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NTT123/r-notebook.ipynb

Last active October 19, 2018 16:47
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R notebook.ipynb
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r-notebook.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "R notebook.ipynb",
"version": "0.3.2",
"provenance": [],
"collapsed_sections": [],
"include_colab_link": true
},
"kernelspec": {
"name": "python2",
"display_name": "Python 2"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"[View in Colaboratory](https://colab.research.google.com/gist/NTT123/30cff7bc5259e3ade33fd44b0adad996/r-notebook.ipynb)"
]
},
{
"metadata": {
"id": "WzpJq3ZrrDS3",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"## Setup\n",
"\n",
"Run the following commands once (~3-4 mins). It will replace your python2 jupyter kernel by R kernel.\n",
"\n",
"Then, go to menu **Runtime -> Manage Sessions -> TERMINATE**. \n",
"\n",
"Finally, **RECONNECT**."
]
},
{
"metadata": {
"id": "84XnTkx80uv0",
"colab_type": "code",
"outputId": "962320ea-25c7-4556-a91c-3ebc6c5332d8",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 204
}
},
"cell_type": "code",
"source": [
"!wget https://repo.continuum.io/miniconda/Miniconda3-latest-Linux-x86_64.sh\n",
"!chmod +x ./Miniconda3-latest-Linux-x86_64.sh\n",
"!./Miniconda3-latest-Linux-x86_64.sh -b -p /conda > /dev/null 2>&1 \n",
"!/conda/bin/conda install -c r r-rstan r-irkernel gxx_linux-64 -y -q > /dev/null 2>&1\n",
"!/conda/bin/R -e \"IRkernel::installspec(name = 'python2', displayname = 'R', user = FALSE)\" > /dev/null 2>&1\n",
"!mkdir /root/.R/\n",
"!echo \"CXX14FLAGS=-O3 -mtune=native -march=native -Wno-ignored-attributes -Wno-deprecated-declarations\" > /root/.R/Makevars\n",
"import os\n",
"os._exit(00)\n"
],
"execution_count": 0,
"outputs": [
{
"output_type": "stream",
"text": [
"--2018-10-19 16:38:03-- https://repo.continuum.io/miniconda/Miniconda3-latest-Linux-x86_64.sh\n",
"Resolving repo.continuum.io (repo.continuum.io)... 104.16.19.10, 104.16.18.10, 2400:cb00:2048:1::6810:120a, ...\n",
"Connecting to repo.continuum.io (repo.continuum.io)|104.16.19.10|:443... connected.\n",
"HTTP request sent, awaiting response... 200 OK\n",
"Length: 62574861 (60M) [application/x-sh]\n",
"Saving to: ‘Miniconda3-latest-Linux-x86_64.sh’\n",
"\n",
"Miniconda3-latest-L 100%[===================>] 59.68M 93.1MB/s in 0.6s \n",
"\n",
"2018-10-19 16:38:09 (93.1 MB/s) - ‘Miniconda3-latest-Linux-x86_64.sh’ saved [62574861/62574861]\n",
