HMM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stan\n",
    "Using the statistical modelling software stan (here its Python interface Pystan) to use the PMCMC algorithm to solve the SARS-CoV-2 model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pystan\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "import sys\n",
    "sys.path.append('utils')\n",
    "from utils.model import *\n",
    "\n",
    "sns.set()  # Nice plot aesthetic\n",
    "np.random.seed(101)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Define the model in stan\n",
    "Structure:\n",
    "\n",
    "1. functions:  external functions needed (here: differential equation)\n",
    "2. data:                    all the data including observations, time and known parameters\n",
    "3. tranformed data:         if the data still needs to be transformed\n",
    "4. parameters:              the parameters (which need to be estimated)\n",
    "5. transformed parameters:  potential transformation of the parameters (here: solve the differential equation)\n",
    "6. model:                   define the probability distributions that define your model\n",
    "7. generated quantities:    in case any other parameters might be needed to be computed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# older model:\n",
    "model = \"\"\"functions {\n",
    "  real[] SEIR(\n",
    "      real t,             // time\n",
    "      matrix[] Z,           // system state {susceptible, exposed, infected, recovered}\n",
    "      real[] theta,       // parameters (t_inc, t_inf, r_t, mu, t_rec, rho = 1, kappa_0, kappa)\n",
    "      real[] X_r,         // --------probably not needed\n",
    "      int[] X_i) {        // --------probably not needed\n",
    "  \n",
    "          real dZ_dt[4];\n",
    "          \n",
    "          real t_inc   = theta[1];\n",
    "          real t_inf   = theta[2];\n",
    "          real r_t     = theta[3];\n",
    "          real rho     = theta[4];\n",
    "          real kappa_0 = theta[5];\n",
    "          real kappa   = theta[6];\n",
    "         \n",
    "          dZ_dt[1] = - rho * (r_t/t_inf) * Z[1] * Z[2]  - kappa_0 * Z[1] ;     \n",
    "          dZ_dt[2] = (rho * (r_t/t_inf) * Z[1] * Z[2])    -     ((1/t_inc) * Z[2]) - kappa_0 * Z[3] - kappa * Z[3]  ;    \n",
    "          dZ_dt[3] = ((1/t_inc) * Z[2]) -   (1/t_inf) * Z[3];\n",
    "          dZ_dt[4] = (1/t_inf) * Z[3];\n",
    "          \n",
    "          return dZ_dt;\n",
    "      }\n",
    "      real[ , ] integrate_SEIR_euler(real[] initial_state,\n",
    "            real initial_time, \n",
    "            int n_steps, real[] theta, \n",
    "            real[] x_r, int[] x_i){\n",
    "           \n",
    "              real Z_hat[n_steps, size(initial_state)];\n",
    "             Z_hat[1,] = initial_state;\n",
    "              for (t in 1:n_steps-1){\n",
    "                  Z_hat[t+1,] = Z_hat[t,] + SEIR(t,Z_hat[t,],theta,x_r,x_i);\n",
    "              }\n",
    "              return Z_hat;\n",
    "     }\n",
    "  }\n",
    "data {\n",
    "\n",
    "  int<lower=0> N;  // num people\n",
    "  int<lower=0> T;  // num instances\n",
    "  int<lower=0> Z_0 // initial number of cases\n",
    "  int<lower=0, upper=N> X[T];// observations\n",
    "  \n",
    "  \n",
    "  int<lower=0> K;   // dimension of Hidden state\n",
    "  \n",
    "  // unsupervised:\n",
    "  //int<lower=0, upper=N> Z[T];\n",
    "}\n",
    "parameters {\n",
    "  real<lower=0, upper = 1> p_inf;\n",
    "  real<lower=0, upper = 1> p_obs;\n",
    "}\n",
    "\n",
    "transformed parameters {\n",
    "  vector[K] logalpha[T];\n",
    "  \n",
    "  { // Forward algorithm log p(z_t = j | y_{1:t})\n",
    "    real accumulator[K];\n",
    "    logalpha[1] = log(pi1) + normal_lpdf(y[1] | mu, sigma);\n",
    "    \n",
    "    for (t in 2:T) {\n",
    "      for (j in 1:K) { // j = current (t)\n",
    "        for (i in 1:K) { // i = previous (t-1)\n",
    "          // Murphy (2012) p. 609 eq. 17.48\n",
    "          // belief state + transition prob + local evidence at t\n",
    "          accumulator[i] = logalpha[t-1, i] + log(A[i, j]) + normal_lpdf(y[t] | mu[j], sigma[j]);\n",
    "        }\n",
    "        logalpha[t, j] = log_sum_exp(accumulator);\n",
    "      }\n",
    "    }\n",
    "  } // Forward\n",
    "}\n",
    "model {\n",
    "  // priors\n",
    "\n",
    "\n",
    "  // forward algorithm\n",
    "  {\n",
    "  real acc[K];\n",
    "  real gamma[N, K];                                  //log marginal probability of the inputs\n",
    "  for (k in 1:K)\n",
    "    gamma[1, k] = Z_0;\n",
    "  for (t in 2:N) {\n",
    "    for (k in 1:K) {\n",
    "      for (j in 1:K)\n",
    "        acc[j] = gamma[t-1, j] + log(theta[j, k]) + normal_lpdf(y[t] | mu[k], 1);\n",
    "      gamma[t, k] = log_sum_exp(acc);\n",
    "    }\n",
    "  }\n",
    "  target += log_sum_exp(gamma[N]);\n",
    "  }\n",
    "\n",
    "\n",
    "  for (t in 2:T)\n",
    "    Z[t] ~ binomial(N-Z[t-1], p_inf); //+  Z[t - 1]\n",
    "  for (t in 1:T)\n",
    "    X[t] ~ neg_binomial(Z[t], p_obs);    // p_obs = probability of observation\n",
    "}\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = \"\"\"functions {\n",
    "  real[] SEIR(\n",
    "      real t,             // time\n",
    "      real[] Z,           // system state {susceptible, exposed, infected, recovered}\n",
    "      real[] theta,       // parameters (t_inc, t_inf, r_t, mu, t_rec, rho = 1, kappa_0, kappa)\n",
    "      real[] X_r,         // --------probably not needed\n",
    "      int[] X_i) {        // --------probably not needed\n",
    "  \n",
    "          real dZ_dt[4];\n",
    "          \n",
    "          real t_inc   = theta[1];\n",
    "          real t_inf   = theta[2];\n",
    "          real r_t     = theta[3];\n",
    "          real rho     = theta[4];\n",
    "          real kappa_0 = theta[5];\n",
    "          real kappa   = theta[6];\n",
    "         \n",
    "          dZ_dt[1] = - rho * (r_t/t_inf) * Z[1] * Z[2]  - kappa_0 * Z[1] ;     \n",
    "          dZ_dt[2] = (rho * (r_t/t_inf) * Z[1] * Z[2])    -     ((1/t_inc) * Z[2]) - kappa_0 * Z[3] - kappa * Z[3]  ;    \n",
    "          dZ_dt[3] = ((1/t_inc) * Z[2]) -   (1/t_inf) * Z[3];\n",
    "          dZ_dt[4] = (1/t_inf) * Z[3];\n",
    "          \n",
    "          return dZ_dt;\n",
    "      }\n",
    "      real[ , ] integrate_SEIR_euler(real[] initial_state,\n",
    "            real initial_time, \n",
    "            int n_steps, real[] theta, \n",
    "            real[] x_r, int[] x_i){\n",
    "           \n",
    "            real dZ_dt[size(initial_state)];\n",
    "            real Z_hat[n_steps, size(initial_state)];\n",
    "            Z_hat[1,] = initial_state;\n",
    "            for (t in 1:n_steps-1){\n",
    "                dZ_dt = SEIR(t,Z_hat[t,],theta,x_r,x_i);\n",
    "                for (i in 1:size(initial_state)){\n",
    "                    Z_hat[t+1,i] = Z_hat[t,i] + dZ_dt[i];\n",
    "                }\n",
    "            }\n",
    "            return Z_hat;\n",
    "     }\n",
    "  }\n",
    "  \n",
    "  data {\n",
    "     int<lower = 1> n_obs;       // number of days observed\n",
    "     int<lower = 1> n_theta;     // number of model parameters (=8)\n",
    "     int<lower = 1> n_difeq;     // number of differential equations (=4)\n",
    "     real<lower = 1> n_pop;      // population \n",
    "     int X[n_obs];               // data, total number of infected individuals each day\n",
    "     real t0;                    // initial time point (zero)\n",
    "     real ts[n_obs];             // time points that were observed\n",
    "     \n",
    "     // known parameters:\n",
    "     real kappa_0;\n",
    "     real kappa;\n",
    "     real p_obs;\n",
    "  }\n",
    "  \n",
    "  transformed data {\n",
    "    real X_r[0];\n",
    "    int X_i[0];\n",
    "  }\n",
    "  \n",
    "  parameters {\n",
    "    // theta:\n",
    "    real<lower=0.1, upper= 50> t_inc;\n",
    "    real<lower=0.1, upper= 50> t_inf;\n",
    "    real<lower=0, upper= 20> r_t;\n",
    "    real<lower=0, upper=1> rho;\n",
    "    \n",
    "    real<lower = 0, upper = 1> S0;  // initial fraction of susceptible individuals\n",
    "    \n",
    "    //real<lower = 0, upper = 1> p_obs;\n",
    "    //real<lower = 0, upper = 1> p_inf;\n",
    "  }\n",
    "  \n",
    "  transformed parameters{\n",
    "    real Z_hat[n_obs, n_difeq];       // solution from the ODE solver\n",
    "    //int Z_i[n_obs, n_difeq];          // integer values\n",
    "    real Z_init[n_difeq];             // initial conditions for both fractions of S and I\n",
    "    \n",
    "    real theta[n_theta];\n",
    "    theta[1] = t_inc;\n",
    "    theta[2] = t_inf;\n",
    "    theta[3] = r_t;\n",
    "    theta[4] = rho;\n",
    "    theta[5] = kappa_0;\n",
    "    theta[6] = kappa;\n",
    "\n",
    "    //Z_init[1] = S0 ;\n",
    "    //Z_init[2] = 0;\n",
    "    //Z_init[3] = 1-S0;\n",
    "    //Z_init[4] = 0;\n",
    "    Z_init[1] = S0*n_pop ;\n",
    "    Z_init[2] = 0;\n",
    "    Z_init[3] = (1-S0)*n_pop;\n",
    "    Z_init[4] = 0;\n",
    "    \n",
    "    //Z_hat = integrate_ode_rk45(SEIR, Z_init, t0, ts, theta, X_r, X_i);\n",
    "    Z_hat = integrate_SEIR_euler( Z_init, t0, n_obs, theta, X_r, X_i);\n",
    "    \n",
    "  }\n",
    "  \n",
