{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "CmdStan path set to: /mnt/d/nlint/Dropbox/Programs/cmdstan\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "'2.26.0'"
      ],
      "text/latex": [
       "'2.26.0'"
      ],
      "text/markdown": [
       "'2.26.0'"
      ],
      "text/plain": [
       "[1] \"2.26.0\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Packages\n",
    "libs = c('dplyr','magrittr','tidyr','readxl','MASS','lubridate','openxlsx','scales','data.table',\n",
    "         'ggplot2','viridis','gridExtra',\n",
    "         'loo','StanHeaders','cmdstanr')\n",
    "for (x in libs) {library(x, character.only = T, warn.conflicts = F)}\n",
    "set_cmdstan_path('/mnt/d/nlint/Dropbox/Programs/cmdstan')\n",
    "cmdstan_version()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load datasets\n",
    "clusters_info <- readRDS(\"../data/clusters_info.rds\")\n",
    "clusters_df <- readRDS(\"../data/clusters_df.rds\")\n",
    "key <- readRDS(\"../data/key.rds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Establish reference date and values\n",
    "t0 = as.Date(\"2020-01-01\")\n",
    "daystocalc = 14*3\n",
    "first_onset_date <- clusters_info %>% pull(firstonset); names(first_onset_date) <- key\n",
    "last_report_date <- clusters_info %>% pull(lastreport); names(last_report_date) <- key\n",
    "last_report_day <- as.integer(last_report_date - t0); names(last_report_day) <- key\n",
    "calc_overall_end_date <- last_report_date + daystocalc - 1; names(calc_overall_end_date) <- key\n",
    "calc_overall_end_day <- as.integer(calc_overall_end_date - t0); names(calc_overall_end_day) <- key\n",
    "\n",
    "# Varied parameters\n",
    "Re = c(0.5, 1.5, 3)\n",
    "k_mu = c(0.11, 0.25, 0.58)\n",
    "k_sigma = c(0.051, 0.191, 0.212)\n",
    "si_mean = c(4.848, 0.610) # mu, sigma\n",
    "si_par1 = c(2.305, 0.439) # mu, sigma\n",
    "q = c(0.2, 0.5) # Underascertainment\n",
    "\n",
    "# Fixed parameters for reporting delay (fit to gamma distribution)\n",
    "# Code for reporting delay shared elsewhere\n",
    "gm_mean <- 7.207005\n",
    "gm_sd <- 4.678002\n",
    "gm_alpha <- (gm_mean/gm_sd)^2\n",
    "gm_beta <- gm_mean/(gm_sd^2)\n",
    "rd_par <- c(gm_alpha, gm_beta)\n",
    "max_poss_underasc = 50\n",
    "y = 50\n",
    "\n",
    "# Fit specs\n",
    "ncores = parallel::detectCores()\n",
    "nchains = 4\n",
    "niter = 2000\n",
    "nwarm = 1000"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model without underascertainment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Compiling Stan program...\n",
      "\n"
     ]
    }
   ],
   "source": [
    "## Model\n",
    "stan_code <- \"functions {\n",
    "    /* discretized Weibull distribution */\n",
    "    vector pweibull(real kappa, real theta, int K) {\n",
    "      vector[K] res;\n",
    "      for (k in 1:K)\n",
    "        res[k] = -expm1(-pow(1.0*k/theta, kappa)); // alt to weibull_lcdf\n",
    "        return append_row(res[1], res[2:K]-res[1:(K-1)]);\n",
    "    }\n",
    "\n",
    "    /* discretized gamma distribution */\n",
    "    vector pgamma(real alpha, real beta, int K) {\n",
    "      vector[K] res;\n",
    "      for (k in 1:K)\n",
    "        res[k] = exp(gamma_lcdf(k | alpha, beta)); // with shape alpha and inverse scale beta\n",
    "        return append_row(res[1], res[2:K]-res[1:(K-1)]);\n",
    "    }\n",
    "\n",
    "    /* vector of convolutions */\n",
    "    // X: vector of first function, Yrev: reversed vector of the second function\n",
    "    // N: length of X and Yrev\n",
    "    // result is vector of length N-1, as the first element equal to zero is omitted\n",
    "    vector convolution(vector X, vector Yrev, int N) {\n",
    "        vector[N-1] res;\n",
    "        res[1] = X[1]*Yrev[N];\n",
    "        for (k in 2:N-1) // 2:N-1 is equivalent to 2:(N-1)\n",
    "            res[k] = dot_product(head(X, k), tail(Yrev, k)); // by definition of the convolution\n",
    "        return res;\n",
    "    }\n",
    "    real positive_half_normal_rng(real mu, real sigma) {\n",
    "      real y = -1;\n",
    "      while (y < 0)\n",
    "        y = normal_rng(mu, sigma);\n",
    "      return y;\n",
    "    }\n",
    "}\n",
    "\n",
    "data {\n",
    "    int<lower = 1> M; // number of cases reported in the cluster\n",
    "    int<lower = 0> onset[M]; // vector of onset times\n",
    "\n",
    "    int<lower = 1> D; // max reporting time\n",
    "    int<lower = 1> Y; // upper limit for the sum for y, in this case: y = {0, ..., Y-1}\n",
    "\n",
    "    // reporting delay parameters\n",
    "       real<lower = 0> rd_par1;\n",
    "       real<lower = 0> rd_par2;\n",
    "\n",
    "    // serial interval parameters\n",
    "       real si_mean_mu;\n",
    "       real<lower = 0> si_mean_sigma;\n",