"\n"
],
"name": "stdout"
}
]
},
{
"metadata": {
"id": "8elxrVCMr_pa",
"colab_type": "text"
},
"cell_type": "markdown",
"source": [
"## R Code"
]
},
{
"metadata": {
"id": "GuQ1OjOBZP3Y",
"colab_type": "code",
"outputId": "bdcc5b86-53c0-4854-eb3a-8364b231c364",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 170
}
},
"cell_type": "code",
"source": [
"Sys.setenv(PATH= paste(\"/conda/bin\" , Sys.getenv(\"PATH\"), sep = \":\" ) )\n",
"install.packages('codetools', repos='http://cran.rstudio.com/')\n",
"options(repr.plot.width = 3,\n",
" repr.plot.height = 3)\n",
"Sys.setenv(USE_CXX14 = 1)\n",
"library(\"rstan\") # observe startup messages\n",
"options(mc.cores = parallel::detectCores())\n",
"rstan_options(auto_write = TRUE)"
],
"execution_count": 1,
"outputs": [
{
"output_type": "stream",
"text": [
"Updating HTML index of packages in '.Library'\n",
"Making 'packages.html' ... done\n",
"Loading required package: ggplot2\n",
"Loading required package: StanHeaders\n",
"rstan (Version 2.17.3, 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"
],
"name": "stderr"
}
]
},
{
"metadata": {
"id": "jLDcyeQProYg",
"colab_type": "code",
"outputId": "157f1fc8-ce0d-45b9-8270-a109011676d8",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 377
}
},
"cell_type": "code",
"source": [
"x <- seq(0, 2*pi, length.out=50)\n",
"plot(x, sin(x))"
],
"execution_count": 2,
"outputs": [
{
"output_type": "display_data",
"data": {
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1tuPRVpdouonxCOpXf1Dl2Sm7uzVcwt\nx3vLgBTRle9ROLhrITh+tFX0y8+w/94pwzh0RcY2NX/Gg2ZjZC/aHlJEa5ZW2LDUQTh5wfGj\nraKzVeaf9KV6o0RX0hElAevYzIYaVTvH4za7cFeK6HHQ3vYW3q72MNbBkULjR7Oi17ZQAxOW\nvmSEbzf5OoVWStvSp6EKY8VeT60J6hZricRz9IYgaDxh24kb+TdObJvQGII2CDhYUPxos+jR\n3jP3HssI1TTq/5E8A6TluGsNjPBzFY5Lnw+PX3ds70zvMVIvhvfn1SyNjxs2X/rtDysm0Ts0\nB0zZwm5dZCu2HNEZbLqwXtWUb6JLN/N544D6S8mtjpKD81J6d+qdMu+QnL86k+jnhrP5Y1UU\nD2lRoPnccSpQQHPJSS7AcTYz/Dk3ih99J+2VUhKNohtYgz/77pDh8ypT3F//6qaNyUqvsG4f\nVdEdgC98LZlVDdwofnQl0db1E1Ukmhg+7BbmpUzeuOlVff+qaXjIKdrwaa8WTVlEleE4fnTZ\nqaPqFvcsDDplSk4Eynl7qAw5Tx0LALz9WeSpnBmMi6GJKMv5OSO6asqX8WIYkSzuUiVi4N/c\nvFsXH151sQFvW8eqsuFP+Usv+ah/I01oxnE5mneEqH8Sc6S4gX9Th6VmalV2J8Ay/+4k3JS9\n8IfdfEcseT2MkaPDYiTigIgDRQ/8Fzq10E0wxTU2spl1gfJ3iUZFm2dCZarYW+1SRb+eJuJA\n0QP/Vc2YWPPknPtNHY0diOe2eiebSX7ZnEgVfT958NenzplxfKDogf+q5lZMq525uUtCfbqm\nO7vUi4tvNJb5a8samxOpom2eUeP4QNED/1XOHy9pTKMH49OTlHyxUp1gWw1L5sO65kTyraxh\nqVYcHyh64B+BggzNVlNqubslG0eZa2xmShL7OZg9Q9ED/xjETmXTifGyFmtoOM6c3ghhg89K\nEX3d2HC4XobjA0UP/CPwpzWw1X8ZOR9VvndyW8WTR0jhd43bsmPCUkRDsshztMiBfxSugOUq\nLmdbuni4Mjm9lwb0auUwS1dIiugBxuvHgDKEHSx84B+Hx9qv2Mw2b/lGlqaHmO6eFo3RrCvt\nCHjGqqyqpO8z5kHSki4CfykCeOBtmWrcsexep3TRpt/B45/kndSNKfq0/5AcQnY1VCdOlmuW\nzj6lZR3SkrJVBVJFF6f9lZCL0QAd5FSDKZpkN4NIP/BNndpJOV+eEr/ws2TW1yp9T6roeTCR\nkB7MmDSFnA1+VNHEcGS0OtP0F7lFvVWWArMZy3V1dpvS96SKbtaPkKuMsbOS0kJi7WzBFU1I\nE8vc61fb8O8nkJJItrz7UXNL35MqWr+SkNXwLSHLa3DuLx5k0betUw++Z2SIiVe0skco02o/\nIWcTG5SFhpIq2tcoepCPsbmW6SO9iqUgiy4NhXccciUXdj8x8NW1QzUQVge62NzgkHzqGExu\n6E0rQUY2klzFMpBF52ssoU636KWPS49oYBrkeDiNmXXc9m2pov8J7WvBPkI+1LwusYK2YJ+j\ne3c3t06Ln+zvaE+H3FFbpsn1G1jufami84fr/E1zHcNj5ZxYhS36lN+Qa+T+KC+AOjMlLsXf\no7KMQ6+qX+59uXqGB2SNnYMtmhyOhdpqiNx8ZEVEgrSxpZ3eloxNG9oE7YKzGH5ODssynT9y\nar8lqaAz1hlsUxPLvU9FWygK+JjNLIuUUszDbyMSzD35nKDMchuoaAu/gyVUwyEpn/1piKY+\nA/EX7n1Rv0NhuS1UtIWr1nHpg+B84NLtqrmPyMFYYECTVuF/QEVbKA5ey2YWOT9f2lCPDRt3\nodYrlZYoUNFW0qNuGFVt6KoM6utsUM6j1hjg/2hVaZv7iHYU1riqedCu9rv7O2t0TVakaEY7\nN7q+y9q0+yS00jb3Ee0oUHeVkz+7oQKiM4zXsAM+q50q4QfGcsZY3rDSNvcRbYsrTh1GDLXe\nYTPTmztzeO567aDvzIMlnSuHjaOibbhmnV26n3Fijfj7+sAolbrZSWKY4VU5sg0VbcNvYInR\ncNiJU9dG1fLi4hHKUJ+hjfztLAahom3I17GGbqUHiB4iK6ljjnWUNcm38dv25hJR0bYMaW88\nZZzrBoxC0U/k01qOWhfgvmN/MQ8VbcuVWkn7T4XEN47JyWpbX9zNlq+1lszmILvbqehyXH6W\nYUAx8CYhD5uOF3XkPjjIjhRnVm7amaCiK3BDvZT97DU1RRx1uhsD4DPxkbGJmDDa7h5UdAVK\nH2ghZnDplxq9fsjwfqNuUmHBeL39ZZFUdAWuWB5Le3YOI2CxiIXEPsZ+yjRFM22L8NC99neh\noitgqL3E+Hr0CfBSQleBa3Yvsw87Ojk/Lux9rvhuVHRFMgKPkVP+Azbo1h3vGiFskeN3Ksss\nhc+COfehoitSPFiXGtt0sGoiIY9bCoq3dGwkpGSaJ0J/XJtzJyq6Mpv7MPUGfmPKfVB5uLMS\nhilMvCKpbuDXxvywZzl3wxYtOgisK7CGWSrcKKAei/XfkNRG16bofiW7VNwPd8YVLToIrGu4\nAr8aX3MGagC8xzqIXloUnElIXtuabzbrMFQ1i3s/VNGi14K7CEPkAkKuRbbdOaL1p41a8Vcl\n2zwvsmBRkl7Vly8KIqpot1sLzsVSvx/JkDb529XbSW5dvgcXFCyKg6hnzcuNtvEHLEEV7XZr\nwbkwjFE/p3rxGaVpSfVSnrvi99qHjoZFKSrTze/Ff+EtElW0+60F5+TbF6Bt2kFSsiY5FHp/\nybXXqAY3DNHTyG71DlIYO4m3QFTR7rgWnIsLprstBb38JryheFnDMZB3T7uRkK2qhQUjk2/0\nDudfD0rXgnNQFLSGkBnh58j0lmS/zl6MypspvgD13i76uIZ/A5W6+Sn+8lBFu+NacE6mRVwu\nCvo3ydb/+9YHrWt/Umnq0ZXIVrOYg4uDny3O2/aiLsvRUgHcdrQbrgXnJL9bYBqsmKAbvtan\nVmtFQHiFJyneSoy7ncMcJmf9VxEyy3FkBPQuuLutBeemOLMVBHfbsEO1tCSLyUvT7bCZHnoi\nEYBRpyT1KCFT25NrIY7j7tOxDh7uqb8lpJmxNZFZp7cCwGsM20ssyJqp67yWufVVkyYByVkb\n/TZFJTqeBkJF89EvqegqnCB3I3067V0TMM5H07Dn6NTeASpvHTSDRyQ3YmJ34xfg85qA8Nbu\nEwTWFncRfbFmlzVwaVesX4dCsgf8RgY2Zpgohd6fOXzpKeYTQubFkoeDWwsKP+E+QWBtcRfR\n5LeeDIBqsNp4JeyjuEAGM5t2M08XvQQ/k4KAkDyy04cc8V4nqCRXiXYcBNZNuFdvWP5RuEMK\nVG2Ioaai5HdoTY7A84RkqGOW/d