    "  model {\n",
    "  \n",
    "    //priors\n",
    "    //theta[1] ~ lognormal(0,1);\n",
    "    //theta[2] ~ gamma(0.004,0.02);  //Assume mean infectious period = 5 days \n",
    "    t_inc ~ normal(5, 0.5);\n",
    "    t_inf ~ normal(9, 0.5);\n",
    "    r_t   ~ normal(2.5, 1);\n",
    "    rho   ~ beta(0.5, 0.5);\n",
    "\n",
    "    S0 ~ beta(0.5, 0.5);\n",
    "  \n",
    "    \n",
    "    //likelihood\n",
    "    X ~ neg_binomial(to_vector(Z_hat[,3])+0.1, p_obs);\n",
    "    // X ~ neg_binomial(to_vector(Z_hat[,3])*n_pop, p_obs);\n",
    "    \n",
    "  }\n",
    "  \n",
    "  //generated quantities {\n",
    "  //real R_0;      // Basic reproduction number\n",
    "  //R_0 = theta[1]/theta[2];\n",
    "  //}\n",
    "  \"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_df4b9398b0a160ec9e0caf9fbcca0148 NOW.\n"
     ]
    }
   ],
   "source": [
    "# Compile the model\n",
    "sm = pystan.StanModel(model_code=model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The data\n",
    "For now sample the data from an idealistic model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# data generation parameters:\n",
    "n_obs = 150\n",
    "init_inf  = 5\n",
    "t_inc     = 5\n",
    "t_inf     = 9\n",
    "r_t       = 2.5\n",
    "rho       = 1.0\n",
    "\n",
    "kappa_0   = 0.0\n",
    "kappa     = 0.0\n",
    "\n",
    "n_pop     = 2000\n",
    "\n",
    "seir = SEIRModel(n_obs, n_pop, init_inf, t_inc, t_inf, r_t, rho, kappa_0, kappa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Z_RK45 = seir.run('RK45')* n_pop  # Runge Kutta instead of explicit Euler\n",
    "Z = seir.run()* n_pop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# concatenate vectors into matrix:\n",
    "#Z = np.vstack((s, e,i, r)) * n_pop\n",
    "\n",
    "# generate obserations:\n",
    "p_obs     = 0.7\n",
    "def sample_X(n_obs , I , p_obs):\n",
    "    X = np.zeros(n_obs, dtype=int)\n",
    "    for t in range(0, n_obs):\n",
    "        X[t] =  np.random.negative_binomial(I[t], p_obs, size=1) \n",
    "    return X;\n",
    "\n",
    "X         = sample_X(n_obs , Z[:,2] , p_obs)\n",
    "\n",
    "\n",
    "seir.visualization(n_pop, X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# unknown:\n",
    "init_inf  = 5\n",
    "t_inc     = 5\n",
    "t_inf     = 9\n",
    "r_t       = 2.5\n",
    "rho       = 1.0\n",
    "\n",
    "\n",
    "# known:\n",
    "p_obs     = 0.7\n",
    "kappa_0   = 0.0\n",
    "kappa     = 0.0\n",
    "\n",
    "\n",
    "# Put data in a dictionary\n",
    "n_obs     = 150\n",
    "n_theta   = 6\n",
    "n_difeq   = 4\n",
    "n_pop     = 2000\n",
    "ts = np.arange(1,n_obs+1);\n",
    "\n",
    "data = {'n_obs': n_obs, 'n_theta': n_theta, 'n_difeq': n_difeq, 'n_pop':n_pop, 'X': X, 't0': 0, 'ts': ts, 'kappa_0':kappa_0 ,'kappa':kappa, 'p_obs':0.7}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train the model with the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:pystan:n_eff / iter below 0.001 indicates that the effective sample size has likely been overestimated\n",
      "WARNING:pystan:Rhat above 1.1 or below 0.9 indicates that the chains very likely have not mixed\n",
      "WARNING:pystan:76598 of 132668 iterations ended with a divergence (57.7 %).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n",
      "WARNING:pystan:55701 of 132668 iterations saturated the maximum tree depth of 10 (42 %)\n",
      "WARNING:pystan:Run again with max_treedepth larger than 10 to avoid saturation\n",
      "WARNING:pystan:Chain 1: E-BFMI = 3.78e-05\n",
      "WARNING:pystan:Chain 2: E-BFMI = 2.97e-05\n",
      "WARNING:pystan:Chain 3: E-BFMI = 2.34e-07\n",
      "WARNING:pystan:Chain 4: E-BFMI = 3.89e-05\n",
      "WARNING:pystan:E-BFMI below 0.2 indicates you may need to reparameterize your model\n"
     ]
    }
   ],
   "source": [
    "# Train the model and generate samples\n",
    "from tqdm import tqdm \n",
    "iter = 100000 # could be up to 100.000\n",
    "chains = 4   # 4 \n",
    "warmup = 500 # 500 \n",
    "thin = 3 # take every 3rd sample from chain\n",
    "fit = sm.sampling(data=data, iter=iter, chains=chains, warmup=warmup, thin=3, seed=101,verbose=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inference for Stan model: anon_model_df4b9398b0a160ec9e0caf9fbcca0148.\n",
      "4 chains, each with iter=100000; warmup=500; thin=3; \n",
      "post-warmup draws per chain=33167, total post-warmup draws=132668.\n",
      "\n",
      "               mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
      "t_inc         23.35     9.8  15.81   4.15   5.06  36.07  37.69  37.73      3   3.02\n",
      "t_inf         22.71    1.55   4.68  18.01  19.51  21.28  25.59  37.01      9   1.54\n",
      "r_t            9.31    3.91   6.43    0.9   2.49  10.98  16.96  17.34      3   3.17\n",
      "rho            0.22    0.03    0.1   0.03   0.19    0.2   0.25   0.44     15   1.46\n",
      "S0             0.74    0.17   0.27   0.33   0.36   0.82   0.99   0.99      2   3.35\n",
      "Z_hat[1,1]   1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[2,1]   1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[3,1]   1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[4,1]   1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[5,1]   1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[6,1]   1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[7,1]   1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[8,1]   1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[9,1]   1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[10,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[11,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[12,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[13,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[14,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[15,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[16,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[17,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[18,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[19,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[20,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[21,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[22,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[23,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[24,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[25,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[26,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[27,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[28,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[29,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[30,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[31,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[32,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[33,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[34,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[35,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[36,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[37,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[38,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[39,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[40,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[41,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[42,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[43,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[44,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[45,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[46,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[47,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[48,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[49,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[50,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[51,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[52,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[53,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[54,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[55,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[56,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[57,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[58,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[59,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[60,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[61,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[62,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[63,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[64,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[65,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[66,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[67,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[68,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[69,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[70,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[71,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[72,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[73,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[74,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[75,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[76,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[77,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[78,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[79,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[80,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[81,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[82,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[83,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[84,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[85,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[86,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[87,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[88,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[89,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[90,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[91,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[92,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[93,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[94,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[95,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[96,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[97,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[98,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[99,1]  