    "       real si_par1_mu;\n",
    "       real<lower = 0> si_par1_sigma;\n",
    "\n",
    "    // offspring distribution parameters\n",
    "       real<lower = 0> R0_par;\n",
    "       real k_par_mu;\n",
    "       real<lower = 0> k_par_sigma;\n",
    "}\n",
    "\n",
    "generated quantities {\n",
    "    vector[D] Pr; // probability of extinction\n",
    "\n",
    "    // offspring distribution parameter k values\n",
    "       real<lower = 0> k_par = positive_half_normal_rng(k_par_mu, k_par_sigma);\n",
    "\n",
    "    // serial interval parameters\n",
    "       real si_mean = normal_rng(si_mean_mu, si_mean_sigma);\n",
    "       real<lower = 0> si_par1 = normal_rng(si_par1_mu, si_par1_sigma);\n",
    "       real<lower = 0> si_par2 = si_mean/tgamma(1.0 + 1.0 /si_par1);\n",
    "\n",
    "    {\n",
    "       vector[D] ft = pweibull(si_par1, si_par2, D);  // serial interval\n",
    "       vector[D] ht = pgamma(rd_par1, rd_par2, D);    // reporting delay\n",
    "       vector[D] htrev;   // reversed reporting delay , required for convolution()\n",
    "       vector[Y] y;       // vector of indices\n",
    "       vector[Y] py;      // offspring distribution\n",
    "       vector[D-1] conv;  // vector of convolutions\n",
    "\n",
    "        for (t in 1:D)\n",
    "            htrev[t] = ht[D+1-t];\n",
    "        conv = cumulative_sum(convolution(ft, htrev, D));\n",
    "\n",
    "        for (i in 1:Y) {\n",
    "            y[i] = i - 1;\n",
    "            py[i] = exp(neg_binomial_2_lpmf(i - 1 | R0_par, k_par)); // mu, phi\n",
    "        }\n",
    "\n",
    "        for (t in 1:D) {\n",
    "            // if the reporting day t is at least two days following the most recent onset date\n",
    "            // NB: not one day, because of the reporting delay\n",
    "            if (t <= max(onset) + 1)\n",
    "                Pr[t] = 0.0;\n",
    "            else {\n",
    "                real prodsum = 1.0;\n",
    "                for (i in 1:M) {\n",
    "                    int idx = t - onset[i] - 1;\n",
    "                    real cdf = conv[idx];\n",
    "                    prodsum *= sum(py .* exp(y * log(cdf)));\n",
    "                }\n",
    "                Pr[t] = 1.0 - prodsum;\n",
    "            }\n",
    "        }\n",
    "    }\n",
    "}\"\n",
    "stan_file = write_stan_file(stan_code)\n",
    "\n",
    "# Compile model\n",
    "mod = cmdstan_model(stan_file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1] \"2021-03-04 10:09:45 JST\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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    }
   ],
   "source": [
    "prnew = list()\n",
    "\n",
    "(calc_t1 <- Sys.time())\n",
    "\n",
    "key <- readRDS(\"../data/key.rds\")\n",
    "\n",
    "for (cl in key) {\n",
    "    \n",
    "    R_loop_prnew <- NULL\n",
    "    \n",
    "    for (r in seq_along(Re)) {\n",
    "    \n",
    "        k_loop_prnew <- NULL\n",
    "\n",
    "        for (k in seq_along(k_mu)) {\n",
    "    \n",
    "            ## Put data in list\n",
    "            dat <- clusters_df %>% filter(cluster==cl)\n",
    "            onsets <- dat %>% filter(!is.na(onset)) %>% dplyr::select(onset) %>% pull()\n",
    "            onsets_imputed <- dat %>% filter(!is.na(onset_imputed)) %>% dplyr::select(onset_imputed) %>% pull()\n",
    "            Re_par = Re[r]\n",
    "            k_par_mu = k_mu[k]\n",
    "            k_par_sigma = k_sigma[k]\n",
    "\n",
    "            data_list = list(\n",
    "                onset = as.integer(onsets - t0),\n",
    "                M = length(onsets),\n",
    "                D = as.integer(last_report_day[cl] + daystocalc + 1),\n",
    "                Y = y,\n",
    "\n",
    "                R0_par = Re_par, \n",
    "                k_par_mu = k_par_mu,\n",
    "                k_par_sigma = k_par_sigma,\n",
    "\n",
    "                si_mean_mu = si_mean[1],\n",
    "                si_mean_sigma = si_mean[2],\n",
    "                si_par1_mu = si_par1[1],\n",
    "                si_par1_sigma = si_par1[2],\n",
    "\n",
    "                rd_par1 = rd_par[1],\n",
    "                rd_par2 = rd_par[2]\n",
    "            )   \n",
    "\n",
    "\n",
    "            ## Compile and fit\n",
    "            fit_reported <- mod$sample(data = data_list,\n",
    "                                     iter_sampling=niter, \n",
    "                                     chains=nchains,\n",
    "                                     parallel_chains=ncores,\n",
    "                                     seed=123,\n",
    "                                     fixed_param=TRUE)\n",
    "\n",
    "            data_list[[\"onset\"]] <- as.integer(onsets_imputed - t0)\n",