3vTf1QYVN83egc/fuFUua6j2hjz2/lCbj+eDh8T86BlhwA\nPcn38jMFtpsSwyjiVwucSu0y0bkV7zGfZ2ziM4GcgaQkskpXRx0XEgj3yE/QjpwElYG8ABfJ\nxmDypWqn4FJcJnpKpVJyyn7RnwHao5UEcH1VvO/iy8r/ks3wDin2DSXkPa3/+Cda9FeKeIaj\nG4m24Qe3Em3uJaa3jB2pCZxM7gRovi9JSF3dBKIHiXlkKBUtiOJ/dQlUhGZsVY1sGpemCNcO\nba4T1tgoBVX0EzaEeZRoE792BRWAtmMbrxoJf50j9untqKIVCm0pSr5SDkE15BCe6Cm+ZU0N\n3lMHOXrYTHr4x3ykq3k3Z0Am3+Y1MIv3cL+xvJvrD+Dd3K7P4fI4EevNadGFLeNLR8D4RVtY\nyR/WpnTyt30cPAUrH/ijuTt4vmtb/thtA2R4qJzzF8NTusnWLBXtGAmtjrzSWJ37hMTJo6KR\noKKRoKIlsSBB6J5UtCRGCS6AipYEFS0QKtoEFV3K/7zou1eE7rkmlnfzHl/ezRcY3lXGhcps\n3sPr8D+YJZH/GYgv8U1LFghe866A/ysxOFie5uABfQ42X+IPTpnDfxMoV4YH9+GJ/h+HikaC\nikaCikaCikaCikaCikaCikaCikaCikaCikaCikaCikaCikaCikaCikYCS/TdCXXV4ancUW8L\npyqe4D76zqRITVQfzrtVF0ZGa4L7/B/f578GqRxb1lomiP6d69BdHfX+nffyFS4EJNEFreD5\nf6So63HFBDrVypdH9O0o6DljiMrruP3NZ4I0L84aolb/yP35h5Scot+FQVNM7OHYvgbqT58c\nohE/I7o8SKIXwdvG10+AI+BIni7+nJZb9FhYZnzdAj3sb36KMa2L+By4n6tX1KI5p+hZ/JOd\nb+pbPiDknD6NbycBIIlu4WsO7hETan+B2e1JhYRH9KtdTTOEDbq69jdPNz+apljN/dSE+cxX\nnKInAG/c0gVgCoJHJD/BG0d0vpJdxDwcuG+i8ohmeazmnX52FZ7j2nReN+Yup+hhcKv4yi3O\nYpN1heSxgzBuQsARfRaGm9NZwB3lzKHoJeYTCAcP98b5cp4Cuob/yS36OXgzAKDheo7NdZsc\nSWCg/loHlXMIjuhsGGtOFwD3/ApHovdpOnDPGfAHeJHzj2UtbCbcojtB9LyP3vCDlfY3+9YN\nn7R5SSRwfRFCwRI9zpxmAPdT0R2I3qBtdZt769RXnlR04DB9M7AX4RH93WZTEO+T2kD7i8e0\n8KHxNUcfJijuATc4os/BMHM63fTUcQ54RRtmwjMOHqey1yfOfiykgfrLfKIt9IWDdt8PUpoD\neLwAHG1LoeCILlB1MqeDrE+hsQOfaEMK/M3hL2ow2A3utQtmXLly5SQMusJ7SRsF9hvSTyjN\na6LSnFhaWA6k5l1bb9PvoqQWT8hHPtET4J/cG6/GvWRO+9lvEE8qXRxoN2jc/RVseLYOHA2i\ncfCTKXkaHEUVdgCS6FVgeszuv2A29y48orcA7yzDCI3Jxa96vd2nU5/aYWITPL3jtL3NJbX1\npve3QUv7hR9muhi7AIcUcXw1EACS6OJE6DN7IBPLEbBon7ELrAwzvtifMlof/mbuJU+x34Pf\nqlQPfHO4D2Ta3crCfY7ezvikzujL+HFNR30VWsweqdPs5SlcCFiDSvcn11XXHsvVbphn/eu2\n30kr/eO/aP/wn54LUdbo9gXf5/NcDH/sXkNVayhn99CwsrmXfw/7V0oR0GFSJKhoJKhoJKho\nJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKho\nJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKhoJKqL6N3MIFPS\nXbHf1TXhoLqIJqNNESo2w2uurgcX1Ub0/agGjx/UaehGzyAvT7URTfYwsyYreOJXuZjqI5qk\nadWvu7oO3FQj0dkAv7i6DtxUH9El7WsGJUoO5lVlVB/RC2DTWljs6lpwUm1E/6rrQUhn77Ou\nrgcX1UV0SXufS0bb2gT7cZVcT3URvRDMT8qbA++4uiYcVBfRbg8VjQQVjQQVjQQVjQQVjQQV\njQQVjQQVjQQVjQQVjQQVjQQVjQQVjQQVjQQVjQQVjQQVjQQVjQQVjQQVjQQVjQQVjQQVjQQV\njQQVjQQVjQQVjQQVjQQVjQQVjcT/Ax1yi047yrcEAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "345En8SKt-8x",
"colab_type": "code",
"outputId": "92eb8516-4aa4-45ea-9e3b-7bac0639a910",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 221