1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[100,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[101,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[102,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[103,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[104,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[105,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[106,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[107,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[108,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[109,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[110,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[111,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[112,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[113,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[114,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[115,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[116,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[117,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[118,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[119,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[120,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[121,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[122,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[123,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[124,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[125,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[126,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[127,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[128,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[129,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[130,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[131,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[132,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[133,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[134,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[135,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[136,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[137,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[138,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[139,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[140,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[141,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[142,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[143,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[144,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[145,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[146,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[147,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[148,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[149,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[150,1] 1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_hat[1,2]      0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "Z_hat[2,2]      0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "Z_hat[3,2]      0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "Z_hat[4,2]      0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "Z_hat[5,2]      0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "Z_hat[6,2]      0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "Z_hat[7,2]      0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "Z_hat[8,2]      0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "Z_hat[9,2]      0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "Z_hat[10,2]     0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
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      "Z_hat[23,3]  199.23  112.83 204.95   7.22   9.21 153.69 463.11 595.68      3   2.28\n",
      "Z_hat[24,3]  190.94  107.08 196.58   6.82   8.73 147.75 441.37 579.58      3   2.25\n",
      "Z_hat[25,3]  183.01   101.6  188.6   6.44   8.29 142.05 420.66 563.92      3   2.21\n",
      "Z_hat[26,3]  175.41   96.38 180.98   6.09   7.86 136.56 400.91 548.69      4   2.18\n",
      "Z_hat[27,3]  168.14   91.41 173.72   5.75   7.46 131.28 382.08 533.86      4   2.15\n",
      "Z_hat[28,3]  161.19   86.69 166.79   5.43   7.07 126.21 364.14 519.44      4   2.12\n",
      "Z_hat[29,3]  154.53   82.18 160.18   5.13   6.71 121.33 347.04 505.41      4   2.09\n",
      "Z_hat[30,3]  148.15    77.9 153.87   4.85   6.36 116.64 330.74 491.75      4   2.06\n",
      "Z_hat[31,3]  142.05   73.81 147.85   4.58   6.04 112.13 315.22 478.47      4   2.04\n",
      "Z_hat[32,3]  136.21   69.93  142.1   4.33   5.73 107.79 300.42 465.54      4   2.01\n",
      "Z_hat[33,3]  130.62   66.22 136.61   4.09   5.43 103.63 286.31 452.96      4   1.98\n",
      "Z_hat[34,3]  125.27    62.7 131.37   3.86   5.15  99.62 272.86 440.73      4   1.96\n",
      "Z_hat[35,3]  120.14   59.34 126.37   3.65   4.89  95.77 260.04 428.82      5   1.93\n",
      "Z_hat[36,3]  115.23   56.15 121.59   3.45   4.64  92.06 247.83 417.23      5   1.91\n",
      "Z_hat[37,3]  110.53   53.11 117.02   3.26    4.4   88.5 236.19 405.96      5   1.89\n",
      "Z_hat[38,3]  106.03   50.26 112.65   3.08   4.17  85.08 225.09 394.99      5   1.87\n",
      "Z_hat[39,3]  101.72   47.63 108.48   2.91   3.96  81.79 214.53 384.32      5   1.85\n",
      "Z_hat[40,3]   97.59   45.18 104.49   2.75   3.76  78.63 204.45 373.94      5   1.83\n",
      "Z_hat[41,3]   93.64   42.91 100.67   2.59   3.56  75.59 194.84 363.84      6   1.81\n",
      "Z_hat[42,3]   89.85   40.78  97.02   2.45   3.38  72.66 185.69 354.01      6   1.79\n",
      "Z_hat[43,3]   86.22   38.79  93.53   2.32   3.21  69.85 176.96 344.44      6   1.77\n",
      "Z_hat[44,3]   82.75   36.92  90.19   2.19   3.04  67.15 168.65 335.14      6   1.76\n",
      "Z_hat[45,3]   79.42   35.17  86.99   2.07   2.89  64.56 160.73 326.08      6   1.74\n",
      "Z_hat[46,3]   76.23   33.52  83.93   1.95   2.74  62.06 153.18 317.27      6   1.72\n",
      "Z_hat[47,3]   73.17   31.96   81.0   1.84    2.6  59.66 145.98  308.7      6   1.71\n",
      "Z_hat[48,3]   70.24   30.48  78.19   1.74   2.46  57.35 139.12 300.36      7   1.69\n",
      "Z_hat[49,3]   67.43   29.09  75.49   1.65   2.34  55.14 132.58 292.24      7   1.68\n",
      "Z_hat[50,3]   64.74   27.77  72.91   1.55   2.22   53.0 126.35 284.35      7   1.67\n",
      "Z_hat[51,3]   62.17   26.52  70.43   1.47    2.1  50.95 120.42 276.67      7   1.65\n",
      "Z_hat[52,3]    59.7   25.34  68.06   1.39    2.0  48.98 114.76 269.19      7   1.64\n",
      "Z_hat[53,3]   57.33   24.22  65.78   1.31   1.89  47.09 109.37 261.92      7   1.63\n",
      "Z_hat[54,3]   55.06   23.16   63.6   1.24    1.8  45.27 104.23 254.84      8   1.62\n",
      "Z_hat[55,3]   52.88   22.16   61.5   1.17    1.7  43.52  99.33 247.96      8   1.61\n",
      "Z_hat[56,3]    50.8   21.21  59.48   1.11   1.62  41.84  94.66 241.26      8    1.6\n",
      "Z_hat[57,3]    48.8   20.31  57.54   1.04   1.53  40.22  90.22 234.74      8   1.59\n",
      "Z_hat[58,3]   46.88   19.46  55.68   0.99   1.46  38.66  85.98  228.4      8   1.58\n",
      "Z_hat[59,3]   45.04   18.65  53.89   0.93   1.38  37.17  81.94 222.23      8   1.57\n",
      "Z_hat[60,3]   43.28   17.89  52.17   0.88   1.31  35.73  78.09 216.22      9   1.56\n",
      "Z_hat[61,3]   41.59   17.17  50.51   0.83   1.24  34.35  74.42 210.38      9   1.55\n",
      "Z_hat[62,3]   39.97   16.48  48.92   0.78   1.18  33.02  70.92  204.7      9   1.54\n",
      "Z_hat[63,3]   38.41   15.83  47.39   0.74   1.12  31.74  67.59 199.17      9   1.53\n",
      "Z_hat[64,3]   36.92   15.21  45.91    0.7   1.06  30.52  64.42 193.79      9   1.53\n",
      "Z_hat[65,3]   35.49   14.63  44.49   0.66   1.01  29.34  61.39 188.55      9   1.52\n",
      "Z_hat[66,3]   34.12   14.07  43.12   0.62   0.96   28.2   58.5 183.46      9   1.51\n",
      "Z_hat[67,3]    32.8   13.54   41.8   0.59   0.91  27.11  55.76  178.5     10   1.51\n",
      "Z_hat[68,3]   31.53   13.04  40.53   0.56   0.86  26.06  53.14 173.68     10    1.5\n",
      "Z_hat[69,3]   30.32   12.56   39.3   0.53   0.82  25.05  50.64 168.99     10   1.49\n",
