2011outBreak_fixed.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "ir",
      "display_name": "R"
    },
    "language_info": {
      "name": "R"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/RX-93nu/Bert-VITS2/blob/master/2011outBreak_fixed.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "library(readxl)\n",
        "library(ggplot2)\n",
        "library(dplyr)\n",
        "library(lubridate)\n",
        "library(tidyr)\n",
        "system(\"apt install r-cran-moments\")\n",
        "library(moments)\n",
        "system(\"pip install gdown==4.6.0\")\n",
        "system(\"gdown --id 1e6jU3M8orWdjm-EP_BzqSMg0w2HGJUdB\")\n",
        "# https://docs.google.com/spreadsheets/d/1e6jU3M8orWdjm-EP_BzqSMg0w2HGJUdB/edit?usp=sharing&ouid=101312767072026756611&rtpof=true&sd=true\n",
        "# https://drive.google.com/file/d/1vGFuEfsTFP8jt4ueiu_EQ1WIM35hLpqI/view?usp=sharing\n",
        "system(\"gdown --id 1vGFuEfsTFP8jt4ueiu_EQ1WIM35hLpqI\")\n",
        "Sys.setenv(MAKEFLAGS = paste0(\"-j\",parallel::detectCores()))\n",
        "system(\"add-apt-repository ppa:marutter/rrutter4.0\")\n",
        "system(\"add-apt-repository ppa:c2d4u.team/c2d4u4.0+\")\n",
        "system(\"apt update\")\n",
        "system(\"apt install r-cran-rstan\")\n",
        "library(rstan)\n",
        "options(mc.cores = parallel::detectCores())\n",
        "rstan_options(auto_write = TRUE)\n",
        "system(\"apt install r-cran-bayesplot\")\n",
        "library(bayesplot)\n",
        "system(\"apt install r-cran-rstanarm\")\n",
        "library(\"rstanarm\")"
      ],
      "metadata": {
        "collapsed": true,
        "id": "IYr-8YEH-ifx"
      },
      "execution_count": 32,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "library(readr)\n",
        "df_collect = read_csv(\"082712B.csv\",\n",
        "    col_types = cols(Date = col_date(format = \"%Y/%m/%d\"),\n",
        "        Count = col_number()))"
      ],
      "metadata": {
        "id": "jK25kJmpJ6h-"
      },
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "options(repr.plot.width=30, repr.plot.height=6)\n",
        "df_collect |> ggplot(aes(x = Date, y = Count)) +\n",
        "  geom_col() +\n",
        "  scale_x_continuous(breaks = df_collect$Date, labels = df_collect$Date) +\n",
        "  theme(axis.text.x = element_text(angle = 45, hjust = 1)) +\n",
        "  xlab(df_collect$Date) +\n",
        "  labs(title = \"data collection\",\n",
        "       x = \"Date\",\n",
        "       y = \"case\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 377
        },
        "id": "7QHdmF98KMqw",
        "outputId": "71786f6f-4376-4cb4-91fd-e3ced92c5d0e"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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vO/ulkVB8dcH07Wp8MkP+L67Izro0Ou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\nKw3vXV2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          },
          "metadata": {
            "image/png": {
              "width": 1800,
              "height": 360
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "0PYlju88U5F7"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "stan_code = 'data {\n",
        "  int<lower=0> N;  // number of days\n",
        "  real L;          // characteristic transition time\n",
        "  array[N] int<lower=0> incidence;\n",
        "  real<lower=0> R0; // initial reproduction number\n",
        "  real<lower=0> RN; // final reproduction number\n",
        "}\n",
        "\n",
        "parameters {\n",
        "  real<lower=0> R1;\n",
        "  real t0;\n",
        "  real t1;\n",
        "  real<lower=0> base_incidence;\n",
        "}\n",
        "\n",
        "transformed parameters {\n",
        "  vector[N] R;\n",
        "  for (t in 1:N) {\n",
        "    R[t] = 0.5 * (R0 + RN + (R1 - R0) * tanh((t - t0) / L) + (RN - R1) * tanh((t - t1) / L));\n",
        "  }\n",
        "}\n",
        "\n",
        "model {\n",
        "  R1 ~ normal(N, N);\n",
        "  t0 ~ normal(N, N);\n",
        "  t1 ~ normal(N, N);\n",
        "  base_incidence ~ lognormal(log(mean(incidence)), 1);\n",
        "\n",
        "  for (n in 1:N) {\n",
        "    incidence[n] ~ poisson(base_incidence * R[n]);\n",
        "  }\n",
        "}\n",
        "\n",
        "generated quantities {\n",
        "  vector[N] R_pred;\n",
        "  vector[N] case_pred;\n",
        "\n",
        "  for (n in 1:N) {\n",
        "    R_pred[n] = R[n];\n",
        "    case_pred[n] = poisson_rng(base_incidence * R[n]);\n",
        "  }\n",
        "}\n",
        "\n",
        "'\n",
        "\n",
        "stan_data = list(\n",
        "    N = nrow(df_collect),\n",
        "    L = 3,\n",
        "    incidence = df_collect$Count,\n",
        "    R0 = 0.1,\n",
        "    RN = 2\n",
        ")\n",
        "\n",
        "mod = stan_model(model_code = stan_code, verbose = TRUE)\n",
        "fit = sampling(mod, data = stan_data, chains = 4, iter = 10000)"
      ],
      "metadata": {
        "id": "l1ZxlquAVCjo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "331f7e31-b799-4b22-df2f-35f83bd1a756"
      },
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "TRANSLATING MODEL '' FROM Stan CODE TO C++ CODE NOW.\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "recompiling to avoid crashing R session\n",
            "\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "OS: x86_64, linux-gnu; rstan: 2.32.6; Rcpp: 1.0.13; inline: 0.3.19 \n",
            " >> setting environment variables: \n",
            "PKG_LIBS =  '/usr/lib/R/site-library/rstan/lib//libStanServices.a' -L'/usr/lib/R/site-library/StanHeaders/lib/' -lStanHeaders -L'/usr/lib/R/site-library/RcppParallel/lib/' -ltbb \n",
            "PKG_CPPFLAGS =   -I\"/usr/lib/R/site-library/Rcpp/include/\"  -I\"/usr/lib/R/site-library/RcppEigen/include/\"  -I\"/usr/lib/R/site-library/RcppEigen/include/unsupported\"  -I\"/usr/lib/R/site-library/BH/include\" -I\"/usr/lib/R/site-library/StanHeaders/include/src/\"  -I\"/usr/lib/R/site-library/StanHeaders/include/\"  -I\"/usr/lib/R/site-library/RcppParallel/include/\"  -I\"/usr/lib/R/site-library/rstan/include\" -DEIGEN_NO_DEBUG  -DBOOST_DISABLE_ASSERTS  -DBOOST_PENDING_INTEGER_LOG2_HPP  -DSTAN_THREADS  -DUSE_STANC3 -DSTRICT_R_HEADERS  -DBOOST_PHOENIX_NO_VARIADIC_EXPRESSION  -D_HAS_AUTO_PTR_ETC=0  -include '/usr/lib/R/site-library/StanHeaders/include/stan/math/prim/fun/Eigen.hpp'  -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 \n",
            " >> Program source :\n",
            "\n",
            "   1 : \n",
            "   2 : // includes from the plugin\n",
            "   3 : // [[Rcpp::plugins(cpp14)]]\n",
            "   4 : \n",
            "   5 : \n",
            "   6 : // user includes\n",
            "   7 : #include <Rcpp.h>\n",
            "   8 : using namespace Rcpp;\n",
            "   9 : #ifndef MODELS_HPP\n",
            "  10 : #define MODELS_HPP\n",
            "  11 : #define STAN__SERVICES__COMMAND_HPP\n",
            "  12 : #include <rstan/rstaninc.hpp>\n",
            "  13 : #ifndef USE_STANC3\n",
            "  14 : #define USE_STANC3\n",
            "  15 : #endif\n",
            "  16 : // Code generated by stanc v2.32.2\n",
            "  17 : #include <stan/model/model_header.hpp>\n",
            "  18 : namespace model1267c115a09__namespace {\n",
            "  19 : using stan::model::model_base_crtp;\n",
            "  20 : using namespace stan::math;\n",
            "  21 : stan::math::profile_map profiles__;\n",
            "  22 : static constexpr std::array<const char*, 31> locations_array__ =\n",
            "  23 :   {\" (found before start of program)\",\n",
            "  24 :   \" (in 'anon_model', line 9, column 2 to column 19)\",\n",
            "  25 :   \" (in 'anon_model', line 10, column 2 to column 10)\",\n",
            "  26 :   \" (in 'anon_model', line 11, column 2 to column 10)\",\n",
            "  27 :   \" (in 'anon_model', line 12, column 2 to column 31)\",\n",
            "  28 :   \" (in 'anon_model', line 15, column 2 to column 14)\",\n",
            "  29 :   \" (in 'anon_model', line 30, column 2 to column 19)\",\n",
            "  30 :   \" (in 'anon_model', line 31, column 2 to column 22)\",\n",
            "  31 :   \" (in 'anon_model', line 17, column 4 to column 93)\",\n",
            "  32 :   \" (in 'anon_model', line 16, column 17 to line 18, column 3)\",\n",
            "  33 :   \" (in 'anon_model', line 16, column 2 to line 18, column 3)\",\n",
            "  34 :   \" (in 'anon_model', line 33, column 4 to column 21)\",\n",
            "  35 :   \" (in 'anon_model', line 34, column 4 to column 54)\",\n",
            "  36 :   \" (in 'anon_model', line 32, column 17 to line 35, column 3)\",\n",
            "  37 :   \" (in 'anon_model', line 32, column 2 to line 35, column 3)\",\n",
            "  38 :   \" (in 'anon_model', line 21, column 2 to column 20)\",\n",
            "  39 :   \" (in 'anon_model', line 22, column 2 to column 20)\",\n",
            "  40 :   \" (in 'anon_model', line 23, column 2 to column 20)\",\n",
            "  41 :   \" (in 'anon_model', line 24, column 2 to column 54)\",\n",
            "  42 :   \" (in 'anon_model', line 26, column 4 to column 50)\",\n",
            "  43 :   \" (in 'anon_model', line 25, column 17 to line 27, column 3)\",\n",
            "  44 :   \" (in 'anon_model', line 25, column 2 to line 27, column 3)\",\n",
            "  45 :   \" (in 'anon_model', line 2, column 2 to column 17)\",\n",
            "  46 :   \" (in 'anon_model', line 3, column 2 to column 9)\",\n",
            "  47 :   \" (in 'anon_model', line 4, column 8 to column 9)\",\n",
            "  48 :   \" (in 'anon_model', line 4, column 2 to column 34)\",\n",
            "  49 :   \" (in 'anon_model', line 5, column 2 to column 19)\",\n",
            "  50 :   \" (in 'anon_model', line 6, column 2 to column 19)\",\n",
            "  51 :   \" (in 'anon_model', line 15, column 9 to column 10)\",\n",
            "  52 :   \" (in 'anon_model', line 30, column 9 to column 10)\",\n",
            "  53 :   \" (in 'anon_model', line 31, column 9 to column 10)\"};\n",
            "  54 : class model1267c115a09_ final : public model_base_crtp<model1267c115a09_> {\n",
            "  55 : private:\n",
            "  56 :   int N;\n",
            "  57 :   double L;\n",
            "  58 :   std::vector<int> incidence;\n",
            "  59 :   double R0;\n",
            "  60 :   double RN;\n",
            "  61 : public:\n",
            "  62 :   ~model1267c115a09_() {}\n",
            "  63 :   model1267c115a09_(stan::io::var_context& context__, unsigned int\n",
            "  64 :                     random_seed__ = 0, std::ostream* pstream__ = nullptr)\n",
            "  65 :       : model_base_crtp(0) {\n",
            "  66 :     int current_statement__ = 0;\n",
            "  67 :     using local_scalar_t__ = double;\n",
            "  68 :     boost::ecuyer1988 base_rng__ =\n",
            "  69 :       stan::services::util::create_rng(random_seed__, 0);\n",
            "  70 :     // suppress unused var warning\n",
            "  71 :     (void) base_rng__;\n",
            "  72 :     static constexpr const char* function__ =\n",
            "  73 :       \"model1267c115a09__namespace::model1267c115a09_\";\n",
            "  74 :     // suppress unused var warning\n",
            "  75 :     (void) function__;\n",
            "  76 :     local_scalar_t__ DUMMY_VAR__(std::numeric_limits<double>::quiet_NaN());\n",
            "  77 :     // suppress unused var warning\n",
            "  78 :     (void) DUMMY_VAR__;\n",
            "  79 :     try {\n",
            "  80 :       int pos__ = std::numeric_limits<int>::min();\n",
            "  81 :       pos__ = 1;\n",
            "  82 :       current_statement__ = 22;\n",