    "            data_list[[\"M\"]] <- length(onsets_imputed)\n",
    "            fit_imputed <- mod$sample(data = data_list,\n",
    "                                     iter_sampling=niter, \n",
    "                                     chains=nchains,\n",
    "                                     parallel_chains=ncores,\n",
    "                                     seed=123,\n",
    "                                     fixed_param=TRUE)\n",
    "\n",
    "            # Save results\n",
    "            days <- paste0(\"Pr[\",last_report_day[cl]:calc_overall_end_day[cl],\"]\")\n",
    "            prnew_reported <- data.frame(fit_reported$summary(c(\"Pr\"), ~quantile(.x, probs = c(0.025, 0.5, 0.975)))) %>%\n",
    "                              filter(variable %in% days) %>% rename(lci=2, median=3, uci=4) %>% \n",
    "                              mutate(Re = Re_par, k = k_par_mu, data_type = \"Reported\", cluster = cl, \n",
    "                                     day = seq(last_report_day[cl], calc_overall_end_day[cl], 1), days_since_last_case = row_number()-1)\n",
    "            prnew_imputed  <- data.frame(fit_imputed$summary(c(\"Pr\"), ~quantile(.x, probs = c(0.025, 0.5, 0.975)))) %>%\n",
    "                              filter(variable %in% days) %>% rename(lci=2, median=3, uci=4) %>% \n",
    "                              mutate(Re = Re_par, k = k_par_mu, data_type = \"Imputed\", cluster = cl, \n",
    "                                     day = seq(last_report_day[cl], calc_overall_end_day[cl], 1), days_since_last_case = row_number()-1)\n",
    "            \n",
    "            k_loop_prnew <- bind_rows(k_loop_prnew, prnew_reported, prnew_imputed)\n",
    "            \n",
    "            }\n",
    "\n",
    "        R_loop_prnew <- bind_rows(R_loop_prnew, k_loop_prnew)\n",
    "    \n",
    "      }\n",
    "    \n",
    "    prnew[[cl]] <- R_loop_prnew %>% dplyr::select(-variable)\n",
    "    \n",
    "}\n",
    "    \n",
    "print(Sys.time() - calc_t1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Compiling Stan program...\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Model with underascertainment\n",
    "stan_code <- \"functions {\n",
    "    /* discretized Weibull distribution */\n",
    "    vector pweibull(real kappa, real theta, int N) {\n",
    "      vector[N] res;\n",
    "      for (k in 1:N)\n",
    "        res[k] = -expm1(-pow(1.0*k/theta, kappa)); // instead of using Stan function weibull_lcdf it is easier to write it directly\n",
    "        return append_row(res[1], res[2:N]-res[1:(N-1)]);\n",
    "    }\n",
    "\n",
    "    /* discretized gamma distribution */\n",
    "    vector pgamma(real alpha, real beta, int K) {\n",
    "      vector[K] res;\n",
    "      for (k in 1:K)\n",
    "        res[k] = exp(gamma_lcdf(k | alpha, beta)); // with shape alpha and inverse scale beta\n",
    "        return append_row(res[1], res[2:K]-res[1:(K-1)]);\n",
    "    }\n",
    "\n",
    "    /* vector of convolutions */\n",
    "    // X: first function, Yrev: reversed version of the second function\n",
    "    // N: length of X and Yrev\n",
    "    vector convolution(vector X, vector Yrev, int N) {\n",
    "        vector[N-1] res;\n",
    "        res[1] = X[1]*Yrev[N];\n",
    "        for (k in 2:N-1) // 2:N-1 is equivalent to 2:(N-1)\n",
    "            res[k] = dot_product(head(X, k), tail(Yrev, k)); // by definition of the convolution\n",
    "        return append_row(0.0, res);\n",
    "    }\n",
    "\n",
    "    real positive_half_normal_rng(real mu, real sigma) {\n",
    "      real y = -1;\n",
    "      while (y < 0)\n",
    "        y = normal_rng(mu, sigma);\n",
    "      return y;\n",
    "    }\n",
    "}\n",
    "\n",
    "data {\n",
    "    int<lower = 1> D; // number days in the epicurve\n",
    "    int day[D]; // vector of days in the epicurve\n",
    "    int<lower = 0> cases[D]; // number of cases with onsets on that day\n",
    "\n",
    "    int<lower = 1> Dmax; // maximal reporting time\n",
    "    int<lower = 1> Y; // upper limit for the sum for y, in this case: y = {0, ..., Y-1}\n",
    "\n",
    "    int<lower = 1> Umax;\n",
    "\n",
    "    // reporting delay parameters\n",
    "    real<lower = 0> rd_par1;\n",
    "    real<lower = 0> rd_par2;\n",
    "\n",
    "    // serial interval parameters\n",
    "    real si_mean_mu;\n",
    "    real<lower = 0> si_mean_sigma;\n",
    "    real si_par1_mu;\n",
    "    real<lower = 0> si_par1_sigma;\n",
    "\n",
    "    real k_par_mu;\n",
    "    real<lower = 0> k_par_sigma;\n",
    "\n",
    "    // offspring distribution parameters\n",
    "    real<lower = 0> Re_par;\n",
    "\n",
    "    // underascertainment rate\n",
    "    real<lower = 0, upper = 1> q;\n",
    "}\n",
    "\n",
    "transformed data {\n",
    "    int max_onset_in_reported_cases;\n",