      "Z_hat[70,3]   29.16    12.1  38.11    0.5   0.77  24.09  48.26 164.42     10   1.49\n",
      "Z_hat[71,3]   28.04   11.67  36.97   0.47   0.73  23.15  45.99 159.98     10   1.48\n",
      "Z_hat[72,3]   26.97   11.26  35.87   0.44    0.7  22.26  43.83 155.66     10   1.48\n",
      "Z_hat[73,3]   25.94   10.86   34.8   0.42   0.66   21.4  41.77 151.45     10   1.47\n",
      "Z_hat[74,3]   24.95   10.49  33.77    0.4   0.63  20.57  39.81 147.36     10   1.47\n",
      "Z_hat[75,3]   24.01   10.13  32.78   0.37   0.59  19.77  37.94 143.38     10   1.47\n",
      "Z_hat[76,3]    23.1    9.79  31.82   0.35   0.56  19.01  36.16 139.51     11   1.46\n",
      "Z_hat[77,3]   22.22    9.46  30.89   0.33   0.54  18.27  34.46 135.74     11   1.46\n",
      "Z_hat[78,3]   21.38    9.15  29.99   0.32   0.51  17.57  32.84 132.07     11   1.45\n",
      "Z_hat[79,3]   20.58    8.85  29.13    0.3   0.48  16.89   31.3  128.5     11   1.45\n",
      "Z_hat[80,3]   19.81    8.56  28.29   0.28   0.46  16.24  29.82 125.03     11   1.45\n",
      "Z_hat[81,3]   19.06    8.29  27.47   0.27   0.43  15.61  28.42 121.65     11   1.44\n",
      "Z_hat[82,3]   18.35    8.03  26.69   0.25   0.41   15.0  27.09 118.37     11   1.44\n",
      "Z_hat[83,3]   17.66    7.77  25.92   0.24   0.39  14.42  25.82 115.17     11   1.44\n",
      "Z_hat[84,3]   17.01    7.53  25.19   0.22   0.37  13.87   24.6 112.06     11   1.44\n",
      "Z_hat[85,3]   16.37     7.3  24.47   0.21   0.35  13.33  23.45 109.03     11   1.43\n",
      "Z_hat[86,3]   15.77    7.07  23.78    0.2   0.33  12.81  22.34 106.08     11   1.43\n",
      "Z_hat[87,3]   15.18    6.86  23.11   0.19   0.32  12.32  21.29 103.22     11   1.43\n",
      "Z_hat[88,3]   14.62    6.65  22.46   0.18    0.3  11.84  20.29 100.43     11   1.43\n",
      "Z_hat[89,3]   14.08    6.45  21.83   0.17   0.28  11.38  19.34  97.72     11   1.43\n",
      "Z_hat[90,3]   13.56    6.26  21.22   0.16   0.27  10.94  18.43  95.08     11   1.42\n",
      "Z_hat[91,3]   13.07    6.07  20.63   0.15   0.26  10.52  17.57  92.51     12   1.42\n",
      "Z_hat[92,3]   12.59     5.9  20.06   0.14   0.24  10.11  16.74  90.01     12   1.42\n",
      "Z_hat[93,3]   12.13    5.72   19.5   0.13   0.23   9.72  15.95  87.58     12   1.42\n",
      "Z_hat[94,3]   11.69    5.56  18.96   0.13   0.22   9.35   15.2  85.21     12   1.42\n",
      "Z_hat[95,3]   11.26     5.4  18.43   0.12   0.21   8.99  14.49  82.91     12   1.42\n",
      "Z_hat[96,3]   10.85    5.24  17.93   0.11    0.2   8.64  13.81  80.67     12   1.41\n",
      "Z_hat[97,3]   10.46    5.09  17.43   0.11   0.19    8.3  13.16  78.49     12   1.41\n",
      "Z_hat[98,3]   10.08    4.95  16.95    0.1   0.18   7.98  12.54  76.37     12   1.41\n",
      "Z_hat[99,3]    9.72    4.81  16.49    0.1   0.17   7.67  11.95   74.3     12   1.41\n",
      "Z_hat[100,3]   9.37    4.67  16.04   0.09   0.16   7.38  11.39   72.3     12   1.41\n",
      "Z_hat[101,3]   9.03    4.54   15.6   0.08   0.15   7.09  10.86  70.34     12   1.41\n",
      "Z_hat[102,3]   8.71    4.41  15.17   0.08   0.14   6.82  10.35  68.44     12   1.41\n",
      "Z_hat[103,3]    8.4    4.29  14.76   0.08   0.14   6.55   9.86  66.59     12   1.41\n",
      "Z_hat[104,3]    8.1    4.17  14.35   0.07   0.13    6.3    9.4  64.79     12   1.41\n",
      "Z_hat[105,3]   7.81    4.05  13.96   0.07   0.12   6.06   8.95  63.04     12   1.41\n",
      "Z_hat[106,3]   7.53    3.94  13.58   0.06   0.12   5.82   8.53  61.34     12   1.41\n",
      "Z_hat[107,3]   7.26    3.83  13.22   0.06   0.11    5.6   8.13  59.68     12   1.41\n",
      "Z_hat[108,3]   7.01    3.73  12.86   0.06    0.1   5.38   7.75  58.07     12    1.4\n",
      "Z_hat[109,3]   6.76    3.63  12.51   0.05    0.1   5.17   7.39   56.5     12    1.4\n",
      "Z_hat[110,3]   6.52    3.53  12.17   0.05   0.09   4.97   7.04  54.98     12    1.4\n",
      "Z_hat[111,3]   6.29    3.43  11.84   0.05   0.09   4.78   6.71  53.49     12    1.4\n",
      "Z_hat[112,3]   6.07    3.34  11.52   0.05   0.08    4.6   6.39  52.05     12    1.4\n",
      "Z_hat[113,3]   5.86    3.25  11.21   0.04   0.08   4.42   6.09  50.64     12    1.4\n",
      "Z_hat[114,3]   5.65    3.16  10.91   0.04   0.08   4.25   5.81  49.27     12    1.4\n",
      "Z_hat[115,3]   5.46    3.07  10.61   0.04   0.07   4.08   5.53  47.94     12    1.4\n",
      "Z_hat[116,3]   5.27    2.99  10.33   0.04   0.07   3.93   5.27  46.64     12    1.4\n",
      "Z_hat[117,3]   5.09    2.91  10.05   0.03   0.07   3.77   5.03  45.38     12    1.4\n",
      "Z_hat[118,3]   4.91    2.83   9.78   0.03   0.06   3.63   4.79  44.16     12    1.4\n",
      "Z_hat[119,3]   4.74    2.76   9.52   0.03   0.06   3.49   4.56  42.97     12    1.4\n",
      "Z_hat[120,3]   4.58    2.68   9.26   0.03   0.06   3.35   4.35   41.8     12    1.4\n",
      "Z_hat[121,3]   4.42    2.61   9.01   0.03   0.05   3.22   4.15  40.68     12    1.4\n",
      "Z_hat[122,3]   4.27    2.54   8.77   0.03   0.05    3.1   3.95  39.58     12    1.4\n",
      "Z_hat[123,3]   4.12    2.47   8.54   0.02   0.05   2.98   3.77  38.51     12    1.4\n",
      "Z_hat[124,3]   3.98    2.41   8.31   0.02   0.05   2.86   3.59  37.47     12    1.4\n",
      "Z_hat[125,3]   3.85    2.34   8.08   0.02   0.04   2.75   3.42  36.45     12    1.4\n",
      "Z_hat[126,3]   3.71    2.28   7.87   0.02   0.04   2.65   3.26  35.47     12    1.4\n",
      "Z_hat[127,3]   3.59    2.22   7.66   0.02   0.04   2.54   3.11  34.51     12    1.4\n",
      "Z_hat[128,3]   3.47    2.16   7.45   0.02   0.04   2.45   2.96  33.58     12    1.4\n",
      "Z_hat[129,3]   3.35     2.1   7.25   0.02   0.03   2.35   2.82  32.67     12    1.4\n",
      "Z_hat[130,3]   3.24    2.05   7.06   0.02   0.03   2.26   2.69  31.79     12    1.4\n",
      "Z_hat[131,3]   3.13    1.99   6.87   0.02   0.03   2.17   2.56  30.93     12    1.4\n",
      "Z_hat[132,3]   3.02    1.94   6.68   0.01   0.03   2.09   2.44  30.09     12    1.4\n",
      "Z_hat[133,3]   2.92    1.89   6.51   0.01   0.03   2.01   2.33  29.28     12    1.4\n",
      "Z_hat[134,3]   2.82    1.84   6.33   0.01   0.03   1.93   2.22  28.49     12    1.4\n",
      "Z_hat[135,3]   2.73    1.79   6.16   0.01   0.03   1.86   2.11  27.72     12    1.4\n",
      "Z_hat[136,3]   2.64    1.74    6.0   0.01   0.02   1.78   2.01  26.97     12    1.4\n",
      "Z_hat[137,3]   2.55     1.7   5.84   0.01   0.02   1.71   1.92  26.24     12    1.4\n",
      "Z_hat[138,3]   2.47    1.65   5.68   0.01   0.02   1.65   1.83  25.53     12    1.4\n",
      "Z_hat[139,3]   2.38    1.61   5.53 9.7e-3   0.02   1.58   1.74  24.84     12    1.4\n",
      "Z_hat[140,3]   2.31    1.56   5.38 9.2e-3   0.02   1.52   1.66  24.17     12    1.4\n",
      "Z_hat[141,3]   2.23    1.52   5.24 8.7e-3   0.02   1.46   1.58  23.52     12    1.4\n",
      "Z_hat[142,3]   2.16    1.48    5.1 8.2e-3   0.02   1.41   1.51  22.88     12    1.4\n",
      "Z_hat[143,3]   2.09    1.44   4.96 7.7e-3   0.02   1.35   1.44  22.27     12    1.4\n",
      "Z_hat[144,3]   2.02    1.41   4.83 7.3e-3   0.02    1.3   1.37  21.66     12    1.4\n",
      "Z_hat[145,3]   1.95    1.37    4.7 6.9e-3   0.01   1.25   1.31  21.08     12    1.4\n",
      "Z_hat[146,3]   1.89    1.33   4.57 6.5e-3   0.01    1.2   1.24  20.51     12    1.4\n",
      "Z_hat[147,3]   1.83     1.3   4.45 6.2e-3   0.01   1.16   1.19  19.96     12    1.4\n",
      "Z_hat[148,3]   1.77    1.26   4.33 5.8e-3   0.01   1.11   1.13  19.42     12    1.4\n",
      "Z_hat[149,3]   1.71    1.23   4.22 5.5e-3   0.01   1.07   1.08  18.89     12    1.4\n",
      "Z_hat[150,3]   1.65     1.2    4.1 5.2e-3   0.01   1.03   1.03  18.38     12    1.4\n",
      "Z_hat[1,4]      0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "Z_hat[2,4]    22.08   16.96  24.72   1.34   1.51  14.12  47.13  63.18      2   5.81\n",
      "Z_hat[3,4]    43.19   33.11  48.29   2.61   2.95  27.69  92.47 123.39      2   5.75\n",
      "Z_hat[4,4]    63.37   48.47  70.75   3.81   4.31  40.74 136.09 180.78      2   5.69\n",
      "Z_hat[5,4]    82.66    63.1  92.16   4.94    5.6  53.28 178.07 235.47      2   5.63\n",
      "Z_hat[6,4]   101.11   77.02 112.57   6.02   6.83  65.34 218.47 287.58      2   5.57\n",
      "Z_hat[7,4]   118.75   90.28 132.03   7.04   7.99  76.94 257.34 337.25      2   5.52\n",
      "Z_hat[8,4]   135.62  102.89 150.58    8.0   9.09  88.08 294.76 384.59      2   5.46\n",
      "Z_hat[9,4]   151.75  114.89 168.27   8.92  10.14   98.8 330.77 429.71      2   5.41\n",
      "Z_hat[10,4]  167.18  126.32 185.13   9.78  11.13  109.1 365.43 472.75      2   5.36\n",
      "Z_hat[11,4]  181.93  137.19 201.21   10.6  12.07  119.0 398.79 513.72      2   5.31\n",
      "Z_hat[12,4]  196.04  147.54 216.53  11.37  12.96 128.52 430.92  552.8      2   5.26\n",
      "Z_hat[13,4]  209.53  157.38 231.15  12.11   13.8 137.68 461.84 590.04      2   5.21\n",
      "Z_hat[14,4]  222.44  166.75 245.09   12.8   14.6 146.48 491.61 625.52      2   5.17\n",
      "Z_hat[15,4]  234.79  175.67 258.38  13.46  15.36 154.96 520.28 659.33      2   5.12\n",
      "Z_hat[16,4]   246.6  184.15 271.05  14.08  16.09 163.09 547.89 691.54      2   5.08\n",
      "Z_hat[17,4]  257.89  192.23 283.14  14.67  16.77 170.91 574.47 722.24      2   5.03\n",
      "Z_hat[18,4]   268.7  199.91 294.67  15.22  17.42 178.43 600.08 751.56      2   4.99\n",
      "Z_hat[19,4]  279.04  207.22 305.66  15.75  18.03 185.68 624.74 779.52      2   4.95\n",