            "  83 :       context__.validate_dims(\"data initialization\", \"N\", \"int\",\n",
            "  84 :         std::vector<size_t>{});\n",
            "  85 :       N = std::numeric_limits<int>::min();\n",
            "  86 :       current_statement__ = 22;\n",
            "  87 :       N = context__.vals_i(\"N\")[(1 - 1)];\n",
            "  88 :       current_statement__ = 22;\n",
            "  89 :       stan::math::check_greater_or_equal(function__, \"N\", N, 0);\n",
            "  90 :       current_statement__ = 23;\n",
            "  91 :       context__.validate_dims(\"data initialization\", \"L\", \"double\",\n",
            "  92 :         std::vector<size_t>{});\n",
            "  93 :       L = std::numeric_limits<double>::quiet_NaN();\n",
            "  94 :       current_statement__ = 23;\n",
            "  95 :       L = context__.vals_r(\"L\")[(1 - 1)];\n",
            "  96 :       current_statement__ = 24;\n",
            "  97 :       stan::math::validate_non_negative_index(\"incidence\", \"N\", N);\n",
            "  98 :       current_statement__ = 25;\n",
            "  99 :       context__.validate_dims(\"data initialization\", \"incidence\", \"int\",\n",
            " 100 :         std::vector<size_t>{static_cast<size_t>(N)});\n",
            " 101 :       incidence = std::vector<int>(N, std::numeric_limits<int>::min());\n",
            " 102 :       current_statement__ = 25;\n",
            " 103 :       incidence = context__.vals_i(\"incidence\");\n",
            " 104 :       current_statement__ = 25;\n",
            " 105 :       stan::math::check_greater_or_equal(function__, \"incidence\", incidence,\n",
            " 106 :         0);\n",
            " 107 :       current_statement__ = 26;\n",
            " 108 :       context__.validate_dims(\"data initialization\", \"R0\", \"double\",\n",
            " 109 :         std::vector<size_t>{});\n",
            " 110 :       R0 = std::numeric_limits<double>::quiet_NaN();\n",
            " 111 :       current_statement__ = 26;\n",
            " 112 :       R0 = context__.vals_r(\"R0\")[(1 - 1)];\n",
            " 113 :       current_statement__ = 26;\n",
            " 114 :       stan::math::check_greater_or_equal(function__, \"R0\", R0, 0);\n",
            " 115 :       current_statement__ = 27;\n",
            " 116 :       context__.validate_dims(\"data initialization\", \"RN\", \"double\",\n",
            " 117 :         std::vector<size_t>{});\n",
            " 118 :       RN = std::numeric_limits<double>::quiet_NaN();\n",
            " 119 :       current_statement__ = 27;\n",
            " 120 :       RN = context__.vals_r(\"RN\")[(1 - 1)];\n",
            " 121 :       current_statement__ = 27;\n",
            " 122 :       stan::math::check_greater_or_equal(function__, \"RN\", RN, 0);\n",
            " 123 :       current_statement__ = 28;\n",
            " 124 :       stan::math::validate_non_negative_index(\"R\", \"N\", N);\n",
            " 125 :       current_statement__ = 29;\n",
            " 126 :       stan::math::validate_non_negative_index(\"R_pred\", \"N\", N);\n",
            " 127 :       current_statement__ = 30;\n",
            " 128 :       stan::math::validate_non_negative_index(\"case_pred\", \"N\", N);\n",
            " 129 :     } catch (const std::exception& e) {\n",
            " 130 :       stan::lang::rethrow_located(e, locations_array__[current_statement__]);\n",
            " 131 :     }\n",
            " 132 :     num_params_r__ = 1 + 1 + 1 + 1;\n",
            " 133 :   }\n",
            " 134 :   inline std::string model_name() const final {\n",
            " 135 :     return \"model1267c115a09_\";\n",
            " 136 :   }\n",
            " 137 :   inline std::vector<std::string> model_compile_info() const noexcept {\n",
            " 138 :     return std::vector<std::string>{\"stanc_version = stanc3 v2.32.2\",\n",
            " 139 :              \"stancflags = --\"};\n",
            " 140 :   }\n",
            " 141 :   template <bool propto__, bool jacobian__, typename VecR, typename VecI,\n",
            " 142 :             stan::require_vector_like_t<VecR>* = nullptr,\n",
            " 143 :             stan::require_vector_like_vt<std::is_integral, VecI>* = nullptr>\n",
            " 144 :   inline stan::scalar_type_t<VecR>\n",
            " 145 :   log_prob_impl(VecR& params_r__, VecI& params_i__, std::ostream*\n",
            " 146 :                 pstream__ = nullptr) const {\n",
            " 147 :     using T__ = stan::scalar_type_t<VecR>;\n",
            " 148 :     using local_scalar_t__ = T__;\n",
            " 149 :     T__ lp__(0.0);\n",
            " 150 :     stan::math::accumulator<T__> lp_accum__;\n",
            " 151 :     stan::io::deserializer<local_scalar_t__> in__(params_r__, params_i__);\n",
            " 152 :     int current_statement__ = 0;\n",
            " 153 :     local_scalar_t__ DUMMY_VAR__(std::numeric_limits<double>::quiet_NaN());\n",
            " 154 :     // suppress unused var warning\n",
            " 155 :     (void) DUMMY_VAR__;\n",
            " 156 :     static constexpr const char* function__ =\n",
            " 157 :       \"model1267c115a09__namespace::log_prob\";\n",
            " 158 :     // suppress unused var warning\n",
            " 159 :     (void) function__;\n",
            " 160 :     try {\n",
            " 161 :       local_scalar_t__ R1 = DUMMY_VAR__;\n",
            " 162 :       current_statement__ = 1;\n",
            " 163 :       R1 = in__.template read_constrain_lb<local_scalar_t__, jacobian__>(0,\n",
            " 164 :              lp__);\n",
            " 165 :       local_scalar_t__ t0 = DUMMY_VAR__;\n",
            " 166 :       current_statement__ = 2;\n",
            " 167 :       t0 = in__.template read<local_scalar_t__>();\n",
            " 168 :       local_scalar_t__ t1 = DUMMY_VAR__;\n",
            " 169 :       current_statement__ = 3;\n",
            " 170 :       t1 = in__.template read<local_scalar_t__>();\n",
            " 171 :       local_scalar_t__ base_incidence = DUMMY_VAR__;\n",
            " 172 :       current_statement__ = 4;\n",
            " 173 :       base_incidence = in__.template read_constrain_lb<local_scalar_t__,\n",
            " 174 :                          jacobian__>(0, lp__);\n",
            " 175 :       Eigen::Matrix<local_scalar_t__,-1,1> R =\n",
            " 176 :         Eigen::Matrix<local_scalar_t__,-1,1>::Constant(N, DUMMY_VAR__);\n",
            " 177 :       current_statement__ = 10;\n",
            " 178 :       for (int t = 1; t <= N; ++t) {\n",
            " 179 :         current_statement__ = 8;\n",
            " 180 :         stan::model::assign(R, (0.5 * (((R0 + RN) + ((R1 - R0) *\n",
            " 181 :           stan::math::tanh(((t - t0) / L)))) + ((RN - R1) *\n",
            " 182 :           stan::math::tanh(((t - t1) / L))))), \"assigning variable R\",\n",
            " 183 :           stan::model::index_uni(t));\n",
            " 184 :       }\n",
            " 185 :       {\n",
            " 186 :         current_statement__ = 15;\n",
            " 187 :         lp_accum__.add(stan::math::normal_lpdf<propto__>(R1, N, N));\n",
            " 188 :         current_statement__ = 16;\n",
            " 189 :         lp_accum__.add(stan::math::normal_lpdf<propto__>(t0, N, N));\n",
            " 190 :         current_statement__ = 17;\n",
            " 191 :         lp_accum__.add(stan::math::normal_lpdf<propto__>(t1, N, N));\n",
            " 192 :         current_statement__ = 18;\n",
            " 193 :         lp_accum__.add(stan::math::lognormal_lpdf<propto__>(base_incidence,\n",
            " 194 :                          stan::math::log(\n",
            " 195 :                            stan::math::mean(\n",
            " 196 :                              stan::math::promote_scalar<double>(incidence))),\n",
            " 197 :                          1));\n",
            " 198 :         current_statement__ = 21;\n",
            " 199 :         for (int n = 1; n <= N; ++n) {\n",
            " 200 :           current_statement__ = 19;\n",
            " 201 :           lp_accum__.add(stan::math::poisson_lpmf<propto__>(\n",
            " 202 :                            stan::model::rvalue(incidence, \"incidence\",\n",
            " 203 :                              stan::model::index_uni(n)), (base_incidence *\n",
            " 204 :                            stan::model::rvalue(R, \"R\",\n",
            " 205 :                              stan::model::index_uni(n)))));\n",
            " 206 :         }\n",
            " 207 :       }\n",
            " 208 :     } catch (const std::exception& e) {\n",
            " 209 :       stan::lang::rethrow_located(e, locations_array__[current_statement__]);\n",
            " 210 :     }\n",
            " 211 :     lp_accum__.add(lp__);\n",
            " 212 :     return lp_accum__.sum();\n",
            " 213 :   }\n",
            " 214 :   template <typename RNG, typename VecR, typename VecI, typename VecVar,\n",
            " 215 :             stan::require_vector_like_vt<std::is_floating_point,\n",
            " 216 :             VecR>* = nullptr, stan::require_vector_like_vt<std::is_integral,\n",
            " 217 :             VecI>* = nullptr, stan::require_vector_vt<std::is_floating_point,\n",
            " 218 :             VecVar>* = nullptr>\n",
            " 219 :   inline void\n",
            " 220 :   write_array_impl(RNG& base_rng__, VecR& params_r__, VecI& params_i__,\n",
            " 221 :                    VecVar& vars__, const bool\n",
            " 222 :                    emit_transformed_parameters__ = true, const bool\n",
            " 223 :                    emit_generated_quantities__ = true, std::ostream*\n",
            " 224 :                    pstream__ = nullptr) const {\n",
            " 225 :     using local_scalar_t__ = double;\n",
            " 226 :     stan::io::deserializer<local_scalar_t__> in__(params_r__, params_i__);\n",
            " 227 :     stan::io::serializer<local_scalar_t__> out__(vars__);\n",
            " 228 :     static constexpr bool propto__ = true;\n",
            " 229 :     // suppress unused var warning\n",
            " 230 :     (void) propto__;\n",
            " 231 :     double lp__ = 0.0;\n",
            " 232 :     // suppress unused var warning\n",
            " 233 :     (void) lp__;\n",
            " 234 :     int current_statement__ = 0;\n",
            " 235 :     stan::math::accumulator<double> lp_accum__;\n",
            " 236 :     local_scalar_t__ DUMMY_VAR__(std::numeric_limits<double>::quiet_NaN());\n",
            " 237 :     // suppress unused var warning\n",
            " 238 :     (void) DUMMY_VAR__;\n",
            " 239 :     constexpr bool jacobian__ = false;\n",
            " 240 :     static constexpr const char* function__ =\n",
            " 241 :       \"model1267c115a09__namespace::write_array\";\n",
            " 242 :     // suppress unused var warning\n",
            " 243 :     (void) function__;\n",
            " 244 :     try {\n",
            " 245 :       double R1 = std::numeric_limits<double>::quiet_NaN();\n",
            " 246 :       current_statement__ = 1;\n",
            " 247 :       R1 = in__.template read_constrain_lb<local_scalar_t__, jacobian__>(0,\n",
            " 248 :              lp__);\n",
            " 249 :       double t0 = std::numeric_limits<double>::quiet_NaN();\n",
            " 250 :       current_statement__ = 2;\n",
            " 251 :       t0 = in__.template read<local_scalar_t__>();\n",
            " 252 :       double t1 = std::numeric_limits<double>::quiet_NaN();\n",
            " 253 :       current_statement__ = 3;\n",
            " 254 :       t1 = in__.template read<local_scalar_t__>();\n",
            " 255 :       double base_incidence = std::numeric_limits<double>::quiet_NaN();\n",