}
},
"cell_type": "code",
"source": [
"stanmodelcode <- \"\n",
"data {\n",
" int<lower=0> N; \n",
" real y[N];\n",
"}\n",
"\n",
"parameters {\n",
" real mu; \n",
"\n",
"}\n",
"\n",
"model {\n",
" target += normal_lpdf(mu | 0, 10);\n",
" target += normal_lpdf(y | mu, 1);\n",
"}\"\n",
"\n",
"y <- rnorm(20)\n",
"dat <- list(N = 20, y = y);\n",
"\n",
"fit <- stan(model_code = stanmodelcode, model_name = \"example\",\n",
" data = dat, iter = 2012, chains = 8, sample_file = 'norm.csv',\n",
" verbose = FALSE,\n",
" refresh = -1)\n",
"\n",
"print(fit)"
],
"execution_count": 3,
"outputs": [
{
"output_type": "stream",
"text": [
"Inference for Stan model: example.\n",
"8 chains, each with iter=2012; warmup=1006; thin=1; \n",
"post-warmup draws per chain=1006, total post-warmup draws=8048.\n",
"\n",
" mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat\n",
"mu 0.23 0.00 0.22 -0.21 0.08 0.22 0.38 0.67 3076 1\n",
"lp__ -30.69 0.01 0.70 -32.69 -30.83 -30.42 -30.24 -30.19 3098 1\n",
"\n",
"Samples were drawn using NUTS(diag_e) at Fri Oct 19 16:45:46 2018.\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"
],
"name": "stdout"
}
]
},
{
"metadata": {
"id": "GKu9Y8v0iMhG",
"colab_type": "code",
"outputId": "03d54086-9940-4b58-8224-e543f3f96e00",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 411
}
},
"cell_type": "code",
"source": [
"plot(fit)"
],
"execution_count": 4,
"outputs": [
{
"output_type": "stream",
"text": [
"ci_level: 0.8 (80% intervals)\n",
"outer_level: 0.95 (95% intervals)\n"
],
"name": "stderr"
},
{
"output_type": "display_data",
"data": {},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
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"text/plain": [
"plot without title"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "LaY0bTArk6yo",
"colab_type": "code",
"outputId": "c283f360-0ba9-4df0-b7d9-eed9093560c2",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 71
}
},
"cell_type": "code",
"source": [
"y <- as.matrix(read.table('https://raw.github.com/wiki/stan-dev/rstan/rats.txt', header = TRUE))\n",
"x <- c(8, 15, 22, 29, 36)\n",
"xbar <- mean(x)\n",
"N <- nrow(y)\n",
"T <- ncol(y)\n",
"rats_fit <- stan(file = 'https://raw.githubusercontent.com/stan-dev/example-models/master/bugs_examples/vol1/rats/rats.stan')\n"
],
"execution_count": 5,
"outputs": [
{
"output_type": "stream",
"text": [
"Warning message in normalizePath(file):\n",
"“path[1]=\"https://raw.githubusercontent.com/stan-dev/example-models/master/bugs_examples/vol1/rats/rats.stan\": No such file or directory”"