      "Z_hat[20,4]  288.93  214.17 316.15  16.25  18.62 192.63 648.49 806.17      2   4.91\n",
      "Z_hat[21,4]   298.4  220.78 326.15  16.72  19.17 199.31 671.37 831.52      2   4.87\n",
      "Z_hat[22,4]  307.45  227.08 335.69  17.17   19.7 205.73 693.42 855.66      2   4.83\n",
      "Z_hat[23,4]  316.12  233.06  344.8  17.58  20.19 211.91 714.65 878.74      2    4.8\n",
      "Z_hat[24,4]  324.41  238.76 353.48  17.98  20.67 217.84 735.11 900.85      2   4.76\n",
      "Z_hat[25,4]  332.35  244.18 361.76  18.36  21.12 223.55 754.83  922.0      2   4.72\n",
      "Z_hat[26,4]  339.94  249.33 369.67  18.71  21.54 229.03 773.83 941.97      2   4.69\n",
      "Z_hat[27,4]  347.21  254.23 377.21  19.05  21.95  234.3 792.14 961.01      2   4.66\n",
      "Z_hat[28,4]  354.16   258.9 384.41  19.37  22.33 239.38 809.78 979.13      2   4.62\n",
      "Z_hat[29,4]  360.82  263.33 391.27  19.67  22.69 244.26 826.54 996.38      2   4.59\n",
      "Z_hat[30,4]   367.2  267.55 397.83  19.96  23.03 248.94 842.25 1012.8      2   4.56\n",
      "Z_hat[31,4]   373.3  271.56 404.08  20.23  23.36 253.44 857.36 1028.6      2   4.53\n",
      "Z_hat[32,4]  379.14  275.37 410.05  20.49  23.67 257.77 871.89 1043.7      2    4.5\n",
      "Z_hat[33,4]  384.73   279.0 415.75  20.73  23.96 261.93 885.88 1058.0      2   4.47\n",
      "Z_hat[34,4]  390.08  282.45 421.18  20.96  24.24 265.93 899.34 1071.7      2   4.44\n",
      "Z_hat[35,4]  395.21  285.73 426.38  21.17  24.51 269.78  912.3 1084.7      2   4.42\n",
      "Z_hat[36,4]  400.12  288.85 431.33  21.38  24.76 273.48 924.77 1097.2      2   4.39\n",
      "Z_hat[37,4]  404.82  291.81 436.06  21.57   25.0 277.04 936.77 1109.2      2   4.36\n",
      "Z_hat[38,4]  409.32  294.63 440.58  21.75  25.22 280.45 948.33 1120.4      2   4.34\n",
      "Z_hat[39,4]  413.63  297.31 444.89  21.93  25.44 283.74 959.46 1131.0      2   4.31\n",
      "Z_hat[40,4]  417.76  299.85 449.01  22.09  25.64  286.9 970.18 1141.2      2   4.29\n",
      "Z_hat[41,4]  421.71  302.27 452.95  22.25  25.83 289.93  980.5 1150.9      2   4.26\n",
      "Z_hat[42,4]   425.5  304.57  456.7  22.39  26.01 292.86 990.44 1160.1      2   4.24\n",
      "Z_hat[43,4]  429.13  306.76 460.29  22.53  26.19 295.68 1000.0 1168.9      2   4.22\n",
      "Z_hat[44,4]   432.6  308.84 463.72  22.66  26.35 298.39 1009.2 1177.2      2    4.2\n",
      "Z_hat[45,4]  435.93  310.81 466.99  22.79  26.51 301.03 1018.1 1185.2      2   4.17\n",
      "Z_hat[46,4]  439.12  312.69 470.12   22.9  26.66 303.54 1026.7 1192.8      2   4.15\n",
      "Z_hat[47,4]  442.18  314.47  473.1  23.01  26.79 305.95 1034.9 1200.1      2   4.13\n",
      "Z_hat[48,4]  445.11  316.16 475.96  23.12  26.93 308.26 1042.9 1207.0      2   4.11\n",
      "Z_hat[49,4]  447.92  317.77 478.69  23.22  27.05 310.48 1050.6 1213.6      2   4.09\n",
      "Z_hat[50,4]  450.61   319.3 481.29  23.31  27.17 312.61 1058.0 1219.8      2   4.07\n",
      "Z_hat[51,4]  453.18  320.75 483.78   23.4  27.29 314.66 1065.1 1225.8      2   4.06\n",
      "Z_hat[52,4]  455.65  322.13 486.16  23.48  27.39 316.63 1072.0 1231.5      2   4.04\n",
      "Z_hat[53,4]  458.02  323.44 488.44  23.56   27.5 318.52 1078.6 1236.9      2   4.02\n",
      "Z_hat[54,4]  460.29  324.68 490.61  23.64  27.59 320.35 1085.0 1242.1      2    4.0\n",
      "Z_hat[55,4]  462.47  325.86 492.69  23.71  27.68  322.1 1091.2 1247.0      2   3.99\n",
      "Z_hat[56,4]  464.55  326.99 494.68  23.77  27.77 323.78 1097.1 1251.7      2   3.97\n",
      "Z_hat[57,4]  466.55  328.05 496.58  23.84  27.85  325.4 1102.9 1256.2      2   3.96\n",
      "Z_hat[58,4]  468.47  329.06  498.4   23.9  27.93 326.96 1108.4 1260.5      2   3.94\n",
      "Z_hat[59,4]  470.31  330.02 500.14  23.95  28.01 328.46 1113.8 1264.5      2   3.92\n",
      "Z_hat[60,4]  472.07  330.93  501.8  24.01  28.08  329.9 1119.0 1268.4      2   3.91\n",
      "Z_hat[61,4]  473.76  331.79 503.39  24.06  28.14 331.28 1123.9 1272.1      2    3.9\n",
      "Z_hat[62,4]  475.38  332.61 504.91   24.1  28.21  332.6 1128.8 1275.6      2   3.88\n",
      "Z_hat[63,4]  476.94  333.39 506.36  24.15  28.27 333.88 1133.4 1279.0      2   3.87\n",
      "Z_hat[64,4]  478.43  334.13 507.75  24.19  28.32 335.11 1137.9 1282.2      2   3.86\n",
      "Z_hat[65,4]  479.86  334.83 509.08  24.23  28.38 336.29 1142.2 1285.2      2   3.84\n",
      "Z_hat[66,4]  481.24  335.49 510.36  24.27  28.43 337.42 1146.4 1288.1      2   3.83\n",
      "Z_hat[67,4]  482.55  336.12 511.58  24.31  28.48 338.51 1150.5 1290.9      2   3.82\n",
      "Z_hat[68,4]  483.82  336.72 512.74  24.35  28.53 339.56 1154.4 1293.5      2   3.81\n",
      "Z_hat[69,4]  485.03  337.28 513.86  24.38  28.57 340.58 1158.2 1296.0      2   3.79\n",
      "Z_hat[70,4]  486.19  337.82 514.93  24.41  28.61 341.56 1161.8 1298.4      2   3.78\n",
      "Z_hat[71,4]  487.31  338.33 515.95  24.44  28.65 342.49 1165.3 1300.7      2   3.77\n",
      "Z_hat[72,4]  488.38  338.81 516.93  24.46  28.69  343.4 1168.8 1302.9      2   3.76\n",
      "Z_hat[73,4]  489.41  339.27 517.87  24.49  28.72 344.26 1172.1 1304.9      2   3.75\n",
      "Z_hat[74,4]   490.4   339.7 518.77  24.52  28.76 345.09 1175.2 1306.9      2   3.74\n",
      "Z_hat[75,4]  491.34  340.11 519.63  24.54  28.79 345.89 1178.3 1308.8      2   3.73\n",
      "Z_hat[76,4]  492.25   340.5 520.45  24.56  28.82 346.65 1181.3 1310.6      2   3.72\n",
      "Z_hat[77,4]  493.13  340.87 521.24  24.58  28.85  347.4 1184.2 1312.3      2   3.71\n",
      "Z_hat[78,4]  493.97  341.22 521.99   24.6  28.88  348.1 1187.0 1313.9      2    3.7\n",
      "Z_hat[79,4]  494.77  341.55 522.72  24.62   28.9 348.78 1189.7 1315.5      2   3.69\n",
      "Z_hat[80,4]  495.55  341.86 523.41  24.64  28.93 349.44 1192.3 1316.9      2   3.68\n",
      "Z_hat[81,4]  496.29  342.15 524.08  24.65  28.95 350.06 1194.8 1318.4      2   3.68\n",
      "Z_hat[82,4]   497.0  342.43 524.71  24.67  28.97 350.67 1197.2 1319.7      2   3.67\n",
      "Z_hat[83,4]  497.69   342.7 525.32  24.68  28.99 351.25 1199.6 1321.0      2   3.66\n",
      "Z_hat[84,4]  498.34  342.95 525.91   24.7  29.01 351.81 1201.9 1322.2      2   3.65\n",
      "Z_hat[85,4]  498.98  343.18 526.47  24.71  29.03 352.36 1204.1 1323.4      2   3.64\n",
      "Z_hat[86,4]  499.58  343.41 527.01  24.72  29.05 352.87 1206.2 1324.5      2   3.64\n",
      "Z_hat[87,4]  500.17  343.62 527.52  24.73  29.07 353.37 1208.3 1325.5      2   3.63\n",
      "Z_hat[88,4]  500.73  343.82 528.01  24.74  29.08 353.85 1210.3 1326.5      2   3.62\n",
      "Z_hat[89,4]  501.27  344.01 528.49  24.76   29.1 354.31 1212.3 1327.5      2   3.61\n",
      "Z_hat[90,4]  501.79  344.18 528.94  24.77  29.11 354.75 1214.1 1328.4      2   3.61\n",
      "Z_hat[91,4]  502.28  344.35 529.38  24.78  29.13 355.17 1216.0 1329.3      2    3.6\n",
      "Z_hat[92,4]  502.76  344.51  529.8  24.78  29.14 355.58 1217.7 1330.1      2   3.59\n",
      "Z_hat[93,4]  503.22  344.66  530.2  24.79  29.15 355.97 1219.4 1330.9      2   3.59\n",
      "Z_hat[94,4]  503.67   344.8 530.58   24.8  29.16 356.35 1221.1 1331.6      2   3.58\n",
      "Z_hat[95,4]  504.09  344.94 530.95  24.81  29.18 356.71 1222.7 1332.4      2   3.58\n",
      "Z_hat[96,4]   504.5  345.06 531.31  24.82  29.19 357.06 1224.2 1333.0      2   3.57\n",
      "Z_hat[97,4]  504.89  345.18 531.65  24.82   29.2 357.39 1225.7 1333.7      2   3.56\n",
      "Z_hat[98,4]  505.27  345.29 531.97  24.83  29.21 357.71 1227.2 1334.3      2   3.56\n",
      "Z_hat[99,4]  505.63   345.4 532.29  24.84  29.22 358.02 1228.6 1334.9      2   3.55\n",
      "Z_hat[100,4] 505.98  345.49 532.59  24.84  29.23 358.32 1230.0 1335.5      2   3.55\n",
      "Z_hat[101,4] 506.32  345.59 532.88  24.85  29.23  358.6 1231.3 1336.0      2   3.54\n",
      "Z_hat[102,4] 506.64  345.68 533.15  24.85  29.24 358.88 1232.6 1336.5      2   3.54\n",
      "Z_hat[103,4] 506.96  345.76 533.42  24.86  29.25 359.14 1233.8 1337.0      2   3.53\n",
      "Z_hat[104,4] 507.25  345.83 533.68  24.86  29.26 359.39 1235.1 1337.5      2   3.53\n",
      "Z_hat[105,4] 507.54  345.91 533.92  24.87  29.26 359.64 1236.2 1337.9      2   3.52\n",
      "Z_hat[106,4] 507.82  345.98 534.16  24.87  29.27 359.87 1237.4 1338.3      2   3.52\n",
      "Z_hat[107,4] 508.09  346.04 534.39  24.87  29.27  360.1 1238.5 1338.7      2   3.52\n",
      "Z_hat[108,4] 508.34   346.1  534.6  24.88  29.28 360.31 1239.5 1339.1      2   3.51\n",
      "Z_hat[109,4] 508.59  346.16 534.81  24.88  29.29 360.52 1240.6 1339.5      2   3.51\n",
      "Z_hat[110,4] 508.83  346.21 535.01  24.89  29.29 360.72 1241.6 1339.8      2    3.5\n",
      "Z_hat[111,4] 509.06  346.26 535.21  24.89   29.3 360.92 1242.5 1340.2      2    3.5\n",
      "Z_hat[112,4] 509.28   346.3 535.39  24.89   29.3  361.1 1243.5 1340.5      2    3.5\n",
      "Z_hat[113,4] 509.49  346.35 535.57  24.89  29.31 361.28 1244.4 1340.8      2   3.49\n",
      "Z_hat[114,4]  509.7  346.39 535.75   24.9  29.31 361.45 1245.3 1341.1      2   3.49\n",
      "Z_hat[115,4] 509.89  346.42 535.91   24.9  29.31 361.61 1246.2 1341.3      2   3.49\n",
      "Z_hat[116,4] 510.08  346.46 536.07   24.9  29.32 361.77 1247.0 1341.6      2   3.48\n",
      "Z_hat[117,4] 510.26  346.49 536.22   24.9  29.32 361.93 1247.8 1341.9      2   3.48\n",
      "Z_hat[118,4] 510.44  346.52 536.37   24.9  29.32 362.07 1248.6 1342.1      2   3.48\n",