            " 256 :       current_statement__ = 4;\n",
            " 257 :       base_incidence = in__.template read_constrain_lb<local_scalar_t__,\n",
            " 258 :                          jacobian__>(0, lp__);\n",
            " 259 :       Eigen::Matrix<double,-1,1> R =\n",
            " 260 :         Eigen::Matrix<double,-1,1>::Constant(N,\n",
            " 261 :           std::numeric_limits<double>::quiet_NaN());\n",
            " 262 :       out__.write(R1);\n",
            " 263 :       out__.write(t0);\n",
            " 264 :       out__.write(t1);\n",
            " 265 :       out__.write(base_incidence);\n",
            " 266 :       if (stan::math::logical_negation(\n",
            " 267 :             (stan::math::primitive_value(emit_transformed_parameters__) ||\n",
            " 268 :             stan::math::primitive_value(emit_generated_quantities__)))) {\n",
            " 269 :         return ;\n",
            " 270 :       }\n",
            " 271 :       current_statement__ = 10;\n",
            " 272 :       for (int t = 1; t <= N; ++t) {\n",
            " 273 :         current_statement__ = 8;\n",
            " 274 :         stan::model::assign(R, (0.5 * (((R0 + RN) + ((R1 - R0) *\n",
            " 275 :           stan::math::tanh(((t - t0) / L)))) + ((RN - R1) *\n",
            " 276 :           stan::math::tanh(((t - t1) / L))))), \"assigning variable R\",\n",
            " 277 :           stan::model::index_uni(t));\n",
            " 278 :       }\n",
            " 279 :       if (emit_transformed_parameters__) {\n",
            " 280 :         out__.write(R);\n",
            " 281 :       }\n",
            " 282 :       if (stan::math::logical_negation(emit_generated_quantities__)) {\n",
            " 283 :         return ;\n",
            " 284 :       }\n",
            " 285 :       Eigen::Matrix<double,-1,1> R_pred =\n",
            " 286 :         Eigen::Matrix<double,-1,1>::Constant(N,\n",
            " 287 :           std::numeric_limits<double>::quiet_NaN());\n",
            " 288 :       Eigen::Matrix<double,-1,1> case_pred =\n",
            " 289 :         Eigen::Matrix<double,-1,1>::Constant(N,\n",
            " 290 :           std::numeric_limits<double>::quiet_NaN());\n",
            " 291 :       current_statement__ = 14;\n",
            " 292 :       for (int n = 1; n <= N; ++n) {\n",
            " 293 :         current_statement__ = 11;\n",
            " 294 :         stan::model::assign(R_pred,\n",
            " 295 :           stan::model::rvalue(R, \"R\", stan::model::index_uni(n)),\n",
            " 296 :           \"assigning variable R_pred\", stan::model::index_uni(n));\n",
            " 297 :         current_statement__ = 12;\n",
            " 298 :         stan::model::assign(case_pred,\n",
            " 299 :           stan::math::poisson_rng((base_incidence *\n",
            " 300 :             stan::model::rvalue(R, \"R\", stan::model::index_uni(n))),\n",
            " 301 :             base_rng__), \"assigning variable case_pred\",\n",
            " 302 :           stan::model::index_uni(n));\n",
            " 303 :       }\n",
            " 304 :       out__.write(R_pred);\n",
            " 305 :       out__.write(case_pred);\n",
            " 306 :     } catch (const std::exception& e) {\n",
            " 307 :       stan::lang::rethrow_located(e, locations_array__[current_statement__]);\n",
            " 308 :     }\n",
            " 309 :   }\n",
            " 310 :   template <typename VecVar, typename VecI,\n",
            " 311 :             stan::require_vector_t<VecVar>* = nullptr,\n",
            " 312 :             stan::require_vector_like_vt<std::is_integral, VecI>* = nullptr>\n",
            " 313 :   inline void\n",
            " 314 :   unconstrain_array_impl(const VecVar& params_r__, const VecI& params_i__,\n",
            " 315 :                          VecVar& vars__, std::ostream* pstream__ = nullptr) const {\n",
            " 316 :     using local_scalar_t__ = double;\n",
            " 317 :     stan::io::deserializer<local_scalar_t__> in__(params_r__, params_i__);\n",
            " 318 :     stan::io::serializer<local_scalar_t__> out__(vars__);\n",
            " 319 :     int current_statement__ = 0;\n",
            " 320 :     local_scalar_t__ DUMMY_VAR__(std::numeric_limits<double>::quiet_NaN());\n",
            " 321 :     // suppress unused var warning\n",
            " 322 :     (void) DUMMY_VAR__;\n",
            " 323 :     try {\n",
            " 324 :       int pos__ = std::numeric_limits<int>::min();\n",
            " 325 :       pos__ = 1;\n",
            " 326 :       local_scalar_t__ R1 = DUMMY_VAR__;\n",
            " 327 :       current_statement__ = 1;\n",
            " 328 :       R1 = in__.read<local_scalar_t__>();\n",
            " 329 :       out__.write_free_lb(0, R1);\n",
            " 330 :       local_scalar_t__ t0 = DUMMY_VAR__;\n",
            " 331 :       current_statement__ = 2;\n",
            " 332 :       t0 = in__.read<local_scalar_t__>();\n",
            " 333 :       out__.write(t0);\n",
            " 334 :       local_scalar_t__ t1 = DUMMY_VAR__;\n",
            " 335 :       current_statement__ = 3;\n",
            " 336 :       t1 = in__.read<local_scalar_t__>();\n",
            " 337 :       out__.write(t1);\n",
            " 338 :       local_scalar_t__ base_incidence = DUMMY_VAR__;\n",
            " 339 :       current_statement__ = 4;\n",
            " 340 :       base_incidence = in__.read<local_scalar_t__>();\n",
            " 341 :       out__.write_free_lb(0, base_incidence);\n",
            " 342 :     } catch (const std::exception& e) {\n",
            " 343 :       stan::lang::rethrow_located(e, locations_array__[current_statement__]);\n",
            " 344 :     }\n",
            " 345 :   }\n",
            " 346 :   template <typename VecVar, stan::require_vector_t<VecVar>* = nullptr>\n",
            " 347 :   inline void\n",
            " 348 :   transform_inits_impl(const stan::io::var_context& context__, VecVar&\n",
            " 349 :                        vars__, std::ostream* pstream__ = nullptr) const {\n",
            " 350 :     using local_scalar_t__ = double;\n",
            " 351 :     stan::io::serializer<local_scalar_t__> out__(vars__);\n",
            " 352 :     int current_statement__ = 0;\n",
            " 353 :     local_scalar_t__ DUMMY_VAR__(std::numeric_limits<double>::quiet_NaN());\n",
            " 354 :     // suppress unused var warning\n",
            " 355 :     (void) DUMMY_VAR__;\n",
            " 356 :     try {\n",
            " 357 :       current_statement__ = 1;\n",
            " 358 :       context__.validate_dims(\"parameter initialization\", \"R1\", \"double\",\n",
            " 359 :         std::vector<size_t>{});\n",
            " 360 :       current_statement__ = 2;\n",
            " 361 :       context__.validate_dims(\"parameter initialization\", \"t0\", \"double\",\n",
            " 362 :         std::vector<size_t>{});\n",
            " 363 :       current_statement__ = 3;\n",
            " 364 :       context__.validate_dims(\"parameter initialization\", \"t1\", \"double\",\n",
            " 365 :         std::vector<size_t>{});\n",
            " 366 :       current_statement__ = 4;\n",
            " 367 :       context__.validate_dims(\"parameter initialization\", \"base_incidence\",\n",
            " 368 :         \"double\", std::vector<size_t>{});\n",
            " 369 :       int pos__ = std::numeric_limits<int>::min();\n",
            " 370 :       pos__ = 1;\n",
            " 371 :       local_scalar_t__ R1 = DUMMY_VAR__;\n",
            " 372 :       current_statement__ = 1;\n",
            " 373 :       R1 = context__.vals_r(\"R1\")[(1 - 1)];\n",
            " 374 :       out__.write_free_lb(0, R1);\n",
            " 375 :       local_scalar_t__ t0 = DUMMY_VAR__;\n",
            " 376 :       current_statement__ = 2;\n",
            " 377 :       t0 = context__.vals_r(\"t0\")[(1 - 1)];\n",
            " 378 :       out__.write(t0);\n",
            " 379 :       local_scalar_t__ t1 = DUMMY_VAR__;\n",
            " 380 :       current_statement__ = 3;\n",
            " 381 :       t1 = context__.vals_r(\"t1\")[(1 - 1)];\n",
            " 382 :       out__.write(t1);\n",
            " 383 :       local_scalar_t__ base_incidence = DUMMY_VAR__;\n",
            " 384 :       current_statement__ = 4;\n",
            " 385 :       base_incidence = context__.vals_r(\"base_incidence\")[(1 - 1)];\n",
            " 386 :       out__.write_free_lb(0, base_incidence);\n",
            " 387 :     } catch (const std::exception& e) {\n",
            " 388 :       stan::lang::rethrow_located(e, locations_array__[current_statement__]);\n",
            " 389 :     }\n",
            " 390 :   }\n",
            " 391 :   inline void\n",
            " 392 :   get_param_names(std::vector<std::string>& names__, const bool\n",
            " 393 :                   emit_transformed_parameters__ = true, const bool\n",
            " 394 :                   emit_generated_quantities__ = true) const {\n",
            " 395 :     names__ = std::vector<std::string>{\"R1\", \"t0\", \"t1\", \"base_incidence\"};\n",
            " 396 :     if (emit_transformed_parameters__) {\n",
            " 397 :       std::vector<std::string> temp{\"R\"};\n",
            " 398 :       names__.reserve(names__.size() + temp.size());\n",
            " 399 :       names__.insert(names__.end(), temp.begin(), temp.end());\n",
            " 400 :     }\n",
            " 401 :     if (emit_generated_quantities__) {\n",
            " 402 :       std::vector<std::string> temp{\"R_pred\", \"case_pred\"};\n",
            " 403 :       names__.reserve(names__.size() + temp.size());\n",
            " 404 :       names__.insert(names__.end(), temp.begin(), temp.end());\n",
            " 405 :     }\n",
            " 406 :   }\n",
            " 407 :   inline void\n",
            " 408 :   get_dims(std::vector<std::vector<size_t>>& dimss__, const bool\n",
            " 409 :            emit_transformed_parameters__ = true, const bool\n",
            " 410 :            emit_generated_quantities__ = true) const {\n",
            " 411 :     dimss__ = std::vector<std::vector<size_t>>{std::vector<size_t>{},\n",
            " 412 :                 std::vector<size_t>{}, std::vector<size_t>{},\n",
            " 413 :                 std::vector<size_t>{}};\n",
            " 414 :     if (emit_transformed_parameters__) {\n",
            " 415 :       std::vector<std::vector<size_t>>\n",
            " 416 :         temp{std::vector<size_t>{static_cast<size_t>(N)}};\n",
            " 417 :       dimss__.reserve(dimss__.size() + temp.size());\n",
            " 418 :       dimss__.insert(dimss__.end(), temp.begin(), temp.end());\n",
            " 419 :     }\n",
            " 420 :     if (emit_generated_quantities__) {\n",
            " 421 :       std::vector<std::vector<size_t>>\n",
            " 422 :         temp{std::vector<size_t>{static_cast<size_t>(N)},\n",
            " 423 :              std::vector<size_t>{static_cast<size_t>(N)}};\n",
            " 424 :       dimss__.reserve(dimss__.size() + temp.size());\n",
            " 425 :       dimss__.insert(dimss__.end(), temp.begin(), temp.end());\n",
            " 426 :     }\n",
            " 427 :   }\n",
            " 428 :   inline void\n",
            " 429 :   constrained_param_names(std::vector<std::string>& param_names__, bool\n",
            " 430 :                           emit_transformed_parameters__ = true, bool\n",
            " 431 :                           emit_generated_quantities__ = true) const final {\n",
            " 432 :     param_names__.emplace_back(std::string() + \"R1\");\n",
            " 433 :     param_names__.emplace_back(std::string() + \"t0\");\n",
