\n",
" -1.22256875e+00, -1.16193926e+00, -1.35649228e+00, -1.28806770e+00,\n",
" -1.34612346e+00, -1.26867187e+00, -1.35800743e+00, -1.54733396e+00,\n",
" -1.12367022e+00, -1.24031389e+00, -1.49822938e+00, -1.03336418e+00,\n",
" -1.32210517e+00, -1.10395789e+00, -9.47203457e-01, -1.06840205e+00,\n",
" -8.39138806e-01, -1.34642851e+00, -9.80801105e-01, -1.20803571e+00,\n",
" -1.23918319e+00, -1.16634548e+00, -1.09889400e+00, -1.00961328e+00,\n",
" -1.26615226e+00, -8.07362795e-01, -8.92882764e-01, -1.31937730e+00,\n",
" -6.52096331e-01, -5.54312229e-01, -7.01324224e-01, -9.87994015e-01,\n",
" -1.17288804e+00, -7.01496780e-01, -1.00981903e+00, -6.47231162e-01,\n",
" -8.59141767e-01, -6.83197558e-01, -8.09487045e-01, -7.24637508e-01,\n",
" -8.67522597e-01, -4.72641975e-01, -8.25167894e-01, -7.56876528e-01,\n",
" -4.26180691e-01, -1.12094665e+00, -1.09586525e+00, -6.00229383e-01,\n",
" -1.05831683e+00, -3.71978462e-01, -8.76906455e-01, -9.41573620e-01,\n",
" -3.52539301e-01, -4.40953135e-01, -3.48921180e-01, -5.50410628e-01,\n",
" -9.27300274e-01, -3.16598296e-01, -7.82996893e-01, -5.42530656e-01,\n",
" -5.03556550e-01, -7.36013055e-01, -5.61293960e-01, -4.86939639e-01,\n",
" -5.98459184e-01, -9.12419975e-01, -6.01128638e-01, -3.70292425e-01,\n",
" -8.03027630e-01, -6.77439690e-01, -7.32613921e-01, -2.28580877e-01,\n",
" -4.77831721e-01, -5.28630316e-01, -7.78048992e-01, -4.86400932e-01,\n",
" -7.43769526e-01, -5.83409965e-01, -7.22046077e-01, -4.29847121e-01,\n",
" -4.44970250e-01, -6.09192312e-01, -4.71129417e-01, -7.88630605e-01,\n",
" -8.68760943e-01, -4.42118943e-01, -4.94969338e-01, -3.86561006e-01,\n",
" 3.32153402e-04, -3.06261659e-01, -7.03956723e-01, -2.55758196e-01,\n",
" -7.78708279e-01, -5.86303473e-01, -4.94202554e-01, -9.99883115e-02,\n",
" -6.28365636e-01, -6.39584422e-01, -4.74585205e-01, -5.90935051e-01,\n",
" -1.94746435e-01, -6.68253601e-01, -6.76244020e-01, -5.15069187e-01,\n",
" -5.21383047e-01, 1.37212332e-02, -1.92678705e-01, -3.73295069e-01,\n",
" -6.52024209e-01, -1.94556892e-01, -5.88845372e-01, -7.00166523e-01,\n",
" -9.82241035e-02, -2.80461431e-01, -1.41643822e-01, -2.65198857e-01,\n",
" -1.40542626e-01, -4.61028367e-01, -5.36690414e-01, -1.55480370e-01,\n",
" -4.70720321e-01, -4.37930077e-01, -3.78892243e-01, -2.67743409e-01,\n",
" -3.40259761e-01, -5.54003954e-01, -3.86316448e-01, -7.21444011e-01,\n",
" -9.27750096e-02, -5.68573117e-01, -4.51263428e-01, -1.90450951e-01,\n",
" -3.53482693e-01, 1.52621374e-01, -4.54984426e-01, -1.05880812e-01,\n",
" -1.62761375e-01, -3.98487896e-01, -2.03698296e-02, -1.61378950e-01,\n",
" 5.42367361e-02, 7.59656280e-02, 3.78126711e-01, 2.08987206e-01,\n",
" -1.51289046e-01, -1.11988142e-01, 1.90605059e-01, 1.05247945e-01,\n",
" 1.13452449e-01, -3.66072267e-01, -7.70021463e-03, -1.51066601e-01,\n",
" 8.25478658e-02, 1.25176739e-02, 2.44335964e-01, 1.27842024e-01,\n",
" 2.42616594e-01, -1.71590392e-02, -1.08198635e-01, 2.12242398e-02,\n",