      "Z_hat[119,4] 510.61  346.55 536.51  24.91  29.33 362.21 1249.4 1342.3      2   3.47\n",
      "Z_hat[120,4] 510.77  346.58 536.65  24.91  29.33 362.35 1250.1 1342.5      2   3.47\n",
      "Z_hat[121,4] 510.93   346.6 536.78  24.91  29.33 362.48 1250.8 1342.7      2   3.47\n",
      "Z_hat[122,4] 511.08  346.62 536.91  24.91  29.34  362.6 1251.5 1342.9      2   3.46\n",
      "Z_hat[123,4] 511.23  346.65 537.03  24.91  29.34 362.72 1252.2 1343.1      2   3.46\n",
      "Z_hat[124,4] 511.37  346.66 537.14  24.91  29.34 362.84 1252.9 1343.3      2   3.46\n",
      "Z_hat[125,4] 511.51  346.68 537.26  24.92  29.34 362.95 1253.5 1343.5      2   3.45\n",
      "Z_hat[126,4] 511.64   346.7 537.37  24.92  29.35 363.06 1254.1 1343.6      2   3.45\n",
      "Z_hat[127,4] 511.76  346.71 537.47  24.92  29.35 363.16 1254.7 1343.8      2   3.45\n",
      "Z_hat[128,4] 511.88  346.73 537.57  24.92  29.35 363.26 1255.3 1343.9      2   3.45\n",
      "Z_hat[129,4]  512.0  346.74 537.67  24.92  29.35 363.36 1255.9 1344.1      2   3.44\n",
      "Z_hat[130,4] 512.11  346.75 537.76  24.92  29.35 363.45 1256.4 1344.2      2   3.44\n",
      "Z_hat[131,4] 512.22  346.76 537.85  24.92  29.36 363.54 1257.0 1344.3      2   3.44\n",
      "Z_hat[132,4] 512.33  346.77 537.94  24.92  29.36 363.62 1257.5 1344.4      2   3.44\n",
      "Z_hat[133,4] 512.43  346.78 538.02  24.92  29.36  363.7 1258.0 1344.6      2   3.44\n",
      "Z_hat[134,4] 512.53  346.79  538.1  24.93  29.36 363.78 1258.5 1344.7      2   3.43\n",
      "Z_hat[135,4] 512.62  346.79 538.18  24.93  29.36 363.85 1259.0 1344.8      2   3.43\n",
      "Z_hat[136,4] 512.71   346.8 538.25  24.93  29.36 363.93 1259.4 1344.9      2   3.43\n",
      "Z_hat[137,4]  512.8   346.8 538.33  24.93  29.36  364.0 1259.9 1345.0      2   3.43\n",
      "Z_hat[138,4] 512.88  346.81 538.39  24.93  29.36 364.07 1260.3 1345.1      2   3.43\n",
      "Z_hat[139,4] 512.97  346.81 538.46  24.93  29.37 364.13 1260.8 1345.1      2   3.42\n",
      "Z_hat[140,4] 513.04  346.82 538.53  24.93  29.37 364.19 1261.2 1345.2      2   3.42\n",
      "Z_hat[141,4] 513.12  346.82 538.59  24.93  29.37 364.25 1261.6 1345.3      2   3.42\n",
      "Z_hat[142,4] 513.19  346.82 538.65  24.93  29.37 364.31 1262.0 1345.4      2   3.42\n",
      "Z_hat[143,4] 513.26  346.82 538.71  24.93  29.37 364.36 1262.3 1345.4      2   3.42\n",
      "Z_hat[144,4] 513.33  346.83 538.76  24.93  29.37 364.42 1262.7 1345.5      2   3.41\n",
      "Z_hat[145,4]  513.4  346.83 538.82  24.93  29.37 364.47 1263.1 1345.6      2   3.41\n",
      "Z_hat[146,4] 513.46  346.83 538.87  24.93  29.37 364.53 1263.4 1345.6      2   3.41\n",
      "Z_hat[147,4] 513.52  346.83 538.92  24.93  29.37 364.58 1263.8 1345.7      2   3.41\n",
      "Z_hat[148,4] 513.58  346.83 538.97  24.93  29.37 364.62 1264.1 1345.8      2   3.41\n",
      "Z_hat[149,4] 513.64  346.83 539.01  24.93  29.37 364.67 1264.4 1345.8      2   3.41\n",
      "Z_hat[150,4]  513.7  346.83 539.06  24.94  29.37 364.71 1264.7 1345.9      2   3.41\n",
      "Z_init[1]    1484.6  346.59 540.42 653.07 724.12 1634.2 1970.6 1975.0      2   3.35\n",
      "Z_init[2]       0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "Z_init[3]    515.35  346.59 540.42  24.94  29.39 365.76 1275.8 1346.9      2   3.35\n",
      "Z_init[4]       0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "theta[1]      23.35     9.8  15.81   4.15   5.06  36.07  37.69  37.73      3   3.02\n",
      "theta[2]      22.71    1.55   4.68  18.01  19.51  21.28  25.59  37.01      9   1.54\n",
      "theta[3]       9.31    3.91   6.43    0.9   2.49  10.98  16.96  17.34      3   3.17\n",
      "theta[4]       0.22    0.03    0.1   0.03   0.19    0.2   0.25   0.44     15   1.46\n",
      "theta[5]        0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "theta[6]        0.0     nan    0.0    0.0    0.0    0.0    0.0    0.0    nan    nan\n",
      "lp__         -1.2e4  5119.4 9137.7 -3.0e4 -2.5e4  -9938  -4281  -4279      3   2.33\n",
      "\n",
      "Samples were drawn using NUTS at Wed Apr  1 09:58:23 2020.\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"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "convergence, Rhat=1).\n"
     ]
    }
   ],
   "source": [
    "#learned statistics:\n",
    "print(fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "summary_dict = fit.summary()\n",
    "df = pd.DataFrame(summary_dict['summary'], \n",
    "                  columns=summary_dict['summary_colnames'], \n",
    "                  index=summary_dict['summary_rownames'])\n",
    "\n",
    "# Extracting traces\n",
    "#p_obs_hat  = fit['p_obs']\n",
    "t_inc_hat  = fit['t_inc']\n",
    "t_inf_hat  = fit['t_inf']\n",
    "r_t_hat    = fit['r_t']\n",
    "rho_hat    = fit['rho']\n",
    "lp         = fit['lp__']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# extract found Z mean values:\n",
    "Z_hat = np.zeros((n_obs,n_difeq), dtype = int)\n",
    "for i in range(0,4):\n",
    "    for t in range(0,n_obs):\n",
    "        index = 'Z_hat['+str(t+1)+','+str(i+1)+']'\n",
    "        Z_hat[t,i]= int(df.loc[index,'mean'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualizing the process.\n",
    "fig, ax = plt.subplots(figsize=(14,6))\n",
    "ax.plot(Z_hat[:,0], c='b', lw=2, label='$\\hat{S}$', linestyle = '--')\n",
    "ax.plot(Z_hat[:,1], c='orange', lw=2, label='$\\hat{E}$', linestyle = '--')\n",
    "ax.plot(Z_hat[:,2], c='r', lw=2, label='$\\hat{I}$', linestyle = '--')\n",
    "ax.plot(Z_hat[:,3], c='g', lw=2, label='$\\hat{R}$', linestyle = '--')\n",
    "\n",
    "ax.plot(Z[:,0], c='b', lw=2, label='S')\n",
    "ax.plot(Z[:,1], c='orange', lw=2, label='E')\n",
    "ax.plot(Z[:,2], c='r', lw=2, label='I')\n",
    "ax.plot(Z[:,3], c='g', lw=2, label='R')\n",
    "\n",
    "ax.plot(X, c='black', lw=2, label='$I_X$')\n",
    "\n",
    "ax.set_xlabel('Day', fontsize=15)\n",
    "ax.set_ylabel('Individuals', fontsize=15)\n",
    "ax.grid()\n",
    "\n",
    "plt.xticks(fontsize=20)\n",
    "plt.yticks(fontsize=20)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>se_mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>2.5%</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>97.5%</th>\n",
       "      <th>n_eff</th>\n",
       "      <th>Rhat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>t_inc</th>\n",
       "      <td>23.346120</td>\n",
       "      <td>9.795726</td>\n",
       "      <td>15.805188</td>\n",
       "      <td>4.147731</td>\n",
       "      <td>5.059879</td>\n",
       "      <td>36.066159</td>\n",
       "      <td>37.692059</td>\n",
       "      <td>37.732697</td>\n",
       "      <td>2.603311</td>\n",
       "      <td>3.020099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_inf</th>\n",
       "      <td>22.711611</td>\n",
       "      <td>1.547090</td>\n",
       "      <td>4.676723</td>\n",
       "      <td>18.009874</td>\n",
       "      <td>19.510625</td>\n",
       "      <td>21.276597</td>\n",
       "      <td>25.590881</td>\n",
       "      <td>37.013475</td>\n",
       "      <td>9.138017</td>\n",
       "      <td>1.544864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r_t</th>\n",
       "      <td>9.308984</td>\n",
       "      <td>3.913067</td>\n",
       "      <td>6.426815</td>\n",
       "      <td>0.902542</td>\n",
       "      <td>2.493323</td>\n",
       "      <td>10.975670</td>\n",
       "      <td>16.956968</td>\n",
       "      <td>17.337714</td>\n",
       "      <td>2.697472</td>\n",
       "      <td>3.172794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>rho</th>\n",
       "      <td>0.215268</td>\n",
       "      <td>0.025360</td>\n",
       "      <td>0.099201</td>\n",
       "      <td>0.031206</td>\n",
       "      <td>0.189240</td>\n",
       "      <td>0.198604</td>\n",
       "      <td>0.254465</td>\n",
       "      <td>0.441967</td>\n",
       "      <td>15.301790</td>\n",
       "      <td>1.460634</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S0</th>\n",
       "      <td>0.742325</td>\n",
       "      <td>0.173294</td>\n",
       "      <td>0.270212</td>\n",
       "      <td>0.326534</td>\n",
       "      <td>0.362061</td>\n",
       "      <td>0.817119</td>\n",
       "      <td>0.985307</td>\n",
       "      <td>0.987529</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[1,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[2,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[3,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[4,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[5,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[6,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[7,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[8,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[9,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[10,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[11,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[12,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[13,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[14,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[15,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[16,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[17,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[18,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[19,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[20,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[21,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[22,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[23,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[24,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[25,1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[132,4]</th>\n",