            " 434 :     param_names__.emplace_back(std::string() + \"t1\");\n",
            " 435 :     param_names__.emplace_back(std::string() + \"base_incidence\");\n",
            " 436 :     if (emit_transformed_parameters__) {\n",
            " 437 :       for (int sym1__ = 1; sym1__ <= N; ++sym1__) {\n",
            " 438 :         param_names__.emplace_back(std::string() + \"R\" + '.' +\n",
            " 439 :           std::to_string(sym1__));\n",
            " 440 :       }\n",
            " 441 :     }\n",
            " 442 :     if (emit_generated_quantities__) {\n",
            " 443 :       for (int sym1__ = 1; sym1__ <= N; ++sym1__) {\n",
            " 444 :         param_names__.emplace_back(std::string() + \"R_pred\" + '.' +\n",
            " 445 :           std::to_string(sym1__));\n",
            " 446 :       }\n",
            " 447 :       for (int sym1__ = 1; sym1__ <= N; ++sym1__) {\n",
            " 448 :         param_names__.emplace_back(std::string() + \"case_pred\" + '.' +\n",
            " 449 :           std::to_string(sym1__));\n",
            " 450 :       }\n",
            " 451 :     }\n",
            " 452 :   }\n",
            " 453 :   inline void\n",
            " 454 :   unconstrained_param_names(std::vector<std::string>& param_names__, bool\n",
            " 455 :                             emit_transformed_parameters__ = true, bool\n",
            " 456 :                             emit_generated_quantities__ = true) const final {\n",
            " 457 :     param_names__.emplace_back(std::string() + \"R1\");\n",
            " 458 :     param_names__.emplace_back(std::string() + \"t0\");\n",
            " 459 :     param_names__.emplace_back(std::string() + \"t1\");\n",
            " 460 :     param_names__.emplace_back(std::string() + \"base_incidence\");\n",
            " 461 :     if (emit_transformed_parameters__) {\n",
            " 462 :       for (int sym1__ = 1; sym1__ <= N; ++sym1__) {\n",
            " 463 :         param_names__.emplace_back(std::string() + \"R\" + '.' +\n",
            " 464 :           std::to_string(sym1__));\n",
            " 465 :       }\n",
            " 466 :     }\n",
            " 467 :     if (emit_generated_quantities__) {\n",
            " 468 :       for (int sym1__ = 1; sym1__ <= N; ++sym1__) {\n",
            " 469 :         param_names__.emplace_back(std::string() + \"R_pred\" + '.' +\n",
            " 470 :           std::to_string(sym1__));\n",
            " 471 :       }\n",
            " 472 :       for (int sym1__ = 1; sym1__ <= N; ++sym1__) {\n",
            " 473 :         param_names__.emplace_back(std::string() + \"case_pred\" + '.' +\n",
            " 474 :           std::to_string(sym1__));\n",
            " 475 :       }\n",
            " 476 :     }\n",
            " 477 :   }\n",
            " 478 :   inline std::string get_constrained_sizedtypes() const {\n",
            " 479 :     return std::string(\"[{\\\"name\\\":\\\"R1\\\",\\\"type\\\":{\\\"name\\\":\\\"real\\\"},\\\"block\\\":\\\"parameters\\\"},{\\\"name\\\":\\\"t0\\\",\\\"type\\\":{\\\"name\\\":\\\"real\\\"},\\\"block\\\":\\\"parameters\\\"},{\\\"name\\\":\\\"t1\\\",\\\"type\\\":{\\\"name\\\":\\\"real\\\"},\\\"block\\\":\\\"parameters\\\"},{\\\"name\\\":\\\"base_incidence\\\",\\\"type\\\":{\\\"name\\\":\\\"real\\\"},\\\"block\\\":\\\"parameters\\\"},{\\\"name\\\":\\\"R\\\",\\\"type\\\":{\\\"name\\\":\\\"vector\\\",\\\"length\\\":\" + std::to_string(N) + \"},\\\"block\\\":\\\"transformed_parameters\\\"},{\\\"name\\\":\\\"R_pred\\\",\\\"type\\\":{\\\"name\\\":\\\"vector\\\",\\\"length\\\":\" + std::to_string(N) + \"},\\\"block\\\":\\\"generated_quantities\\\"},{\\\"name\\\":\\\"case_pred\\\",\\\"type\\\":{\\\"name\\\":\\\"vector\\\",\\\"length\\\":\" + std::to_string(N) + \"},\\\"block\\\":\\\"generated_quantities\\\"}]\");\n",
            " 480 :   }\n",
            " 481 :   inline std::string get_unconstrained_sizedtypes() const {\n",
            " 482 :     return std::string(\"[{\\\"name\\\":\\\"R1\\\",\\\"type\\\":{\\\"name\\\":\\\"real\\\"},\\\"block\\\":\\\"parameters\\\"},{\\\"name\\\":\\\"t0\\\",\\\"type\\\":{\\\"name\\\":\\\"real\\\"},\\\"block\\\":\\\"parameters\\\"},{\\\"name\\\":\\\"t1\\\",\\\"type\\\":{\\\"name\\\":\\\"real\\\"},\\\"block\\\":\\\"parameters\\\"},{\\\"name\\\":\\\"base_incidence\\\",\\\"type\\\":{\\\"name\\\":\\\"real\\\"},\\\"block\\\":\\\"parameters\\\"},{\\\"name\\\":\\\"R\\\",\\\"type\\\":{\\\"name\\\":\\\"vector\\\",\\\"length\\\":\" + std::to_string(N) + \"},\\\"block\\\":\\\"transformed_parameters\\\"},{\\\"name\\\":\\\"R_pred\\\",\\\"type\\\":{\\\"name\\\":\\\"vector\\\",\\\"length\\\":\" + std::to_string(N) + \"},\\\"block\\\":\\\"generated_quantities\\\"},{\\\"name\\\":\\\"case_pred\\\",\\\"type\\\":{\\\"name\\\":\\\"vector\\\",\\\"length\\\":\" + std::to_string(N) + \"},\\\"block\\\":\\\"generated_quantities\\\"}]\");\n",
            " 483 :   }\n",
            " 484 :   // Begin method overload boilerplate\n",
            " 485 :   template <typename RNG> inline void\n",
            " 486 :   write_array(RNG& base_rng, Eigen::Matrix<double,-1,1>& params_r,\n",
            " 487 :               Eigen::Matrix<double,-1,1>& vars, const bool\n",
            " 488 :               emit_transformed_parameters = true, const bool\n",
            " 489 :               emit_generated_quantities = true, std::ostream*\n",
            " 490 :               pstream = nullptr) const {\n",
            " 491 :     const size_t num_params__ = (((1 + 1) + 1) + 1);\n",
            " 492 :     const size_t num_transformed = emit_transformed_parameters * (N);\n",
            " 493 :     const size_t num_gen_quantities = emit_generated_quantities * ((N + N));\n",
            " 494 :     const size_t num_to_write = num_params__ + num_transformed +\n",
            " 495 :       num_gen_quantities;\n",
            " 496 :     std::vector<int> params_i;\n",
            " 497 :     vars = Eigen::Matrix<double,-1,1>::Constant(num_to_write,\n",
            " 498 :              std::numeric_limits<double>::quiet_NaN());\n",
            " 499 :     write_array_impl(base_rng, params_r, params_i, vars,\n",
            " 500 :       emit_transformed_parameters, emit_generated_quantities, pstream);\n",
            " 501 :   }\n",
            " 502 :   template <typename RNG> inline void\n",
            " 503 :   write_array(RNG& base_rng, std::vector<double>& params_r, std::vector<int>&\n",
            " 504 :               params_i, std::vector<double>& vars, bool\n",
            " 505 :               emit_transformed_parameters = true, bool\n",
            " 506 :               emit_generated_quantities = true, std::ostream*\n",
            " 507 :               pstream = nullptr) const {\n",
            " 508 :     const size_t num_params__ = (((1 + 1) + 1) + 1);\n",
            " 509 :     const size_t num_transformed = emit_transformed_parameters * (N);\n",
            " 510 :     const size_t num_gen_quantities = emit_generated_quantities * ((N + N));\n",
            " 511 :     const size_t num_to_write = num_params__ + num_transformed +\n",
            " 512 :       num_gen_quantities;\n",
            " 513 :     vars = std::vector<double>(num_to_write,\n",
            " 514 :              std::numeric_limits<double>::quiet_NaN());\n",
            " 515 :     write_array_impl(base_rng, params_r, params_i, vars,\n",
            " 516 :       emit_transformed_parameters, emit_generated_quantities, pstream);\n",
            " 517 :   }\n",
            " 518 :   template <bool propto__, bool jacobian__, typename T_> inline T_\n",
            " 519 :   log_prob(Eigen::Matrix<T_,-1,1>& params_r, std::ostream* pstream = nullptr) const {\n",
            " 520 :     Eigen::Matrix<int,-1,1> params_i;\n",
            " 521 :     return log_prob_impl<propto__, jacobian__>(params_r, params_i, pstream);\n",
            " 522 :   }\n",
            " 523 :   template <bool propto__, bool jacobian__, typename T_> inline T_\n",
            " 524 :   log_prob(std::vector<T_>& params_r, std::vector<int>& params_i,\n",
            " 525 :            std::ostream* pstream = nullptr) const {\n",
            " 526 :     return log_prob_impl<propto__, jacobian__>(params_r, params_i, pstream);\n",
            " 527 :   }\n",
            " 528 :   inline void\n",
            " 529 :   transform_inits(const stan::io::var_context& context,\n",
            " 530 :                   Eigen::Matrix<double,-1,1>& params_r, std::ostream*\n",
            " 531 :                   pstream = nullptr) const final {\n",
            " 532 :     std::vector<double> params_r_vec(params_r.size());\n",
            " 533 :     std::vector<int> params_i;\n",
            " 534 :     transform_inits(context, params_i, params_r_vec, pstream);\n",
            " 535 :     params_r = Eigen::Map<Eigen::Matrix<double,-1,1>>(params_r_vec.data(),\n",
            " 536 :                  params_r_vec.size());\n",
            " 537 :   }\n",
            " 538 :   inline void\n",
            " 539 :   transform_inits(const stan::io::var_context& context, std::vector<int>&\n",
            " 540 :                   params_i, std::vector<double>& vars, std::ostream*\n",
            " 541 :                   pstream__ = nullptr) const {\n",
            " 542 :     vars.resize(num_params_r__);\n",
            " 543 :     transform_inits_impl(context, vars, pstream__);\n",
            " 544 :   }\n",
            " 545 :   inline void\n",
            " 546 :   unconstrain_array(const std::vector<double>& params_constrained,\n",
            " 547 :                     std::vector<double>& params_unconstrained, std::ostream*\n",
            " 548 :                     pstream = nullptr) const {\n",
            " 549 :     const std::vector<int> params_i;\n",
            " 550 :     params_unconstrained = std::vector<double>(num_params_r__,\n",
            " 551 :                              std::numeric_limits<double>::quiet_NaN());\n",
            " 552 :     unconstrain_array_impl(params_constrained, params_i,\n",
            " 553 :       params_unconstrained, pstream);\n",
            " 554 :   }\n",
            " 555 :   inline void\n",
            " 556 :   unconstrain_array(const Eigen::Matrix<double,-1,1>& params_constrained,\n",
            " 557 :                     Eigen::Matrix<double,-1,1>& params_unconstrained,\n",
            " 558 :                     std::ostream* pstream = nullptr) const {\n",
            " 559 :     const std::vector<int> params_i;\n",
            " 560 :     params_unconstrained = Eigen::Matrix<double,-1,1>::Constant(num_params_r__,\n",
            " 561 :                              std::numeric_limits<double>::quiet_NaN());\n",
            " 562 :     unconstrain_array_impl(params_constrained, params_i,\n",
            " 563 :       params_unconstrained, pstream);\n",
            " 564 :   }\n",
            " 565 : };\n",
            " 566 : }\n",
            " 567 : using stan_model = model1267c115a09__namespace::model1267c115a09_;\n",
            " 568 : #ifndef USING_R\n",
            " 569 : // Boilerplate\n",
            " 570 : stan::model::model_base&\n",
            " 571 : new_model(stan::io::var_context& data_context, unsigned int seed,\n",
            " 572 :           std::ostream* msg_stream) {\n",
            " 573 :   stan_model* m = new stan_model(data_context, seed, msg_stream);\n",
            " 574 :   return *m;\n",
            " 575 : }\n",
            " 576 : stan::math::profile_map& get_stan_profile_data() {\n",
            " 577 :   return model1267c115a09__namespace::profiles__;\n",
            " 578 : }\n",
            " 579 : #endif\n",
            " 580 : #endif\n",
            " 581 : \n",
            " 582 : RCPP_MODULE(stan_fit4model1267c115a09__mod) {\n",
            " 583 :   class_<rstan::stan_fit<stan_model, boost::random::ecuyer1988> >(\n",