    "    for (d in 1:D)\n",
    "        if (cases[d] > 0)\n",
    "            max_onset_in_reported_cases = d;\n",
    "}\n",
    "\n",
    "parameters {\n",
    "    simplex[Umax] lambda[D];\n",
    "}\n",
    "\n",
    "model {\n",
    "    vector[Umax] log_lambda[D];\n",
    "    vector[Umax] lps;\n",
    "    for (d in 1:D)\n",
    "        log_lambda[d] = log(lambda[d]);\n",
    "\n",
    "    for (d in  1:D) {\n",
    "        lps = log_lambda[d];\n",
    "        for (U in 1:Umax)\n",
    "            lps[U] += binomial_lpmf(cases[d] | cases[d] + U - 1, 1.0 - q);\n",
    "        target += log_sum_exp(lps);\n",
    "    }\n",
    "}\n",
    "\n",
    "generated quantities {\n",
    "    real Pr[D]; // probability of extinction\n",
    "\n",
    "    int unreported_cases[D];\n",
    "    vector[Umax] w[D];\n",
    "    {\n",
    "        int comp;\n",
    "        vector[Umax] lps;\n",
    "        int M = 0;\n",
    "        int total_cases[D] = cases;\n",
    "        for (d in 1:D) {\n",
    "            lps = log(lambda[d]);\n",
    "            for (U in 1:Umax)\n",
    "                lps[U] += binomial_lpmf(cases[d] | cases[d] + U - 1, 1.0 - q);\n",
    "            w[d] = exp(lps - log_sum_exp(lps));\n",
    "            comp = categorical_rng(w[d]);\n",
    "            // if we assume that the underascertained cases can be only within the generation time interval of the latest case\n",
    "            total_cases[d] += (d <= max_onset_in_reported_cases + 5) ? comp - 1 : 0;\n",
    "            // otherwise\n",
    "            // total_cases[d] += comp - 1;\n",
    "            M += total_cases[d];\n",
    "        }\n",
    "\n",
    "        // for our procedure below we need to have a vector of onset times not vector of incidence per day\n",
    "        int onset[M];\n",
    "        int kk = 0;\n",
    "        for (d in 1:D)\n",
    "            for (case_ in 1:total_cases[d]) {\n",
    "                kk += 1;\n",
    "                onset[kk] = d;\n",
    "            }\n",
    "        int max_onset = max(onset);\n",
    "\n",
    "        // offspring distribution parameter k values\n",
    "           real k_par = positive_half_normal_rng(k_par_mu, k_par_sigma);\n",
    "\n",
    "        // serial interval parameters\n",
    "           real si_mean = positive_half_normal_rng(si_mean_mu, si_mean_sigma);\n",
    "           real si_par1 = positive_half_normal_rng(si_par1_mu, si_par1_sigma);\n",
    "           real si_par2 = si_mean / tgamma(1.0 + 1.0 / si_par1);\n",
    "\n",
    "        vector[D] ft = pweibull(si_par1, si_par2, D); // serial interval\n",
    "        vector[D] ht = pgamma(rd_par1, rd_par2, D); // reporting delay\n",
    "        vector[D] htrev; // reversed reporting delay, required for convolution()\n",
    "        for (d in 1:D)\n",
    "            htrev[d] = ht[D + 1 - d];\n",
    "        vector[D] conv = cumulative_sum(convolution(ft, htrev, D)); // vector of convolutions\n",
    "\n",
    "        vector[Y] y; // vector of indices\n",
    "        vector[Y] log_py; // offspring distribution\n",
    "        for (k in 1:Y) {\n",
    "            y[k] = k - 1;\n",
    "            log_py[k] = neg_binomial_2_lpmf(k - 1 | Re_par, k_par);\n",
    "        }\n",
    "\n",
    "        for (d in 1:D) {\n",
    "            if (d <= max_onset + 1)\n",
    "                Pr[d] = 1.0;\n",
    "            else {\n",
    "                real log_prodsum = 0.0;\n",
    "                int idx; real cdf;\n",
    "                for (i in 1:M) {\n",
    "                    idx = d - onset[i];\n",
    "                    cdf = conv[idx];\n",
    "                    log_prodsum += log_sum_exp(log_py + y * log(cdf));\n",
    "                }\n",
    "                Pr[d] = 1.0 - exp(log_prodsum);\n",
    "            }\n",
    "        }\n",
    "    }\n",
    "}\"\n",
    "stan_file_with_ut = write_stan_file(stan_code)\n",
    "\n",
    "# Compile model\n",
    "mod_with_ut = cmdstan_model(stan_file_with_ut)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1] \"2021-03-04 10:13:48 JST\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "\n",
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      "Mean chain execution time: 131.1 seconds.\n",
      "Total execution time: 131.8 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 4 finished in 131.9 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 131.5 seconds.\n",
      "Total execution time: 132.3 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 132.4 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 131.4 seconds.\n",
      "Total execution time: 132.7 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 1 finished in 131.9 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 131.4 seconds.\n",