       "      <td>512.327554</td>\n",
       "      <td>346.770491</td>\n",
       "      <td>537.937164</td>\n",
       "      <td>24.923854</td>\n",
       "      <td>29.356881</td>\n",
       "      <td>363.619751</td>\n",
       "      <td>1257.545233</td>\n",
       "      <td>1344.488673</td>\n",
       "      <td>2.406461</td>\n",
       "      <td>3.437432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[133,4]</th>\n",
       "      <td>512.428858</td>\n",
       "      <td>346.778938</td>\n",
       "      <td>538.020637</td>\n",
       "      <td>24.924662</td>\n",
       "      <td>29.358564</td>\n",
       "      <td>363.700485</td>\n",
       "      <td>1258.051545</td>\n",
       "      <td>1344.603649</td>\n",
       "      <td>2.407091</td>\n",
       "      <td>3.435244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[134,4]</th>\n",
       "      <td>512.526564</td>\n",
       "      <td>346.786519</td>\n",
       "      <td>538.101081</td>\n",
       "      <td>24.925534</td>\n",
       "      <td>29.360077</td>\n",
       "      <td>363.778097</td>\n",
       "      <td>1258.543332</td>\n",
       "      <td>1344.713216</td>\n",
       "      <td>2.407705</td>\n",
       "      <td>3.433113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[135,4]</th>\n",
       "      <td>512.620807</td>\n",
       "      <td>346.793289</td>\n",
       "      <td>538.178616</td>\n",
       "      <td>24.926807</td>\n",
       "      <td>29.361106</td>\n",
       "      <td>363.853529</td>\n",
       "      <td>1259.021033</td>\n",
       "      <td>1344.817629</td>\n",
       "      <td>2.408305</td>\n",
       "      <td>3.431038</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[136,4]</th>\n",
       "      <td>512.711719</td>\n",
       "      <td>346.799298</td>\n",
       "      <td>538.253354</td>\n",
       "      <td>24.927448</td>\n",
       "      <td>29.362277</td>\n",
       "      <td>363.927194</td>\n",
       "      <td>1259.485075</td>\n",
       "      <td>1344.917131</td>\n",
       "      <td>2.408891</td>\n",
       "      <td>3.429017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[137,4]</th>\n",
       "      <td>512.799423</td>\n",
       "      <td>346.804594</td>\n",
       "      <td>538.325405</td>\n",
       "      <td>24.928135</td>\n",
       "      <td>29.363425</td>\n",
       "      <td>363.996148</td>\n",
       "      <td>1259.935871</td>\n",
       "      <td>1345.011952</td>\n",
       "      <td>2.409462</td>\n",
       "      <td>3.427049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[138,4]</th>\n",
       "      <td>512.884040</td>\n",
       "      <td>346.809222</td>\n",
       "      <td>538.394873</td>\n",
       "      <td>24.928726</td>\n",
       "      <td>29.364542</td>\n",
       "      <td>364.065740</td>\n",
       "      <td>1260.373821</td>\n",
       "      <td>1345.102313</td>\n",
       "      <td>2.410019</td>\n",
       "      <td>3.425133</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[139,4]</th>\n",
       "      <td>512.965684</td>\n",
       "      <td>346.813226</td>\n",
       "      <td>538.461857</td>\n",
       "      <td>24.929404</td>\n",
       "      <td>29.365712</td>\n",
       "      <td>364.129465</td>\n",
       "      <td>1260.799309</td>\n",
       "      <td>1345.188423</td>\n",
       "      <td>2.410564</td>\n",
       "      <td>3.423266</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[140,4]</th>\n",
       "      <td>513.044467</td>\n",
       "      <td>346.816646</td>\n",
       "      <td>538.526454</td>\n",
       "      <td>24.929938</td>\n",
       "      <td>29.366941</td>\n",
       "      <td>364.190726</td>\n",
       "      <td>1261.212711</td>\n",
       "      <td>1345.270483</td>\n",
       "      <td>2.411094</td>\n",
       "      <td>3.421449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[141,4]</th>\n",
       "      <td>513.120495</td>\n",
       "      <td>346.819521</td>\n",
       "      <td>538.588755</td>\n",
       "      <td>24.930443</td>\n",
       "      <td>29.368013</td>\n",
       "      <td>364.251806</td>\n",
       "      <td>1261.614387</td>\n",
       "      <td>1345.348682</td>\n",
       "      <td>2.411612</td>\n",
       "      <td>3.419680</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[142,4]</th>\n",
       "      <td>513.193869</td>\n",
       "      <td>346.821886</td>\n",
       "      <td>538.648849</td>\n",
       "      <td>24.930956</td>\n",
       "      <td>29.369071</td>\n",
       "      <td>364.308422</td>\n",
       "      <td>1262.004687</td>\n",
       "      <td>1345.423203</td>\n",
       "      <td>2.412118</td>\n",
       "      <td>3.417957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[143,4]</th>\n",
       "      <td>513.264688</td>\n",
       "      <td>346.823777</td>\n",
       "      <td>538.706820</td>\n",
       "      <td>24.931513</td>\n",
       "      <td>29.370007</td>\n",
       "      <td>364.362848</td>\n",
       "      <td>1262.383952</td>\n",
       "      <td>1345.494219</td>\n",
       "      <td>2.412611</td>\n",
       "      <td>3.416279</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[144,4]</th>\n",
       "      <td>513.333046</td>\n",
       "      <td>346.825224</td>\n",
       "      <td>538.762750</td>\n",
       "      <td>24.932079</td>\n",
       "      <td>29.370822</td>\n",
       "      <td>364.421860</td>\n",
       "      <td>1262.752508</td>\n",
       "      <td>1345.561894</td>\n",
       "      <td>2.413091</td>\n",
       "      <td>3.414645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[145,4]</th>\n",
       "      <td>513.399034</td>\n",
       "      <td>346.826260</td>\n",
       "      <td>538.816714</td>\n",
       "      <td>24.932703</td>\n",
       "      <td>29.371464</td>\n",
       "      <td>364.472159</td>\n",
       "      <td>1263.110673</td>\n",
       "      <td>1345.626385</td>\n",
       "      <td>2.413560</td>\n",
       "      <td>3.413054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[146,4]</th>\n",
       "      <td>513.462739</td>\n",
       "      <td>346.826913</td>\n",
       "      <td>538.868790</td>\n",
       "      <td>24.933296</td>\n",
       "      <td>29.372019</td>\n",
       "      <td>364.526479</td>\n",
       "      <td>1263.458756</td>\n",
       "      <td>1345.687843</td>\n",
       "      <td>2.414018</td>\n",
       "      <td>3.411505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[147,4]</th>\n",
       "      <td>513.524244</td>\n",
       "      <td>346.827210</td>\n",
       "      <td>538.919047</td>\n",
       "      <td>24.933857</td>\n",
       "      <td>29.372637</td>\n",
       "      <td>364.575702</td>\n",
       "      <td>1263.797052</td>\n",
       "      <td>1345.746410</td>\n",
       "      <td>2.414464</td>\n",
       "      <td>3.409997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[148,4]</th>\n",
       "      <td>513.583631</td>\n",
       "      <td>346.827177</td>\n",
       "      <td>538.967555</td>\n",
       "      <td>24.934389</td>\n",
       "      <td>29.373372</td>\n",
       "      <td>364.620389</td>\n",
       "      <td>1264.125852</td>\n",
       "      <td>1345.802222</td>\n",
       "      <td>2.414899</td>\n",
       "      <td>3.408528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[149,4]</th>\n",
       "      <td>513.640976</td>\n",
       "      <td>346.826837</td>\n",
       "      <td>539.014379</td>\n",
       "      <td>24.934894</td>\n",
       "      <td>29.374091</td>\n",
       "      <td>364.665531</td>\n",
       "      <td>1264.445434</td>\n",
       "      <td>1345.855409</td>\n",
       "      <td>2.415324</td>\n",
       "      <td>3.407098</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_hat[150,4]</th>\n",
       "      <td>513.696354</td>\n",
       "      <td>346.826215</td>\n",
       "      <td>539.059582</td>\n",
       "      <td>24.935372</td>\n",
       "      <td>29.374719</td>\n",
       "      <td>364.706830</td>\n",
       "      <td>1264.756069</td>\n",
       "      <td>1345.906094</td>\n",
       "      <td>2.415737</td>\n",
       "      <td>3.405706</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_init[1]</th>\n",
       "      <td>1484.649570</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>653.067105</td>\n",
       "      <td>724.121394</td>\n",
       "      <td>1634.237542</td>\n",
       "      <td>1970.613176</td>\n",
       "      <td>1975.057103</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_init[2]</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_init[3]</th>\n",
       "      <td>515.350430</td>\n",
       "      <td>346.588531</td>\n",
       "      <td>540.424321</td>\n",
       "      <td>24.942897</td>\n",
       "      <td>29.386824</td>\n",
       "      <td>365.762458</td>\n",
       "      <td>1275.878606</td>\n",
       "      <td>1346.932895</td>\n",
       "      <td>2.431316</td>\n",
       "      <td>3.354659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Z_init[4]</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[1]</th>\n",