            " 584 :       \"stan_fit4model1267c115a09_\")\n",
            " 585 : \n",
            " 586 :       .constructor<SEXP, SEXP, SEXP>()\n",
            " 587 : \n",
            " 588 :       .method(\n",
            " 589 :           \"call_sampler\",\n",
            " 590 :           &rstan::stan_fit<stan_model, boost::random::ecuyer1988>::call_sampler)\n",
            " 591 :       .method(\n",
            " 592 :           \"param_names\",\n",
            " 593 :           &rstan::stan_fit<stan_model, boost::random::ecuyer1988>::param_names)\n",
            " 594 :       .method(\"param_names_oi\",\n",
            " 595 :               &rstan::stan_fit<stan_model,\n",
            " 596 :                                boost::random::ecuyer1988>::param_names_oi)\n",
            " 597 :       .method(\"param_fnames_oi\",\n",
            " 598 :               &rstan::stan_fit<stan_model,\n",
            " 599 :                                boost::random::ecuyer1988>::param_fnames_oi)\n",
            " 600 :       .method(\n",
            " 601 :           \"param_dims\",\n",
            " 602 :           &rstan::stan_fit<stan_model, boost::random::ecuyer1988>::param_dims)\n",
            " 603 :       .method(\"param_dims_oi\",\n",
            " 604 :               &rstan::stan_fit<stan_model,\n",
            " 605 :                                boost::random::ecuyer1988>::param_dims_oi)\n",
            " 606 :       .method(\"update_param_oi\",\n",
            " 607 :               &rstan::stan_fit<stan_model,\n",
            " 608 :                                boost::random::ecuyer1988>::update_param_oi)\n",
            " 609 :       .method(\"param_oi_tidx\",\n",
            " 610 :               &rstan::stan_fit<stan_model,\n",
            " 611 :                                boost::random::ecuyer1988>::param_oi_tidx)\n",
            " 612 :       .method(\"grad_log_prob\",\n",
            " 613 :               &rstan::stan_fit<stan_model,\n",
            " 614 :                                boost::random::ecuyer1988>::grad_log_prob)\n",
            " 615 :       .method(\"log_prob\",\n",
            " 616 :               &rstan::stan_fit<stan_model, boost::random::ecuyer1988>::log_prob)\n",
            " 617 :       .method(\"unconstrain_pars\",\n",
            " 618 :               &rstan::stan_fit<stan_model,\n",
            " 619 :                                boost::random::ecuyer1988>::unconstrain_pars)\n",
            " 620 :       .method(\"constrain_pars\",\n",
            " 621 :               &rstan::stan_fit<stan_model,\n",
            " 622 :                                boost::random::ecuyer1988>::constrain_pars)\n",
            " 623 :       .method(\n",
            " 624 :           \"num_pars_unconstrained\",\n",
            " 625 :           &rstan::stan_fit<stan_model,\n",
            " 626 :                            boost::random::ecuyer1988>::num_pars_unconstrained)\n",
            " 627 :       .method(\n",
            " 628 :           \"unconstrained_param_names\",\n",
            " 629 :           &rstan::stan_fit<\n",
            " 630 :               stan_model, boost::random::ecuyer1988>::unconstrained_param_names)\n",
            " 631 :       .method(\n",
            " 632 :           \"constrained_param_names\",\n",
            " 633 :           &rstan::stan_fit<stan_model,\n",
            " 634 :                            boost::random::ecuyer1988>::constrained_param_names)\n",
            " 635 :       .method(\"standalone_gqs\",\n",
            " 636 :               &rstan::stan_fit<stan_model,\n",
            " 637 :                                boost::random::ecuyer1988>::standalone_gqs);\n",
            " 638 : }\n",
            " 639 : \n",
            " 640 : \n",
            " 641 : // declarations\n",
            " 642 : extern \"C\" {\n",
            " 643 : SEXP file12629cb7b0f( ) ;\n",
            " 644 : }\n",
            " 645 : \n",
            " 646 : // definition\n",
            " 647 : SEXP file12629cb7b0f() {\n",
            " 648 :  return Rcpp::wrap(\"anon_model\");\n",
            " 649 : }\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "fit"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "QzUYAw4FXz7z",
        "outputId": "47a37578-4096-408f-a20a-a11f5c1d7eea"
      },
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Inference for Stan model: anon_model.\n",
              "4 chains, each with iter=10000; warmup=5000; thin=1; \n",
              "post-warmup draws per chain=5000, total post-warmup draws=20000.\n",
              "\n",
              "                 mean se_mean   sd   2.5%    25%    50%    75%  97.5% n_eff\n",
              "R1              13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "t0              21.15    0.01 1.49  18.25  20.15  21.13  22.12  24.12 13061\n",
              "t1              66.63    0.02 2.09  62.51  65.27  66.66  68.04  70.58 11497\n",
              "base_incidence   0.23    0.00 0.06   0.13   0.19   0.23   0.27   0.37  7706\n",
              "R[1]             0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.10 10324\n",
              "R[2]             0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.10 10324\n",
              "R[3]             0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.10 10324\n",
              "R[4]             0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.10 10324\n",
              "R[5]             0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.10 10324\n",
              "R[6]             0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.10 10324\n",
              "R[7]             0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.11 10325\n",
              "R[8]             0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.11 10326\n",
              "R[9]             0.11    0.00 0.01   0.10   0.10   0.10   0.11   0.13 10328\n",
              "R[10]            0.11    0.00 0.02   0.10   0.10   0.11   0.11   0.15 10332\n",
              "R[11]            0.12    0.00 0.03   0.10   0.11   0.11   0.13   0.20 10340\n",
              "R[12]            0.15    0.00 0.06   0.10   0.11   0.13   0.16   0.30 10356\n",
              "R[13]            0.19    0.00 0.12   0.11   0.13   0.16   0.21   0.49 10387\n",
              "R[14]            0.28    0.00 0.22   0.11   0.16   0.21   0.31   0.84 10445\n",
              "R[15]            0.43    0.00 0.39   0.13   0.21   0.31   0.50   1.47 10541\n",
              "R[16]            0.71    0.01 0.68   0.15   0.31   0.50   0.87   2.54 10688\n",
              "R[17]            1.20    0.01 1.10   0.20   0.50   0.86   1.51   4.18 10886\n",
              "R[18]            1.99    0.02 1.65   0.29   0.86   1.50   2.59   6.42 11066\n",
              "R[19]            3.14    0.02 2.29   0.47   1.48   2.56   4.18   9.06 11074\n",
              "R[20]            4.67    0.03 2.90   0.79   2.52   4.11   6.21  11.67 10673\n",
              "R[21]            6.45    0.03 3.36   1.36   4.03   6.02   8.33  14.26  9863\n",
              "R[22]            8.26    0.04 3.63   2.31   5.78   7.88  10.28  16.74  8905\n",
              "R[23]            9.88    0.04 3.75   3.64   7.39   9.45  11.87  18.86  8061\n",
              "R[24]           11.15    0.04 3.81   5.15   8.58  10.64  13.08  20.33  7536\n",
              "R[25]           12.05    0.05 3.86   6.33   9.41  11.44  13.98  21.37  7303\n",
              "R[26]           12.62    0.05 3.92   6.98   9.88  11.99  14.57  22.14  7244\n",
              "R[27]           12.96    0.05 3.97   7.31  10.16  12.28  14.93  22.59  7255\n",
              "R[28]           13.15    0.05 4.01   7.47  10.33  12.44  15.15  22.99  7280\n",
              "R[29]           13.25    0.05 4.03   7.52  10.42  12.55  15.27  23.15  7301\n",
              "R[30]           13.31    0.05 4.05   7.56  10.46  12.60  15.33  23.24  7314\n",
              "R[31]           13.34    0.05 4.05   7.57  10.49  12.63  15.36  23.27  7322\n",
              "R[32]           13.35    0.05 4.06   7.58  10.50  12.64  15.38  23.32  7327\n",
              "R[33]           13.36    0.05 4.06   7.59  10.51  12.65  15.38  23.34  7329\n",
              "R[34]           13.36    0.05 4.06   7.59  10.51  12.66  15.39  23.34  7330\n",
              "R[35]           13.36    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[36]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[37]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[38]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[39]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[40]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[41]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[42]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[43]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[44]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[45]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[46]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[47]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[48]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[49]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R[50]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7330\n",
              "R[51]           13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7329\n",
              "R[52]           13.36    0.05 4.06   7.58  10.51  12.66  15.39  23.35  7327\n",
              "R[53]           13.36    0.05 4.06   7.58  10.51  12.66  15.39  23.35  7323\n",
              "R[54]           13.36    0.05 4.06   7.57  10.51  12.65  15.38  23.34  7316\n",
              "R[55]           13.35    0.05 4.07   7.57  10.50  12.65  15.38  23.33  7304\n",
              "R[56]           13.34    0.05 4.07   7.55  10.49  12.63  15.37  23.32  7285\n",
              "R[57]           13.32    0.05 4.07   7.52  10.47  12.62  15.36  23.32  7257\n",
              "R[58]           13.28    0.05 4.08   7.46  10.43  12.58  15.32  23.26  7217\n",
              "R[59]           13.21    0.05 4.09   7.35  10.36  12.51  15.25  23.20  7166\n",
              "R[60]           13.08    0.05 4.10   7.18  10.23  12.40  15.15  23.08  7109\n",
              "R[61]           12.86    0.05 4.12   6.81  10.03  12.20  14.93  22.87  7074\n",
              "R[62]           12.50    0.05 4.16   6.20   9.68  11.86  14.61  22.53  7087\n",
              "R[63]           11.94    0.05 4.21   5.29   9.11  11.35  14.13  22.06  7199\n",
              "R[64]           11.13    0.05 4.26   4.22   8.25  10.58  13.39  21.19  7439\n",
              "R[65]           10.06    0.05 4.27   3.33   7.08   9.53  12.39  20.09  7812\n",
              "R[66]            8.77    0.05 4.15   2.75   5.69   8.24  11.09  18.57  8195\n",
              "R[67]            7.37    0.04 3.86   2.41   4.37   6.66   9.53  16.57  8505\n",
              "R[68]            5.99    0.04 3.38   2.21   3.39   5.11   7.74  14.48  8714\n",
              "R[69]            4.78    0.03 2.76   2.11   2.77   3.88   5.94  12.03  8891\n",
              "R[70]            3.82    0.02 2.11   2.06   2.41   3.06   4.43   9.62  9046\n",
              "R[71]            3.12    0.02 1.51   2.03   2.22   2.57   3.40   7.32  9201\n",
              "R[72]            2.66    0.01 1.03   2.02   2.11   2.30   2.76   5.41  9354\n",
              "R[73]            2.37    0.01 0.67   2.01   2.06   2.16   2.41   4.01  9493\n",
              "R[74]            2.20    0.00 0.43   2.00   2.03   2.08   2.21   3.12  9610\n",
              "R[75]            2.11    0.00 0.28   2.00   2.02   2.04   2.11   2.60  9685\n",
              "R[76]            2.06    0.00 0.18   2.00   2.01   2.02   2.06   2.32  9741\n",
              "R[77]            2.03    0.00 0.12   2.00   2.00   2.01   2.03   2.16  9940\n",