],
"name": "stderr"
}
]
},
{
"metadata": {
"id": "_FDcLeSQk7v4",
"colab_type": "code",
"outputId": "16ed3a7f-0a0b-4f5e-cc97-fbee89f6f0d9",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 2584
}
},
"cell_type": "code",
"source": [
"rats_fit"
],
"execution_count": 6,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"Inference for Stan model: rats.\n",
"4 chains, each with iter=2000; warmup=1000; thin=1; \n",
"post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
"\n",
" mean se_mean sd 2.5% 25% 50% 75% 97.5%\n",
"alpha[1] 239.93 0.04 2.67 234.63 238.15 239.92 241.76 245.17\n",
"alpha[2] 247.84 0.04 2.67 242.54 246.00 247.83 249.66 253.02\n",
"alpha[3] 252.39 0.04 2.69 247.00 250.65 252.41 254.12 257.78\n",
"alpha[4] 232.55 0.04 2.63 227.47 230.76 232.51 234.40 237.62\n",
"alpha[5] 231.61 0.04 2.70 226.33 229.83 231.57 233.38 236.93\n",
"alpha[6] 249.74 0.04 2.80 244.32 247.84 249.75 251.68 255.27\n",
"alpha[7] 228.66 0.04 2.74 223.31 226.85 228.61 230.48 234.10\n",
"alpha[8] 248.41 0.04 2.72 243.05 246.56 248.47 250.27 253.61\n",
"alpha[9] 283.29 0.04 2.64 278.10 281.58 283.30 285.05 288.43\n",
"alpha[10] 219.24 0.04 2.66 214.05 217.48 219.21 221.06 224.39\n",
"alpha[11] 258.20 0.04 2.82 252.58 256.35 258.24 260.13 263.74\n",
"alpha[12] 228.19 0.04 2.70 222.95 226.37 228.18 230.04 233.44\n",
"alpha[13] 242.43 0.04 2.78 236.91 240.63 242.49 244.34 247.79\n",
"alpha[14] 268.25 0.04 2.65 262.93 266.53 268.26 269.98 273.62\n",
"alpha[15] 242.78 0.04 2.74 237.45 240.96 242.83 244.53 248.07\n",
"alpha[16] 245.33 0.04 2.64 240.13 243.56 245.35 247.10 250.39\n",
"alpha[17] 232.17 0.04 2.72 226.72 230.36 232.18 234.02 237.57\n",
"alpha[18] 240.51 0.04 2.69 235.19 238.72 240.53 242.33 245.81\n",
"alpha[19] 253.76 0.04 2.66 248.60 251.89 253.72 255.60 258.86\n",
"alpha[20] 241.68 0.04 2.69 236.25 239.89 241.69 243.43 246.98\n",
"alpha[21] 248.59 0.04 2.65 243.33 246.85 248.59 250.39 253.73\n",
"alpha[22] 225.18 0.04 2.61 220.13 223.44 225.22 226.92 230.24\n",
"alpha[23] 228.53 0.04 2.73 223.09 226.74 228.53 230.29 233.94\n",
"alpha[24] 245.14 0.04 2.57 240.06 243.35 245.16 246.85 250.26\n",
"alpha[25] 234.46 0.04 2.68 229.33 232.60 234.47 236.29 239.68\n",
"alpha[26] 253.97 0.04 2.69 248.68 252.17 253.97 255.77 259.19\n",
"alpha[27] 254.35 0.04 2.69 249.03 252.58 254.38 256.21 259.53\n",
"alpha[28] 242.97 0.04 2.71 237.72 241.16 242.96 244.79 248.18\n",