      "Total execution time: 132.1 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 131.2 seconds.\n",
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      "Chain 3 finished in 131.5 seconds.\n",
      "Chain 1 finished in 131.7 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 131.4 seconds.\n",
      "Total execution time: 131.9 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
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      "Mean chain execution time: 131.8 seconds.\n",
      "Total execution time: 132.8 seconds.\n",
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      "Chain 4 finished in 131.6 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 131.4 seconds.\n",
      "Total execution time: 132.0 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 4 finished in 131.7 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 131.1 seconds.\n",
      "Total execution time: 132.0 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 131.7 seconds.\n",
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      "Chain 4 finished in 133.5 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 132.7 seconds.\n",
      "Total execution time: 133.8 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 132.2 seconds.\n",
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      "Chain 1 finished in 132.6 seconds.\n",
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      "Chain 4 finished in 133.2 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 132.6 seconds.\n",
      "Total execution time: 133.6 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
      "\n",
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      "\n",
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      "Mean chain execution time: 133.2 seconds.\n",
      "Total execution time: 134.9 seconds.\n",
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      "Chain 1 finished in 134.3 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 132.9 seconds.\n",
      "Total execution time: 134.5 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 4 finished in 132.7 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 132.4 seconds.\n",
      "Total execution time: 133.1 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 133.3 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 132.4 seconds.\n",
      "Total execution time: 133.5 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 133.9 seconds.\n",
      "Chain 1 finished in 134.0 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 133.1 seconds.\n",
      "Total execution time: 134.2 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 131.9 seconds.\n",
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      "Chain 4 finished in 133.8 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 133.0 seconds.\n",
      "Total execution time: 134.1 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 131.6 seconds.\n",
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      "Chain 2 finished in 133.7 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 132.5 seconds.\n",
      "Total execution time: 133.9 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 4 finished in 135.3 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 133.3 seconds.\n",
      "Total execution time: 135.6 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 4 finished in 129.1 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 128.9 seconds.\n",
      "Total execution time: 129.5 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 4 finished in 129.3 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 128.8 seconds.\n",
      "Total execution time: 129.7 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 128.2 seconds.\n",
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      "Chain 4 finished in 129.7 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 129.2 seconds.\n",
      "Total execution time: 130.1 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 128.4 seconds.\n",
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      "Chain 1 finished in 129.2 seconds.\n",
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      "Chain 4 finished in 130.1 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 129.2 seconds.\n",
      "Total execution time: 130.4 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
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      "Mean chain execution time: 128.5 seconds.\n",
      "Total execution time: 129.9 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 130.1 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 129.1 seconds.\n",
      "Total execution time: 130.3 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 131.7 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 130.4 seconds.\n",