              "R[78]            2.02    0.00 0.08   2.00   2.00   2.01   2.01   2.08 10449\n",
              "R[79]            2.01    0.00 0.05   2.00   2.00   2.00   2.01   2.04 11113\n",
              "R[80]            2.00    0.00 0.03   2.00   2.00   2.00   2.00   2.02 11706\n",
              "R[81]            2.00    0.00 0.02   2.00   2.00   2.00   2.00   2.01 12121\n",
              "R[82]            2.00    0.00 0.01   2.00   2.00   2.00   2.00   2.01 12373\n",
              "R[83]            2.00    0.00 0.01   2.00   2.00   2.00   2.00   2.00 12515\n",
              "R[84]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12591\n",
              "R[85]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12631\n",
              "R[86]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12652\n",
              "R[87]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12663\n",
              "R[88]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12669\n",
              "R[89]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12671\n",
              "R[90]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12673\n",
              "R[91]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R[92]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R[93]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R[94]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R[95]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R[96]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R[97]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R[98]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R[99]            2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R[100]           2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R[101]           2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R_pred[1]        0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.10 10324\n",
              "R_pred[2]        0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.10 10324\n",
              "R_pred[3]        0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.10 10324\n",
              "R_pred[4]        0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.10 10324\n",
              "R_pred[5]        0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.10 10324\n",
              "R_pred[6]        0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.10 10324\n",
              "R_pred[7]        0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.11 10325\n",
              "R_pred[8]        0.10    0.00 0.00   0.10   0.10   0.10   0.10   0.11 10326\n",
              "R_pred[9]        0.11    0.00 0.01   0.10   0.10   0.10   0.11   0.13 10328\n",
              "R_pred[10]       0.11    0.00 0.02   0.10   0.10   0.11   0.11   0.15 10332\n",
              "R_pred[11]       0.12    0.00 0.03   0.10   0.11   0.11   0.13   0.20 10340\n",
              "R_pred[12]       0.15    0.00 0.06   0.10   0.11   0.13   0.16   0.30 10356\n",
              "R_pred[13]       0.19    0.00 0.12   0.11   0.13   0.16   0.21   0.49 10387\n",
              "R_pred[14]       0.28    0.00 0.22   0.11   0.16   0.21   0.31   0.84 10445\n",
              "R_pred[15]       0.43    0.00 0.39   0.13   0.21   0.31   0.50   1.47 10541\n",
              "R_pred[16]       0.71    0.01 0.68   0.15   0.31   0.50   0.87   2.54 10688\n",
              "R_pred[17]       1.20    0.01 1.10   0.20   0.50   0.86   1.51   4.18 10886\n",
              "R_pred[18]       1.99    0.02 1.65   0.29   0.86   1.50   2.59   6.42 11066\n",
              "R_pred[19]       3.14    0.02 2.29   0.47   1.48   2.56   4.18   9.06 11074\n",
              "R_pred[20]       4.67    0.03 2.90   0.79   2.52   4.11   6.21  11.67 10673\n",
              "R_pred[21]       6.45    0.03 3.36   1.36   4.03   6.02   8.33  14.26  9863\n",
              "R_pred[22]       8.26    0.04 3.63   2.31   5.78   7.88  10.28  16.74  8905\n",
              "R_pred[23]       9.88    0.04 3.75   3.64   7.39   9.45  11.87  18.86  8061\n",
              "R_pred[24]      11.15    0.04 3.81   5.15   8.58  10.64  13.08  20.33  7536\n",
              "R_pred[25]      12.05    0.05 3.86   6.33   9.41  11.44  13.98  21.37  7303\n",
              "R_pred[26]      12.62    0.05 3.92   6.98   9.88  11.99  14.57  22.14  7244\n",
              "R_pred[27]      12.96    0.05 3.97   7.31  10.16  12.28  14.93  22.59  7255\n",
              "R_pred[28]      13.15    0.05 4.01   7.47  10.33  12.44  15.15  22.99  7280\n",
              "R_pred[29]      13.25    0.05 4.03   7.52  10.42  12.55  15.27  23.15  7301\n",
              "R_pred[30]      13.31    0.05 4.05   7.56  10.46  12.60  15.33  23.24  7314\n",
              "R_pred[31]      13.34    0.05 4.05   7.57  10.49  12.63  15.36  23.27  7322\n",
              "R_pred[32]      13.35    0.05 4.06   7.58  10.50  12.64  15.38  23.32  7327\n",
              "R_pred[33]      13.36    0.05 4.06   7.59  10.51  12.65  15.38  23.34  7329\n",
              "R_pred[34]      13.36    0.05 4.06   7.59  10.51  12.66  15.39  23.34  7330\n",
              "R_pred[35]      13.36    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[36]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[37]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[38]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[39]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[40]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[41]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[42]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[43]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[44]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[45]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[46]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[47]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[48]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[49]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7331\n",
              "R_pred[50]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7330\n",
              "R_pred[51]      13.37    0.05 4.06   7.59  10.51  12.66  15.39  23.35  7329\n",
              "R_pred[52]      13.36    0.05 4.06   7.58  10.51  12.66  15.39  23.35  7327\n",
              "R_pred[53]      13.36    0.05 4.06   7.58  10.51  12.66  15.39  23.35  7323\n",
              "R_pred[54]      13.36    0.05 4.06   7.57  10.51  12.65  15.38  23.34  7316\n",
              "R_pred[55]      13.35    0.05 4.07   7.57  10.50  12.65  15.38  23.33  7304\n",
              "R_pred[56]      13.34    0.05 4.07   7.55  10.49  12.63  15.37  23.32  7285\n",
              "R_pred[57]      13.32    0.05 4.07   7.52  10.47  12.62  15.36  23.32  7257\n",
              "R_pred[58]      13.28    0.05 4.08   7.46  10.43  12.58  15.32  23.26  7217\n",
              "R_pred[59]      13.21    0.05 4.09   7.35  10.36  12.51  15.25  23.20  7166\n",
              "R_pred[60]      13.08    0.05 4.10   7.18  10.23  12.40  15.15  23.08  7109\n",
              "R_pred[61]      12.86    0.05 4.12   6.81  10.03  12.20  14.93  22.87  7074\n",
              "R_pred[62]      12.50    0.05 4.16   6.20   9.68  11.86  14.61  22.53  7087\n",
              "R_pred[63]      11.94    0.05 4.21   5.29   9.11  11.35  14.13  22.06  7199\n",
              "R_pred[64]      11.13    0.05 4.26   4.22   8.25  10.58  13.39  21.19  7439\n",
              "R_pred[65]      10.06    0.05 4.27   3.33   7.08   9.53  12.39  20.09  7812\n",
              "R_pred[66]       8.77    0.05 4.15   2.75   5.69   8.24  11.09  18.57  8195\n",
              "R_pred[67]       7.37    0.04 3.86   2.41   4.37   6.66   9.53  16.57  8505\n",
              "R_pred[68]       5.99    0.04 3.38   2.21   3.39   5.11   7.74  14.48  8714\n",
              "R_pred[69]       4.78    0.03 2.76   2.11   2.77   3.88   5.94  12.03  8891\n",
              "R_pred[70]       3.82    0.02 2.11   2.06   2.41   3.06   4.43   9.62  9046\n",
              "R_pred[71]       3.12    0.02 1.51   2.03   2.22   2.57   3.40   7.32  9201\n",
              "R_pred[72]       2.66    0.01 1.03   2.02   2.11   2.30   2.76   5.41  9354\n",
              "R_pred[73]       2.37    0.01 0.67   2.01   2.06   2.16   2.41   4.01  9493\n",
              "R_pred[74]       2.20    0.00 0.43   2.00   2.03   2.08   2.21   3.12  9610\n",
              "R_pred[75]       2.11    0.00 0.28   2.00   2.02   2.04   2.11   2.60  9685\n",
              "R_pred[76]       2.06    0.00 0.18   2.00   2.01   2.02   2.06   2.32  9741\n",
              "R_pred[77]       2.03    0.00 0.12   2.00   2.00   2.01   2.03   2.16  9940\n",
              "R_pred[78]       2.02    0.00 0.08   2.00   2.00   2.01   2.01   2.08 10449\n",
              "R_pred[79]       2.01    0.00 0.05   2.00   2.00   2.00   2.01   2.04 11113\n",
              "R_pred[80]       2.00    0.00 0.03   2.00   2.00   2.00   2.00   2.02 11706\n",
              "R_pred[81]       2.00    0.00 0.02   2.00   2.00   2.00   2.00   2.01 12121\n",
              "R_pred[82]       2.00    0.00 0.01   2.00   2.00   2.00   2.00   2.01 12373\n",
              "R_pred[83]       2.00    0.00 0.01   2.00   2.00   2.00   2.00   2.00 12515\n",
              "R_pred[84]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12591\n",
              "R_pred[85]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12631\n",
              "R_pred[86]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12652\n",
              "R_pred[87]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12663\n",
              "R_pred[88]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12669\n",
              "R_pred[89]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12671\n",
              "R_pred[90]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12673\n",
              "R_pred[91]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R_pred[92]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R_pred[93]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R_pred[94]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R_pred[95]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R_pred[96]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R_pred[97]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R_pred[98]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R_pred[99]       2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R_pred[100]      2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "R_pred[101]      2.00    0.00 0.00   2.00   2.00   2.00   2.00   2.00 12674\n",
              "case_pred[1]     0.02    0.00 0.15   0.00   0.00   0.00   0.00   0.00 19718\n",
              "case_pred[2]     0.02    0.00 0.15   0.00   0.00   0.00   0.00   0.00 20015\n",
              "case_pred[3]     0.02    0.00 0.15   0.00   0.00   0.00   0.00   0.00 20158\n",
              "case_pred[4]     0.02    0.00 0.15   0.00   0.00   0.00   0.00   0.00 20502\n",
              "case_pred[5]     0.02    0.00 0.16   0.00   0.00   0.00   0.00   0.00 20033\n",
              "case_pred[6]     0.02    0.00 0.15   0.00   0.00   0.00   0.00   0.00 19860\n",
              "case_pred[7]     0.02    0.00 0.15   0.00   0.00   0.00   0.00   0.00 20226\n",
              "case_pred[8]     0.03    0.00 0.16   0.00   0.00   0.00   0.00   0.02 19249\n",
              "case_pred[9]     0.03    0.00 0.16   0.00   0.00   0.00   0.00   1.00 20200\n",
              "case_pred[10]    0.03    0.00 0.16   0.00   0.00   0.00   0.00   1.00 19393\n",
              "case_pred[11]    0.03    0.00 0.17   0.00   0.00   0.00   0.00   1.00 19701\n",
              "case_pred[12]    0.04    0.00 0.19   0.00   0.00   0.00   0.00   1.00 19632\n",
              "case_pred[13]    0.04    0.00 0.21   0.00   0.00   0.00   0.00   1.00 19800\n",
              "case_pred[14]    0.06    0.00 0.25   0.00   0.00   0.00   0.00   1.00 19569\n",