" 1.20028958e-01, 2.19661608e-01, 6.42370999e-01, 1.55225292e-01,\n",
" -2.97607854e-02, 1.16956837e-01, 1.05480276e-01, 3.25392842e-01,\n",
" -1.00297339e-01, 2.63279080e-01, 2.98209816e-01, 3.29441279e-01,\n",
" 1.63817316e-01, 2.57029712e-01, 1.40296342e-02, 2.31801853e-01,\n",
" 2.36360759e-01, 4.60477114e-01, 1.33885875e-01, 5.71128786e-01,\n",
" 7.42087066e-01, -1.77595075e-02, 5.41367948e-01, 6.11906409e-01,\n",
" 3.41958553e-01, 4.10363644e-01, 4.84107792e-01, 4.64492381e-01,\n",
" 4.78378445e-01, 1.97283834e-01, 8.29192102e-01, 8.29836190e-01,\n",
" 4.34401929e-01, 3.08820307e-01, 7.57879853e-01, 5.35765350e-01,\n",
" 7.08541632e-01, 6.24753296e-01, 8.61322820e-01, 8.78606915e-01,\n",
" 5.86093307e-01, 4.59507287e-01, 4.32603449e-01, 9.26390231e-01,\n",
" 5.51305950e-01, 7.16133237e-01, 7.13009775e-01, 8.47627461e-01,\n",
" 4.53931242e-01, 9.32519436e-01, 1.02151036e+00, 9.42723274e-01,\n",
" 8.71708155e-01, 9.76331532e-01, 1.05763686e+00, 3.82991612e-01,\n",
" 1.42739165e+00, 1.10193217e+00, 8.90211225e-01, 9.62098479e-01,\n",
" 1.16945362e+00, 1.05141282e+00, 6.49272680e-01, 1.55475271e+00,\n",
" 1.09556723e+00, 1.35555935e+00, 9.96689558e-01, 1.49514532e+00,\n",
" 1.23642552e+00, 1.31968403e+00, 9.72576916e-01, 1.47620368e+00,\n",
" 1.37511408e+00, 1.52040243e+00, 1.11226511e+00, 1.15583909e+00,\n",
" 1.77317393e+00, 1.05215120e+00, 1.26396155e+00, 1.55137277e+00,\n",
" 1.33535743e+00, 1.45075941e+00, 1.24646902e+00, 1.42309225e+00,\n",
" 1.06708586e+00, 1.72073638e+00, 1.34235299e+00, 1.22786462e+00,\n",
" 1.52835262e+00, 1.29017985e+00, 1.10682094e+00, 1.11047339e+00,\n",
" 1.56049860e+00, 1.38040698e+00, 1.39125919e+00, 1.65971708e+00,\n",
" 1.18441141e+00, 1.27465653e+00, 1.35354161e+00, 1.46105683e+00,\n",
" 1.43416500e+00, 1.38331473e+00, 1.43432009e+00, 1.42594492e+00,\n",
" 1.29384243e+00, 1.27423537e+00, 1.51117861e+00, 1.25742221e+00,\n",
" 1.19886529e+00, 1.38175142e+00, 1.41395390e+00, 1.93747330e+00,\n",
" 1.29070938e+00, 1.64656770e+00, 1.60070157e+00, 1.17573738e+00,\n",
" 1.59866071e+00, 1.16824937e+00, 8.42254996e-01, 1.54747844e+00,\n",
" 1.02760661e+00, 1.50158119e+00, 1.24791133e+00, 1.75077868e+00,\n",
" 1.61461127e+00, 1.27545261e+00, 1.21603596e+00, 1.09270358e+00,\n",
" 1.25172055e+00, 1.27701879e+00, 1.24861538e+00, 1.35162449e+00,\n",
" 1.43256557e+00, 1.37151599e+00, 1.11750638e+00, 9.58896697e-01,\n",
" 1.55632663e+00, 1.09659278e+00, 1.09155345e+00, 1.10660207e+00,\n",
" 8.05113196e-01, 1.08800280e+00, 1.07313013e+00, 1.29767454e+00,\n",
" 1.29951954e+00, 1.13288736e+00, 1.31908953e+00, 1.17423820e+00,\n",
" 1.08051360e+00, 1.10234380e+00, 1.00897157e+00, 9.47421432e-01,\n",
" 9.57729101e-01, 7.52938211e-01, 1.04163444e+00, 7.46482909e-01,\n",
" 1.12754726e+00, 8.71727884e-01, 9.18229997e-01, 9.96212959e-01,\n",
" 1.00988507e+00, 5.09116769e-01, 7.86774158e-01, 1.00412714e+00,\n",