      "Total execution time: 131.9 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 1 finished in 130.2 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 129.5 seconds.\n",
      "Total execution time: 130.4 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 128.3 seconds.\n",
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      "Chain 4 finished in 132.1 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 130.3 seconds.\n",
      "Total execution time: 132.4 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
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      "Mean chain execution time: 133.7 seconds.\n",
      "Total execution time: 135.4 seconds.\n",
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      "Chain 2 finished in 134.7 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 133.3 seconds.\n",
      "Total execution time: 134.9 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 1 finished in 133.8 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 133.2 seconds.\n",
      "Total execution time: 134.0 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 134.0 seconds.\n",
      "Chain 3 finished in 134.1 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 133.3 seconds.\n",
      "Total execution time: 134.4 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 134.1 seconds.\n",
      "Total execution time: 136.1 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 4 finished in 132.4 seconds.\n",
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      "Chain 3 finished in 134.5 seconds.\n",
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      "Chain 1 finished in 138.2 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 134.9 seconds.\n",
      "Total execution time: 138.4 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 132.7 seconds.\n",
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      "Chain 4 finished in 133.1 seconds.\n",
      "Chain 1 finished in 133.3 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 133.0 seconds.\n",
      "Total execution time: 133.5 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 133.0 seconds.\n",
      "Total execution time: 133.7 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 133.3 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 132.8 seconds.\n",
      "Total execution time: 133.6 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 4 finished in 138.8 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 138.2 seconds.\n",
      "Total execution time: 139.1 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 137.0 seconds.\n",
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      "Chain 2 finished in 138.4 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 137.6 seconds.\n",
      "Total execution time: 138.6 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 137.0 seconds.\n",
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      "Chain 2 finished in 138.6 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 137.8 seconds.\n",
      "Total execution time: 138.8 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
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      "Mean chain execution time: 137.7 seconds.\n",
      "Total execution time: 138.4 seconds.\n",
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      "Chain 2 finished in 140.2 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 139.1 seconds.\n",
      "Total execution time: 140.4 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 1 finished in 140.2 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 138.1 seconds.\n",
      "Total execution time: 140.4 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 138.2 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 137.7 seconds.\n",
      "Total execution time: 138.4 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 136.9 seconds.\n",
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      "Chain 2 finished in 139.4 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 138.1 seconds.\n",
      "Total execution time: 139.6 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 137.7 seconds.\n",
      "Total execution time: 138.4 seconds.\n",
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      "Chain 1 finished in 142.4 seconds.\n",
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      "Chain 4 finished in 143.0 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 142.6 seconds.\n",
      "Total execution time: 143.3 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 143.8 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 142.6 seconds.\n",
      "Total execution time: 144.0 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 142.5 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 141.7 seconds.\n",
      "Total execution time: 142.6 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 4 finished in 141.3 seconds.\n",