              "case_pred[15]    0.10    0.00 0.32   0.00   0.00   0.00   0.00   1.00 18197\n",
              "case_pred[16]    0.16    0.00 0.42   0.00   0.00   0.00   0.00   1.00 18687\n",
              "case_pred[17]    0.26    0.00 0.55   0.00   0.00   0.00   0.00   2.00 17455\n",
              "case_pred[18]    0.42    0.01 0.72   0.00   0.00   0.00   1.00   2.00 18902\n",
              "case_pred[19]    0.67    0.01 0.92   0.00   0.00   0.00   1.00   3.00 17783\n",
              "case_pred[20]    1.01    0.01 1.13   0.00   0.00   1.00   2.00   4.00 18936\n",
              "case_pred[21]    1.40    0.01 1.32   0.00   0.00   1.00   2.00   5.00 18886\n",
              "case_pred[22]    1.80    0.01 1.45   0.00   1.00   2.00   3.00   5.00 18738\n",
              "case_pred[23]    2.14    0.01 1.55   0.00   1.00   2.00   3.00   6.00 19500\n",
              "case_pred[24]    2.43    0.01 1.61   0.00   1.00   2.00   3.00   6.00 19791\n",
              "case_pred[25]    2.63    0.01 1.65   0.00   1.00   2.00   4.00   6.00 19328\n",
              "case_pred[26]    2.76    0.01 1.68   0.00   2.00   3.00   4.00   6.00 19726\n",
              "case_pred[27]    2.81    0.01 1.69   0.00   2.00   3.00   4.00   7.00 19812\n",
              "case_pred[28]    2.86    0.01 1.72   0.00   2.00   3.00   4.00   7.00 19754\n",
              "case_pred[29]    2.90    0.01 1.73   0.00   2.00   3.00   4.00   7.00 20043\n",
              "case_pred[30]    2.89    0.01 1.71   0.00   2.00   3.00   4.00   7.00 19999\n",
              "case_pred[31]    2.90    0.01 1.73   0.00   2.00   3.00   4.00   7.00 19993\n",
              "case_pred[32]    2.89    0.01 1.72   0.00   2.00   3.00   4.00   7.00 20191\n",
              "case_pred[33]    2.88    0.01 1.72   0.00   2.00   3.00   4.00   7.00 19915\n",
              "case_pred[34]    2.90    0.01 1.72   0.00   2.00   3.00   4.00   7.00 19675\n",
              "case_pred[35]    2.94    0.01 1.74   0.00   2.00   3.00   4.00   7.00 19862\n",
              "case_pred[36]    2.90    0.01 1.74   0.00   2.00   3.00   4.00   7.00 20078\n",
              "case_pred[37]    2.90    0.01 1.73   0.00   2.00   3.00   4.00   7.00 20184\n",
              "case_pred[38]    2.90    0.01 1.73   0.00   2.00   3.00   4.00   7.00 19407\n",
              "case_pred[39]    2.91    0.01 1.73   0.00   2.00   3.00   4.00   7.00 19906\n",
              "case_pred[40]    2.92    0.01 1.75   0.00   2.00   3.00   4.00   7.00 19817\n",
              "case_pred[41]    2.91    0.01 1.74   0.00   2.00   3.00   4.00   7.00 19943\n",
              "case_pred[42]    2.90    0.01 1.73   0.00   2.00   3.00   4.00   7.00 19803\n",
              "case_pred[43]    2.92    0.01 1.73   0.00   2.00   3.00   4.00   7.00 18391\n",
              "case_pred[44]    2.89    0.01 1.72   0.00   2.00   3.00   4.00   7.00 18334\n",
              "case_pred[45]    2.91    0.01 1.74   0.00   2.00   3.00   4.00   7.00 19361\n",
              "case_pred[46]    2.91    0.01 1.73   0.00   2.00   3.00   4.00   7.00 19772\n",
              "case_pred[47]    2.90    0.01 1.72   0.00   2.00   3.00   4.00   7.00 20157\n",
              "case_pred[48]    2.92    0.01 1.71   0.00   2.00   3.00   4.00   7.00 19605\n",
              "case_pred[49]    2.90    0.01 1.71   0.00   2.00   3.00   4.00   7.00 20050\n",
              "case_pred[50]    2.92    0.01 1.72   0.00   2.00   3.00   4.00   7.00 18767\n",
              "case_pred[51]    2.90    0.01 1.72   0.00   2.00   3.00   4.00   7.00 20127\n",
              "case_pred[52]    2.93    0.01 1.74   0.00   2.00   3.00   4.00   7.00 19938\n",
              "case_pred[53]    2.90    0.01 1.72   0.00   2.00   3.00   4.00   7.00 19399\n",
              "case_pred[54]    2.92    0.01 1.74   0.00   2.00   3.00   4.00   7.00 18989\n",
              "case_pred[55]    2.92    0.01 1.73   0.00   2.00   3.00   4.00   7.00 19504\n",
              "case_pred[56]    2.92    0.01 1.74   0.00   2.00   3.00   4.00   7.00 19933\n",
              "case_pred[57]    2.92    0.01 1.75   0.00   2.00   3.00   4.00   7.00 19720\n",
              "case_pred[58]    2.89    0.01 1.73   0.00   2.00   3.00   4.00   7.00 19489\n",
              "case_pred[59]    2.86    0.01 1.71   0.00   2.00   3.00   4.00   7.00 19173\n",
              "case_pred[60]    2.82    0.01 1.70   0.00   2.00   3.00   4.00   6.00 20264\n",
              "case_pred[61]    2.78    0.01 1.69   0.00   2.00   3.00   4.00   7.00 19686\n",
              "case_pred[62]    2.69    0.01 1.68   0.00   1.00   2.00   4.00   6.00 18818\n",
              "case_pred[63]    2.58    0.01 1.65   0.00   1.00   2.00   4.00   6.00 19016\n",
              "case_pred[64]    2.39    0.01 1.63   0.00   1.00   2.00   3.00   6.00 18591\n",
              "case_pred[65]    2.15    0.01 1.56   0.00   1.00   2.00   3.00   6.00 19233\n",
              "case_pred[66]    1.87    0.01 1.49   0.00   1.00   2.00   3.00   5.00 17766\n",
              "case_pred[67]    1.57    0.01 1.39   0.00   1.00   1.00   2.00   5.00 19014\n",
              "case_pred[68]    1.29    0.01 1.27   0.00   0.00   1.00   2.00   4.00 18032\n",
              "case_pred[69]    1.03    0.01 1.11   0.00   0.00   1.00   2.00   4.00 18340\n",
              "case_pred[70]    0.83    0.01 0.97   0.00   0.00   1.00   1.00   3.00 18127\n",
              "case_pred[71]    0.69    0.01 0.88   0.00   0.00   0.00   1.00   3.00 19220\n",
              "case_pred[72]    0.60    0.01 0.79   0.00   0.00   0.00   1.00   3.00 18978\n",
              "case_pred[73]    0.55    0.01 0.76   0.00   0.00   0.00   1.00   2.00 19088\n",
              "case_pred[74]    0.51    0.01 0.73   0.00   0.00   0.00   1.00   2.00 19567\n",
              "case_pred[75]    0.49    0.01 0.71   0.00   0.00   0.00   1.00   2.00 19942\n",
              "case_pred[76]    0.48    0.01 0.70   0.00   0.00   0.00   1.00   2.00 17311\n",
              "case_pred[77]    0.48    0.01 0.70   0.00   0.00   0.00   1.00   2.00 18850\n",
              "case_pred[78]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 19368\n",
              "case_pred[79]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 19182\n",
              "case_pred[80]    0.46    0.01 0.69   0.00   0.00   0.00   1.00   2.00 18990\n",
              "case_pred[81]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 18413\n",
              "case_pred[82]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 19004\n",
              "case_pred[83]    0.46    0.01 0.69   0.00   0.00   0.00   1.00   2.00 18446\n",
              "case_pred[84]    0.47    0.00 0.70   0.00   0.00   0.00   1.00   2.00 19577\n",
              "case_pred[85]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 19107\n",
              "case_pred[86]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 18160\n",
              "case_pred[87]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 19221\n",
              "case_pred[88]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 17771\n",
              "case_pred[89]    0.46    0.01 0.69   0.00   0.00   0.00   1.00   2.00 18829\n",
              "case_pred[90]    0.46    0.01 0.69   0.00   0.00   0.00   1.00   2.00 18372\n",
              "case_pred[91]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 18974\n",
              "case_pred[92]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 18933\n",
              "case_pred[93]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 18741\n",
              "case_pred[94]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 19018\n",
              "case_pred[95]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 19374\n",
              "case_pred[96]    0.47    0.00 0.70   0.00   0.00   0.00   1.00   2.00 19631\n",
              "case_pred[97]    0.47    0.01 0.69   0.00   0.00   0.00   1.00   2.00 18997\n",
              "case_pred[98]    0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 17830\n",
              "case_pred[99]    0.47    0.01 0.69   0.00   0.00   0.00   1.00   2.00 19140\n",
              "case_pred[100]   0.47    0.01 0.70   0.00   0.00   0.00   1.00   2.00 18949\n",
              "case_pred[101]   0.48    0.01 0.70   0.00   0.00   0.00   1.00   2.00 18557\n",
              "lp__           -35.74    0.02 1.49 -39.63 -36.43 -35.38 -34.65 -33.94  6870\n",
              "               Rhat\n",
              "R1                1\n",
              "t0                1\n",
              "t1                1\n",
              "base_incidence    1\n",
              "R[1]              1\n",
              "R[2]              1\n",
              "R[3]              1\n",
              "R[4]              1\n",
              "R[5]              1\n",
              "R[6]              1\n",
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              "R[10]             1\n",
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              "R[98]             1\n",
              "R[99]             1\n",
              "R[100]            1\n",
              "R[101]            1\n",
              "R_pred[1]         1\n",
              "R_pred[2]         1\n",
              "R_pred[3]         1\n",
              "R_pred[4]         1\n",
              "R_pred[5]         1\n",
              "R_pred[6]         1\n",
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              "R_pred[8]         1\n",
              "R_pred[9]         1\n",
              "R_pred[10]        1\n",
              "R_pred[11]        1\n",
              "R_pred[12]        1\n",
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              "R_pred[39]        1\n",
              "R_pred[40]        1\n",
              "R_pred[41]        1\n",
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              "case_pred[101]    1\n",
              "lp__              1\n",
              "\n",
              "Samples were drawn using NUTS(diag_e) at Mon Jul 29 07:10:54 2024.\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": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df_res = extract(fit)"
      ],
      "metadata": {
        "id": "4j56ZGyxuPTk"
      },
      "execution_count": 58,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "case_mean = apply(df_res$case_pred, 2, mean)\n",
        "case_ci = apply(df_res$case_pred, 2, quantile, probs = c(0.025, 0.975))"
      ],
      "metadata": {
        "id": "ASwzp64KP2YI"
      },
      "execution_count": 59,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "case_data = data.frame(\n",
        "    x = 1:length(case_mean),\n",
        "    mean = case_mean,\n",
        "    lower = case_ci[1,],\n",
        "    upper = case_ci[2,]\n",
        ")"
      ],
      "metadata": {
        "id": "pZdIakNLQJ7B"
      },
      "execution_count": 60,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "case_data"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "PJLwVQUlSSs-",
        "outputId": "89bda29d-0a4e-41a9-f7a2-d17e7968aa38"
      },
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<table class=\"dataframe\">\n",
              "<caption>A data.frame: 101 × 4</caption>\n",
              "<thead>\n",
              "\t<tr><th scope=col>x</th><th scope=col>mean</th><th scope=col>lower</th><th scope=col>upper</th></tr>\n",
              "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
              "</thead>\n",
              "<tbody>\n",
              "\t<tr><td> 1</td><td>0.02260</td><td>0</td><td>0.000</td></tr>\n",
              "\t<tr><td> 2</td><td>0.02250</td><td>0</td><td>0.000</td></tr>\n",
              "\t<tr><td> 3</td><td>0.02320</td><td>0</td><td>0.000</td></tr>\n",
              "\t<tr><td> 4</td><td>0.02360</td><td>0</td><td>0.000</td></tr>\n",
              "\t<tr><td> 5</td><td>0.02485</td><td>0</td><td>0.000</td></tr>\n",
              "\t<tr><td> 6</td><td>0.02245</td><td>0</td><td>0.000</td></tr>\n",
              "\t<tr><td> 7</td><td>0.02395</td><td>0</td><td>0.000</td></tr>\n",