" 4.23758954e-01, 8.58188510e-01, 2.63632536e-01, 5.12474358e-01,\n",
" 7.23871231e-01, 3.35404187e-01, 4.61925775e-01, 3.36566716e-01,\n",
" 9.96011138e-01, 6.53636873e-01, 7.21950591e-01, 5.30722260e-01,\n",
" 4.83037710e-01, 1.89061865e-01, 4.58322763e-01, 3.37264091e-01,\n",
" 6.70972407e-01, 7.14073479e-01, 7.66571760e-01, 6.14831567e-01)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"compiling: 37.197 sec elapsed\n"
]
}
],
"source": [
"tic('compiling')\n",
"mod <- stan_model(model_code = stancode)\n",
"toc()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"SAMPLING FOR MODEL '967ef64942372780f885f69caed4e508' NOW (CHAIN 1).\n",
"Chain 1: \n",
"Chain 1: Gradient evaluation took 0.022902 seconds\n",
"Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 229.02 seconds.\n",
"Chain 1: Adjust your expectations accordingly!\n",
"Chain 1: \n",
"Chain 1: \n",
"Chain 1: Iteration: 1 / 2000 [ 0%] (Warmup)\n",
"Chain 1: Iteration: 200 / 2000 [ 10%] (Warmup)\n",
"Chain 1: Iteration: 400 / 2000 [ 20%] (Warmup)\n",
"Chain 1: Iteration: 600 / 2000 [ 30%] (Warmup)\n",
"Chain 1: Iteration: 800 / 2000 [ 40%] (Warmup)\n",
"Chain 1: Iteration: 1000 / 2000 [ 50%] (Warmup)\n",
"Chain 1: Iteration: 1001 / 2000 [ 50%] (Sampling)\n",
"Chain 1: Iteration: 1200 / 2000 [ 60%] (Sampling)\n",
"Chain 1: Iteration: 1400 / 2000 [ 70%] (Sampling)\n",
"Chain 1: Iteration: 1600 / 2000 [ 80%] (Sampling)\n",
"Chain 1: Iteration: 1800 / 2000 [ 90%] (Sampling)\n",
"Chain 1: Iteration: 2000 / 2000 [100%] (Sampling)\n",
"Chain 1: \n",
"Chain 1: Elapsed Time: 162.566 seconds (Warm-up)\n",
"Chain 1: 143.71 seconds (Sampling)\n",
"Chain 1: 306.276 seconds (Total)\n",
"Chain 1: \n"
]
}
],
"source": [
"fit <- sampling(mod, data = list(N = N, x = x, y = y), chains=1)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Inference for Stan model: 967ef64942372780f885f69caed4e508.\n",
"1 chains, each with iter=2000; warmup=1000; thin=1; \n",
"post-warmup draws per chain=1000, total post-warmup draws=1000.\n",
"\n",
" mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat\n",
"length 0.41 0.00 0.07 0.29 0.36 0.41 0.46 0.56 600 1\n",
"alpha 1.04 0.02 0.42 0.54 0.77 0.94 1.20 2.15 476 1\n",
"noise 0.04 0.00 0.00 0.04 0.04 0.04 0.05 0.05 727 1\n",
"lp__ 399.96 0.06 1.24 396.56 399.45 400.35 400.86 401.25 439 1\n",
"\n",
"Samples were drawn using NUTS(diag_e) at Thu Jun 6 00:25:45 2019.\n",
"For each parameter, n_eff is a crude measure of effective sample size,\n",
"and Rhat is the potential scale reduction factor on split chains (at \n",
"convergence, Rhat=1).\n"
]
}
],
"source": [
"print(fit)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "R",
"language": "R",
"name": "ir"
},
"language_info": {
"codemirror_mode": "r",
"file_extension": ".r",
"mimetype": "text/x-r-source",
"name": "R",
"pygments_lexer": "r",
"version": "3.5.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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