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      "Chain 1 finished in 142.1 seconds.\n",
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      "Chain 2 finished in 143.4 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 142.2 seconds.\n",
      "Total execution time: 143.6 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
      "\n",
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      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 143.0 seconds.\n",
      "Total execution time: 144.0 seconds.\n",
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      "Chain 2 finished in 141.9 seconds.\n",
      "Chain 3 finished in 141.8 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 141.6 seconds.\n",
      "Total execution time: 142.1 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 142.0 seconds.\n",
      "Total execution time: 144.2 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 143.6 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 142.6 seconds.\n",
      "Total execution time: 143.9 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 142.2 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 141.7 seconds.\n",
      "Total execution time: 142.5 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 1 finished in 150.0 seconds.\n",
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      "Chain 2 finished in 151.2 seconds.\n",
      "Chain 4 finished in 151.1 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 150.6 seconds.\n",
      "Total execution time: 151.5 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 3 finished in 150.3 seconds.\n",
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      "Chain 2 finished in 151.2 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 150.7 seconds.\n",
      "Total execution time: 151.3 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 149.6 seconds.\n",
      "Total execution time: 150.7 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 4 finished in 151.4 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 149.9 seconds.\n",
      "Total execution time: 151.9 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 1 finished in 151.8 seconds.\n",
      "Chain 4 finished in 151.6 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 151.2 seconds.\n",
      "Total execution time: 152.0 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 151.0 seconds.\n",
      "Total execution time: 155.3 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 2 finished in 149.3 seconds.\n",
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      "Chain 1 finished in 149.6 seconds.\n",
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      "Chain 4 finished in 149.8 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 149.5 seconds.\n",
      "Total execution time: 150.1 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 4 finished in 150.9 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 149.9 seconds.\n",
      "Total execution time: 151.3 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 1 finished in 150.4 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 149.6 seconds.\n",
      "Total execution time: 150.6 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 1 finished in 154.9 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 153.9 seconds.\n",
      "Total execution time: 155.1 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 154.1 seconds.\n",
      "Total execution time: 156.4 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Chain 4 finished in 153.4 seconds.\n",
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      "Chain 1 finished in 154.6 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 153.9 seconds.\n",
      "Total execution time: 154.8 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
      "\n",
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      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 156.1 seconds.\n",
      "Total execution time: 160.8 seconds.\n",
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      "Chain 3 finished in 154.9 seconds.\n",
      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 153.8 seconds.\n",
      "Total execution time: 155.3 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
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      "Mean chain execution time: 154.0 seconds.\n",
      "Total execution time: 154.5 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "\n",
      "All 4 chains finished successfully.\n",
      "Mean chain execution time: 154.3 seconds.\n",
      "Total execution time: 157.1 seconds.\n",
      "Running MCMC with 4 chains, at most 48 in parallel...\n",
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      "Time difference of 3.101741 hours\n"