              "\t<tr><td> 8</td><td>0.02545</td><td>0</td><td>0.025</td></tr>\n",
              "\t<tr><td> 9</td><td>0.02600</td><td>0</td><td>1.000</td></tr>\n",
              "\t<tr><td>10</td><td>0.02585</td><td>0</td><td>1.000</td></tr>\n",
              "\t<tr><td>11</td><td>0.02880</td><td>0</td><td>1.000</td></tr>\n",
              "\t<tr><td>12</td><td>0.03550</td><td>0</td><td>1.000</td></tr>\n",
              "\t<tr><td>13</td><td>0.04380</td><td>0</td><td>1.000</td></tr>\n",
              "\t<tr><td>14</td><td>0.06075</td><td>0</td><td>1.000</td></tr>\n",
              "\t<tr><td>15</td><td>0.09510</td><td>0</td><td>1.000</td></tr>\n",
              "\t<tr><td>16</td><td>0.15565</td><td>0</td><td>1.000</td></tr>\n",
              "\t<tr><td>17</td><td>0.25775</td><td>0</td><td>2.000</td></tr>\n",
              "\t<tr><td>18</td><td>0.42415</td><td>0</td><td>2.000</td></tr>\n",
              "\t<tr><td>19</td><td>0.67250</td><td>0</td><td>3.000</td></tr>\n",
              "\t<tr><td>20</td><td>1.01055</td><td>0</td><td>4.000</td></tr>\n",
              "\t<tr><td>21</td><td>1.40205</td><td>0</td><td>5.000</td></tr>\n",
              "\t<tr><td>22</td><td>1.80255</td><td>0</td><td>5.000</td></tr>\n",
              "\t<tr><td>23</td><td>2.14475</td><td>0</td><td>6.000</td></tr>\n",
              "\t<tr><td>24</td><td>2.43105</td><td>0</td><td>6.000</td></tr>\n",
              "\t<tr><td>25</td><td>2.62915</td><td>0</td><td>6.000</td></tr>\n",
              "\t<tr><td>26</td><td>2.75705</td><td>0</td><td>6.000</td></tr>\n",
              "\t<tr><td>27</td><td>2.80970</td><td>0</td><td>7.000</td></tr>\n",
              "\t<tr><td>28</td><td>2.85610</td><td>0</td><td>7.000</td></tr>\n",
              "\t<tr><td>29</td><td>2.90440</td><td>0</td><td>7.000</td></tr>\n",
              "\t<tr><td>30</td><td>2.88775</td><td>0</td><td>7.000</td></tr>\n",
              "\t<tr><td>⋮</td><td>⋮</td><td>⋮</td><td>⋮</td></tr>\n",
              "\t<tr><td> 72</td><td>0.59675</td><td>0</td><td>3</td></tr>\n",
              "\t<tr><td> 73</td><td>0.54840</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 74</td><td>0.51150</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 75</td><td>0.48780</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 76</td><td>0.47520</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 77</td><td>0.47525</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 78</td><td>0.47215</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 79</td><td>0.47145</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 80</td><td>0.46060</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 81</td><td>0.47125</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 82</td><td>0.46675</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 83</td><td>0.45785</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 84</td><td>0.47190</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 85</td><td>0.46900</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 86</td><td>0.47060</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 87</td><td>0.47125</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 88</td><td>0.47010</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 89</td><td>0.46390</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 90</td><td>0.46085</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 91</td><td>0.46985</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 92</td><td>0.47045</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 93</td><td>0.46770</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 94</td><td>0.47255</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 95</td><td>0.46675</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 96</td><td>0.47325</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 97</td><td>0.47070</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 98</td><td>0.47320</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td> 99</td><td>0.46785</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td>100</td><td>0.47245</td><td>0</td><td>2</td></tr>\n",
              "\t<tr><td>101</td><td>0.47585</td><td>0</td><td>2</td></tr>\n",
              "</tbody>\n",
              "</table>\n"
            ],
            "text/markdown": "\nA data.frame: 101 × 4\n\n| x &lt;int&gt; | mean &lt;dbl&gt; | lower &lt;dbl&gt; | upper &lt;dbl&gt; |\n|---|---|---|---|\n|  1 | 0.02260 | 0 | 0.000 |\n|  2 | 0.02250 | 0 | 0.000 |\n|  3 | 0.02320 | 0 | 0.000 |\n|  4 | 0.02360 | 0 | 0.000 |\n|  5 | 0.02485 | 0 | 0.000 |\n|  6 | 0.02245 | 0 | 0.000 |\n|  7 | 0.02395 | 0 | 0.000 |\n|  8 | 0.02545 | 0 | 0.025 |\n|  9 | 0.02600 | 0 | 1.000 |\n| 10 | 0.02585 | 0 | 1.000 |\n| 11 | 0.02880 | 0 | 1.000 |\n| 12 | 0.03550 | 0 | 1.000 |\n| 13 | 0.04380 | 0 | 1.000 |\n| 14 | 0.06075 | 0 | 1.000 |\n| 15 | 0.09510 | 0 | 1.000 |\n| 16 | 0.15565 | 0 | 1.000 |\n| 17 | 0.25775 | 0 | 2.000 |\n| 18 | 0.42415 | 0 | 2.000 |\n| 19 | 0.67250 | 0 | 3.000 |\n| 20 | 1.01055 | 0 | 4.000 |\n| 21 | 1.40205 | 0 | 5.000 |\n| 22 | 1.80255 | 0 | 5.000 |\n| 23 | 2.14475 | 0 | 6.000 |\n| 24 | 2.43105 | 0 | 6.000 |\n| 25 | 2.62915 | 0 | 6.000 |\n| 26 | 2.75705 | 0 | 6.000 |\n| 27 | 2.80970 | 0 | 7.000 |\n| 28 | 2.85610 | 0 | 7.000 |\n| 29 | 2.90440 | 0 | 7.000 |\n| 30 | 2.88775 | 0 | 7.000 |\n| ⋮ | ⋮ | ⋮ | ⋮ |\n|  72 | 0.59675 | 0 | 3 |\n|  73 | 0.54840 | 0 | 2 |\n|  74 | 0.51150 | 0 | 2 |\n|  75 | 0.48780 | 0 | 2 |\n|  76 | 0.47520 | 0 | 2 |\n|  77 | 0.47525 | 0 | 2 |\n|  78 | 0.47215 | 0 | 2 |\n|  79 | 0.47145 | 0 | 2 |\n|  80 | 0.46060 | 0 | 2 |\n|  81 | 0.47125 | 0 | 2 |\n|  82 | 0.46675 | 0 | 2 |\n|  83 | 0.45785 | 0 | 2 |\n|  84 | 0.47190 | 0 | 2 |\n|  85 | 0.46900 | 0 | 2 |\n|  86 | 0.47060 | 0 | 2 |\n|  87 | 0.47125 | 0 | 2 |\n|  88 | 0.47010 | 0 | 2 |\n|  89 | 0.46390 | 0 | 2 |\n|  90 | 0.46085 | 0 | 2 |\n|  91 | 0.46985 | 0 | 2 |\n|  92 | 0.47045 | 0 | 2 |\n|  93 | 0.46770 | 0 | 2 |\n|  94 | 0.47255 | 0 | 2 |\n|  95 | 0.46675 | 0 | 2 |\n|  96 | 0.47325 | 0 | 2 |\n|  97 | 0.47070 | 0 | 2 |\n|  98 | 0.47320 | 0 | 2 |\n|  99 | 0.46785 | 0 | 2 |\n| 100 | 0.47245 | 0 | 2 |\n| 101 | 0.47585 | 0 | 2 |\n\n",
            "text/latex": "A data.frame: 101 × 4\n\\begin{tabular}{llll}\n x & mean & lower & upper\\\\\n <int> & <dbl> & <dbl> & <dbl>\\\\\n\\hline\n\t  1 & 0.02260 & 0 & 0.000\\\\\n\t  2 & 0.02250 & 0 & 0.000\\\\\n\t  3 & 0.02320 & 0 & 0.000\\\\\n\t  4 & 0.02360 & 0 & 0.000\\\\\n\t  5 & 0.02485 & 0 & 0.000\\\\\n\t  6 & 0.02245 & 0 & 0.000\\\\\n\t  7 & 0.02395 & 0 & 0.000\\\\\n\t  8 & 0.02545 & 0 & 0.025\\\\\n\t  9 & 0.02600 & 0 & 1.000\\\\\n\t 10 & 0.02585 & 0 & 1.000\\\\\n\t 11 & 0.02880 & 0 & 1.000\\\\\n\t 12 & 0.03550 & 0 & 1.000\\\\\n\t 13 & 0.04380 & 0 & 1.000\\\\\n\t 14 & 0.06075 & 0 & 1.000\\\\\n\t 15 & 0.09510 & 0 & 1.000\\\\\n\t 16 & 0.15565 & 0 & 1.000\\\\\n\t 17 & 0.25775 & 0 & 2.000\\\\\n\t 18 & 0.42415 & 0 & 2.000\\\\\n\t 19 & 0.67250 & 0 & 3.000\\\\\n\t 20 & 1.01055 & 0 & 4.000\\\\\n\t 21 & 1.40205 & 0 & 5.000\\\\\n\t 22 & 1.80255 & 0 & 5.000\\\\\n\t 23 & 2.14475 & 0 & 6.000\\\\\n\t 24 & 2.43105 & 0 & 6.000\\\\\n\t 25 & 2.62915 & 0 & 6.000\\\\\n\t 26 & 2.75705 & 0 & 6.000\\\\\n\t 27 & 2.80970 & 0 & 7.000\\\\\n\t 28 & 2.85610 & 0 & 7.000\\\\\n\t 29 & 2.90440 & 0 & 7.000\\\\\n\t 30 & 2.88775 & 0 & 7.000\\\\\n\t ⋮ & ⋮ & ⋮ & ⋮\\\\\n\t  72 & 0.59675 & 0 & 3\\\\\n\t  73 & 0.54840 & 0 & 2\\\\\n\t  74 & 0.51150 & 0 & 2\\\\\n\t  75 & 0.48780 & 0 & 2\\\\\n\t  76 & 0.47520 & 0 & 2\\\\\n\t  77 & 0.47525 & 0 & 2\\\\\n\t  78 & 0.47215 & 0 & 2\\\\\n\t  79 & 0.47145 & 0 & 2\\\\\n\t  80 & 0.46060 & 0 & 2\\\\\n\t  81 & 0.47125 & 0 & 2\\\\\n\t  82 & 0.46675 & 0 & 2\\\\\n\t  83 & 0.45785 & 0 & 2\\\\\n\t  84 & 0.47190 & 0 & 2\\\\\n\t  85 & 0.46900 & 0 & 2\\\\\n\t  86 & 0.47060 & 0 & 2\\\\\n\t  87 & 0.47125 & 0 & 2\\\\\n\t  88 & 0.47010 & 0 & 2\\\\\n\t  89 & 0.46390 & 0 & 2\\\\\n\t  90 & 0.46085 & 0 & 2\\\\\n\t  91 & 0.46985 & 0 & 2\\\\\n\t  92 & 0.47045 & 0 & 2\\\\\n\t  93 & 0.46770 & 0 & 2\\\\\n\t  94 & 0.47255 & 0 & 2\\\\\n\t  95 & 0.46675 & 0 & 2\\\\\n\t  96 & 0.47325 & 0 & 2\\\\\n\t  97 & 0.47070 & 0 & 2\\\\\n\t  98 & 0.47320 & 0 & 2\\\\\n\t  99 & 0.46785 & 0 & 2\\\\\n\t 100 & 0.47245 & 0 & 2\\\\\n\t 101 & 0.47585 & 0 & 2\\\\\n\\end{tabular}\n",
            "text/plain": [
              "    x   mean    lower upper\n",
              "1    1  0.02260 0     0.000\n",
              "2    2  0.02250 0     0.000\n",
              "3    3  0.02320 0     0.000\n",
              "4    4  0.02360 0     0.000\n",
              "5    5  0.02485 0     0.000\n",
              "6    6  0.02245 0     0.000\n",
              "7    7  0.02395 0     0.000\n",
              "8    8  0.02545 0     0.025\n",
              "9    9  0.02600 0     1.000\n",
              "10  10  0.02585 0     1.000\n",
              "11  11  0.02880 0     1.000\n",
              "12  12  0.03550 0     1.000\n",
              "13  13  0.04380 0     1.000\n",
              "14  14  0.06075 0     1.000\n",
              "15  15  0.09510 0     1.000\n",
              "16  16  0.15565 0     1.000\n",
              "17  17  0.25775 0     2.000\n",
              "18  18  0.42415 0     2.000\n",
              "19  19  0.67250 0     3.000\n",
              "20  20  1.01055 0     4.000\n",
              "21  21  1.40205 0     5.000\n",
              "22  22  1.80255 0     5.000\n",
              "23  23  2.14475 0     6.000\n",
              "24  24  2.43105 0     6.000\n",
              "25  25  2.62915 0     6.000\n",
              "26  26  2.75705 0     6.000\n",
              "27  27  2.80970 0     7.000\n",
              "28  28  2.85610 0     7.000\n",
              "29  29  2.90440 0     7.000\n",
              "30  30  2.88775 0     7.000\n",
              "⋮   ⋮   ⋮       ⋮     ⋮    \n",
              "72   72 0.59675 0     3    \n",
              "73   73 0.54840 0     2    \n",
              "74   74 0.51150 0     2    \n",
              "75   75 0.48780 0     2    \n",
              "76   76 0.47520 0     2    \n",
              "77   77 0.47525 0     2    \n",
              "78   78 0.47215 0     2    \n",
              "79   79 0.47145 0     2    \n",
              "80   80 0.46060 0     2    \n",
              "81   81 0.47125 0     2    \n",
              "82   82 0.46675 0     2    \n",
              "83   83 0.45785 0     2    \n",
              "84   84 0.47190 0     2    \n",
              "85   85 0.46900 0     2    \n",
              "86   86 0.47060 0     2    \n",
              "87   87 0.47125 0     2    \n",
              "88   88 0.47010 0     2    \n",
              "89   89 0.46390 0     2    \n",
              "90   90 0.46085 0     2    \n",
              "91   91 0.46985 0     2    \n",
              "92   92 0.47045 0     2    \n",
              "93   93 0.46770 0     2    \n",
              "94   94 0.47255 0     2    \n",
              "95   95 0.46675 0     2    \n",
              "96   96 0.47325 0     2    \n",
              "97   97 0.47070 0     2    \n",
              "98   98 0.47320 0     2    \n",
              "99   99 0.46785 0     2    \n",
              "100 100 0.47245 0     2    \n",
              "101 101 0.47585 0     2    "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ggplot(case_data, aes(x = x, y = mean)) +\n",
        "  geom_line() +\n",
        "  geom_ribbon(aes(ymin = lower, ymax = upper), alpha = 0.2) +\n",
        "  theme_minimal() +\n",
        "  labs(title = \"case Estimates with 95% CI\",\n",
        "       x = \"date\",\n",
        "       y = \"case count\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 377
        },
        "id": "TIsgDHG6QcNN",
        "outputId": "05c1ad6f-5bb9-4c9b-a97a-807bbf5f437c"
      },
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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QCWAlgOYCmA5QCWAlhBAMsBLAWwHMBS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}