"alpha[29] 217.93 0.04 2.65 212.69 216.18 217.92 219.78 222.99\n",
"alpha[30] 241.47 0.04 2.68 236.06 239.68 241.46 243.24 246.65\n",
"beta[1] 6.06 0.00 0.25 5.58 5.90 6.06 6.23 6.55\n",
"beta[2] 7.06 0.00 0.26 6.55 6.88 7.05 7.22 7.56\n",
"beta[3] 6.48 0.00 0.25 5.98 6.32 6.48 6.65 6.98\n",
"beta[4] 5.34 0.00 0.26 4.85 5.17 5.35 5.51 5.85\n",
"beta[5] 6.56 0.00 0.24 6.10 6.40 6.57 6.73 7.04\n",
"beta[6] 6.17 0.00 0.24 5.70 6.01 6.17 6.33 6.62\n",
"beta[7] 5.97 0.00 0.24 5.51 5.81 5.97 6.14 6.44\n",
"beta[8] 6.42 0.00 0.24 5.94 6.26 6.42 6.58 6.90\n",
"beta[9] 7.05 0.00 0.26 6.54 6.88 7.06 7.23 7.54\n",
"beta[10] 5.84 0.00 0.25 5.34 5.67 5.84 6.01 6.34\n",
"beta[11] 6.80 0.00 0.25 6.31 6.63 6.80 6.97 7.30\n",
"beta[12] 6.12 0.00 0.24 5.65 5.95 6.12 6.28 6.59\n",
"beta[13] 6.16 0.00 0.25 5.67 5.99 6.16 6.33 6.66\n",
"beta[14] 6.69 0.00 0.25 6.20 6.53 6.68 6.86 7.17\n",
"beta[15] 5.42 0.00 0.26 4.92 5.24 5.41 5.59 5.92\n",
"beta[16] 5.92 0.00 0.25 5.44 5.76 5.92 6.09 6.41\n",
"beta[17] 6.28 0.00 0.24 5.82 6.11 6.28 6.45 6.74\n",
"beta[18] 5.84 0.00 0.24 5.37 5.68 5.85 6.00 6.31\n",
"beta[19] 6.40 0.00 0.25 5.93 6.24 6.41 6.57 6.88\n",
"beta[20] 6.06 0.00 0.24 5.58 5.89 6.06 6.23 6.54\n",
"beta[21] 6.40 0.00 0.24 5.93 6.24 6.40 6.57 6.88\n",
"beta[22] 5.86 0.00 0.24 5.39 5.70 5.86 6.03 6.33\n",
"beta[23] 5.75 0.00 0.24 5.28 5.58 5.75 5.91 6.22\n",
"beta[24] 5.89 0.00 0.25 5.39 5.73 5.89 6.06 6.38\n",
"beta[25] 6.91 0.00 0.25 6.42 6.75 6.91 7.07 7.40\n",
"beta[26] 6.54 0.00 0.24 6.08 6.38 6.54 6.71 7.01\n",
"beta[27] 5.90 0.00 0.24 5.45 5.75 5.90 6.07 6.37\n",
"beta[28] 5.84 0.00 0.24 5.37 5.67 5.84 6.00 6.31\n",
"beta[29] 5.67 0.00 0.24 5.18 5.51 5.67 5.83 6.14\n",
"beta[30] 6.13 0.00 0.24 5.66 5.97 6.13 6.30 6.60\n",
"mu_alpha 242.50 0.04 2.69 237.07 240.75 242.54 244.26 247.64\n",
"mu_beta 6.18 0.00 0.11 5.98 6.11 6.19 6.26 6.40\n",
"sigmasq_y 37.30 0.12 5.77 27.82 33.27 36.68 40.78 50.39\n",
"sigmasq_alpha 217.53 1.00 63.00 126.36 173.10 206.88 250.35 368.64\n",
"sigmasq_beta 0.28 0.00 0.10 0.13 0.21 0.26 0.33 0.53\n",
"sigma_y 6.09 0.01 0.46 5.27 5.77 6.06 6.39 7.10\n",
"sigma_alpha 14.61 0.03 2.05 11.24 13.16 14.38 15.82 19.20\n",
"sigma_beta 0.52 0.00 0.09 0.36 0.45 0.51 0.57 0.73\n",
"alpha0 106.45 0.06 3.62 99.51 103.99 106.45 108.86 113.59\n",
"lp__ -438.52 0.20 7.11 -454.14 -442.90 -438.12 -433.51 -425.64\n",
" n_eff Rhat\n",
"alpha[1] 4000 1\n",
"alpha[2] 4000 1\n",
"alpha[3] 4000 1\n",
"alpha[4] 4000 1\n",
"alpha[5] 4000 1\n",
"alpha[6] 4000 1\n",
"alpha[7] 4000 1\n",