     ]
    }
   ],
   "source": [
    "# Model with underascertainment\n",
    "\n",
    "prnew_with_ut = list()\n",
    "\n",
    "(calc_t1 <- Sys.time())\n",
    "\n",
    "key <- readRDS(\"../data/key.rds\")\n",
    "\n",
    "for (cl in key) {\n",
    "    \n",
    "    df <- clusters_df %>% filter(cluster==cl) %>% count(onset_imputed) %>% rename(date=onset_imputed, n_imp=n) %>%                          ## imputed onsets by day\n",
    "          left_join(clusters_df %>% filter(cluster==cl) %>% count(onset), by=c(\"date\"=\"onset\")) %>%                                         ## reported onsets by day \n",
    "          complete(date = seq.Date(first_onset_date[cl], last_report_date[cl]+daystocalc, by=\"day\")) %>% replace_na(list(n=0, n_imp=0)) %>%  ## add 0 case days\n",
    "          mutate(day = seq(0, as.numeric((last_report_date[cl]+daystocalc)-first_onset_date[cl]), 1)) %>%                                    ## add day d to first onset\n",
    "          rbind(data.frame(date=seq.Date(first_onset_date[cl]-5,first_onset_date[cl]-1, 1), n_imp=0, n=0, day=seq(-5,-1,1))) %>%            ## add 5 day initial buffer\n",
    "          arrange(date)\n",
    "    \n",
    "    q_loop_prnew <- NULL\n",
    "    \n",
    "    for (i in seq_along(q)) {\n",
    "    \n",
    "        R_loop_prnew <- NULL\n",
    "\n",
    "        for (r in seq_along(Re)) {\n",
    "\n",
    "            k_loop_prnew <- NULL\n",
    "\n",
    "            for (k in seq_along(k_mu)) {\n",
    "\n",
    "                Re_par = Re[r]\n",
    "                k_par_mu = k_mu[k]\n",
    "                k_par_sigma = k_sigma[k]\n",
    "\n",
    "\n",
    "                data_list = list(\n",
    "                    D = nrow(df),\n",
    "                    Dmax = max(df$day)+1,\n",
    "                    day = df$day,\n",
    "                    cases = df$n_imp,\n",
    "\n",
    "                    Y = 100,\n",
    "                    Umax = max_poss_underasc,\n",
    "                    q = q[i],\n",
    "\n",
    "                    Re_par = Re_par, \n",
    "                    k_par_mu = k_par_mu,\n",
    "                    k_par_sigma = k_par_sigma,\n",
    "\n",
    "                    si_mean_mu = si_mean[1],\n",
    "                    si_mean_sigma = si_mean[2],\n",
    "                    si_par1_mu = si_par1[1],\n",
    "                    si_par1_sigma = si_par1[2],\n",
    "\n",
    "                    rd_par1 = rd_par[1],\n",
    "                    rd_par2 = rd_par[2]\n",
    "                )\n",
    "\n",
    "                ## Fit model\n",
    "                fit <- mod_with_ut$sample(data = data_list, \n",
    "                                     iter_sampling=niter, \n",
    "                                     iter_warmup=nwarm, \n",
    "                                     chains=nchains,\n",
    "                                     parallel_chains=ncores,\n",
    "                                     save_warmup = TRUE,\n",
    "                                     seed=123)\n",
    "\n",
    "                # Save results\n",
    "                days_lower <- df %>% filter(date==last_report_date[cl]) %>% pull(day)\n",
    "                max_calc <- nrow(fit$summary(c(\"Pr\")))\n",
    "                max_poss <- days_lower+daystocalc+1\n",
    "                days_range <- seq(days_lower+1, ifelse(max_calc<max_poss, max_calc, max_poss), 1)\n",
    "                days <- paste0(\"Pr[\",days_range,\"]\")\n",
    "                prnew_ut <- data.frame(fit$summary(c(\"Pr\"), ~quantile(.x, probs = c(0.025, 0.5, 0.975)))) %>%\n",
    "                               filter(variable %in% days) %>% rename(lci=2, median=3, uci=4) %>% \n",
    "                               mutate(Re = Re_par, k = k_par_mu, data_type = sprintf(\"%i%% underascertainment\", q[i]*100), cluster = cl, \n",
    "                                      day = days_range, days_since_last_case = row_number()-1) %>% dplyr::select(-variable)\n",
    "\n",
    "                k_loop_prnew <- bind_rows(k_loop_prnew, prnew_ut)\n",
    "\n",
    "                }\n",
    "\n",
    "            R_loop_prnew <- bind_rows(R_loop_prnew, k_loop_prnew)\n",
    "\n",
    "            }\n",
    "\n",
    "        q_loop_prnew <- bind_rows(q_loop_prnew, R_loop_prnew)\n",
    "\n",
    "        }\n",
    "    \n",
    "    prnew_with_ut[[cl]] <- q_loop_prnew\n",
    "    \n",
    "}\n",
    "    \n",
    "print(Sys.time() - calc_t1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_prnew <- bind_rows(rbindlist(prnew), rbindlist(prnew_with_ut))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "saveRDS(all_prnew, \"../results/prnew.rds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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