"alpha[8] 4000 1\n",
"alpha[9] 4000 1\n",
"alpha[10] 4000 1\n",
"alpha[11] 4000 1\n",
"alpha[12] 4000 1\n",
"alpha[13] 4000 1\n",
"alpha[14] 4000 1\n",
"alpha[15] 4000 1\n",
"alpha[16] 4000 1\n",
"alpha[17] 4000 1\n",
"alpha[18] 4000 1\n",
"alpha[19] 4000 1\n",
"alpha[20] 4000 1\n",
"alpha[21] 4000 1\n",
"alpha[22] 4000 1\n",
"alpha[23] 4000 1\n",
"alpha[24] 4000 1\n",
"alpha[25] 4000 1\n",
"alpha[26] 4000 1\n",
"alpha[27] 4000 1\n",
"alpha[28] 4000 1\n",
"alpha[29] 4000 1\n",
"alpha[30] 4000 1\n",
"beta[1] 4000 1\n",
"beta[2] 4000 1\n",
"beta[3] 4000 1\n",
"beta[4] 4000 1\n",
"beta[5] 4000 1\n",
"beta[6] 4000 1\n",
"beta[7] 4000 1\n",
"beta[8] 4000 1\n",
"beta[9] 4000 1\n",
"beta[10] 4000 1\n",
"beta[11] 4000 1\n",
"beta[12] 4000 1\n",
"beta[13] 4000 1\n",
"beta[14] 4000 1\n",
"beta[15] 4000 1\n",
"beta[16] 4000 1\n",
"beta[17] 4000 1\n",
"beta[18] 4000 1\n",
"beta[19] 4000 1\n",
"beta[20] 4000 1\n",
"beta[21] 4000 1\n",
"beta[22] 4000 1\n",
"beta[23] 4000 1\n",
"beta[24] 4000 1\n",
"beta[25] 4000 1\n",
"beta[26] 4000 1\n",
"beta[27] 4000 1\n",
"beta[28] 4000 1\n",
"beta[29] 4000 1\n",
"beta[30] 4000 1\n",
"mu_alpha 4000 1\n",
"mu_beta 4000 1\n",
"sigmasq_y 2444 1\n",
"sigmasq_alpha 4000 1\n",
"sigmasq_beta 4000 1\n",
"sigma_y 2420 1\n",
"sigma_alpha 4000 1\n",
"sigma_beta 4000 1\n",
"alpha0 4000 1\n",
"lp__ 1279 1\n",
"\n",
"Samples were drawn using NUTS(diag_e) at Fri Oct 19 16:46:50 2018.\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)."
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "UTE9jjocnOL1",
"colab_type": "code",
"outputId": "dd32082c-3ed5-4bb1-8c96-27c54ed396b0",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 428
}
},
"cell_type": "code",
"source": [
"plot(rats_fit)"
],
"execution_count": 7,
"outputs": [
{
"output_type": "stream",
"text": [
"'pars' not specified. Showing first 10 parameters by default.\n",
"ci_level: 0.8 (80% intervals)\n",
"outer_level: 0.95 (95% intervals)\n"
],
"name": "stderr"
},
{
"output_type": "display_data",
"data": {},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
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GHjQAhRhtmxWmB2rLGRFAhf7z4qPHul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\n1kYTy5iITwQAAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"metadata": {
"id": "RTwsDP44nV7m",
"colab_type": "code",
"colab": {}
},
"cell_type": "code",
"source": [
""
],
"execution_count": 0,
"outputs": []
}
]
}
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