       "      <td>23.346120</td>\n",
       "      <td>9.795726</td>\n",
       "      <td>15.805188</td>\n",
       "      <td>4.147731</td>\n",
       "      <td>5.059879</td>\n",
       "      <td>36.066159</td>\n",
       "      <td>37.692059</td>\n",
       "      <td>37.732697</td>\n",
       "      <td>2.603311</td>\n",
       "      <td>3.020099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[2]</th>\n",
       "      <td>22.711611</td>\n",
       "      <td>1.547090</td>\n",
       "      <td>4.676723</td>\n",
       "      <td>18.009874</td>\n",
       "      <td>19.510625</td>\n",
       "      <td>21.276597</td>\n",
       "      <td>25.590881</td>\n",
       "      <td>37.013475</td>\n",
       "      <td>9.138017</td>\n",
       "      <td>1.544864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[3]</th>\n",
       "      <td>9.308984</td>\n",
       "      <td>3.913067</td>\n",
       "      <td>6.426815</td>\n",
       "      <td>0.902542</td>\n",
       "      <td>2.493323</td>\n",
       "      <td>10.975670</td>\n",
       "      <td>16.956968</td>\n",
       "      <td>17.337714</td>\n",
       "      <td>2.697472</td>\n",
       "      <td>3.172794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[4]</th>\n",
       "      <td>0.215268</td>\n",
       "      <td>0.025360</td>\n",
       "      <td>0.099201</td>\n",
       "      <td>0.031206</td>\n",
       "      <td>0.189240</td>\n",
       "      <td>0.198604</td>\n",
       "      <td>0.254465</td>\n",
       "      <td>0.441967</td>\n",
       "      <td>15.301790</td>\n",
       "      <td>1.460634</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[5]</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>theta[6]</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>lp__</th>\n",
       "      <td>-12498.151566</td>\n",
       "      <td>5119.480905</td>\n",
       "      <td>9137.734189</td>\n",
       "      <td>-29988.990545</td>\n",
       "      <td>-24584.712075</td>\n",
       "      <td>-9938.561453</td>\n",
       "      <td>-4281.189125</td>\n",
       "      <td>-4279.113187</td>\n",
       "      <td>3.185849</td>\n",
       "      <td>2.328114</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>616 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                      mean      se_mean           sd          2.5%  \\\n",
       "t_inc            23.346120     9.795726    15.805188      4.147731   \n",
       "t_inf            22.711611     1.547090     4.676723     18.009874   \n",
       "r_t               9.308984     3.913067     6.426815      0.902542   \n",
       "rho               0.215268     0.025360     0.099201      0.031206   \n",
       "S0                0.742325     0.173294     0.270212      0.326534   \n",
       "Z_hat[1,1]     1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[2,1]     1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[3,1]     1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[4,1]     1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[5,1]     1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[6,1]     1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[7,1]     1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[8,1]     1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[9,1]     1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[10,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[11,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[12,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[13,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[14,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[15,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[16,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[17,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[18,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[19,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[20,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[21,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[22,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[23,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[24,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_hat[25,1]    1484.649570   346.588531   540.424321    653.067105   \n",
       "...                    ...          ...          ...           ...   \n",
       "Z_hat[132,4]    512.327554   346.770491   537.937164     24.923854   \n",
       "Z_hat[133,4]    512.428858   346.778938   538.020637     24.924662   \n",
       "Z_hat[134,4]    512.526564   346.786519   538.101081     24.925534   \n",
       "Z_hat[135,4]    512.620807   346.793289   538.178616     24.926807   \n",
       "Z_hat[136,4]    512.711719   346.799298   538.253354     24.927448   \n",
       "Z_hat[137,4]    512.799423   346.804594   538.325405     24.928135   \n",
       "Z_hat[138,4]    512.884040   346.809222   538.394873     24.928726   \n",
       "Z_hat[139,4]    512.965684   346.813226   538.461857     24.929404   \n",
       "Z_hat[140,4]    513.044467   346.816646   538.526454     24.929938   \n",
       "Z_hat[141,4]    513.120495   346.819521   538.588755     24.930443   \n",
       "Z_hat[142,4]    513.193869   346.821886   538.648849     24.930956   \n",
       "Z_hat[143,4]    513.264688   346.823777   538.706820     24.931513   \n",
       "Z_hat[144,4]    513.333046   346.825224   538.762750     24.932079   \n",
       "Z_hat[145,4]    513.399034   346.826260   538.816714     24.932703   \n",
       "Z_hat[146,4]    513.462739   346.826913   538.868790     24.933296   \n",
       "Z_hat[147,4]    513.524244   346.827210   538.919047     24.933857   \n",
       "Z_hat[148,4]    513.583631   346.827177   538.967555     24.934389   \n",
       "Z_hat[149,4]    513.640976   346.826837   539.014379     24.934894   \n",
       "Z_hat[150,4]    513.696354   346.826215   539.059582     24.935372   \n",
       "Z_init[1]      1484.649570   346.588531   540.424321    653.067105   \n",
       "Z_init[2]         0.000000          NaN     0.000000      0.000000   \n",
       "Z_init[3]       515.350430   346.588531   540.424321     24.942897   \n",
       "Z_init[4]         0.000000          NaN     0.000000      0.000000   \n",
       "theta[1]         23.346120     9.795726    15.805188      4.147731   \n",
       "theta[2]         22.711611     1.547090     4.676723     18.009874   \n",
       "theta[3]          9.308984     3.913067     6.426815      0.902542   \n",
       "theta[4]          0.215268     0.025360     0.099201      0.031206   \n",
       "theta[5]          0.000000          NaN     0.000000      0.000000   \n",
       "theta[6]          0.000000          NaN     0.000000      0.000000   \n",
       "lp__         -12498.151566  5119.480905  9137.734189 -29988.990545   \n",
       "\n",
       "                       25%          50%          75%        97.5%      n_eff  \\\n",
       "t_inc             5.059879    36.066159    37.692059    37.732697   2.603311   \n",
       "t_inf            19.510625    21.276597    25.590881    37.013475   9.138017   \n",
       "r_t               2.493323    10.975670    16.956968    17.337714   2.697472   \n",
       "rho               0.189240     0.198604     0.254465     0.441967  15.301790   \n",
       "S0                0.362061     0.817119     0.985307     0.987529   2.431316   \n",
       "Z_hat[1,1]      724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[2,1]      724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[3,1]      724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[4,1]      724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[5,1]      724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[6,1]      724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[7,1]      724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[8,1]      724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[9,1]      724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[10,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[11,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[12,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[13,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[14,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[15,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[16,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[17,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[18,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[19,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[20,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[21,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[22,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[23,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[24,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_hat[25,1]     724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "...                    ...          ...          ...          ...        ...   \n",
       "Z_hat[132,4]     29.356881   363.619751  1257.545233  1344.488673   2.406461   \n",
       "Z_hat[133,4]     29.358564   363.700485  1258.051545  1344.603649   2.407091   \n",
       "Z_hat[134,4]     29.360077   363.778097  1258.543332  1344.713216   2.407705   \n",
       "Z_hat[135,4]     29.361106   363.853529  1259.021033  1344.817629   2.408305   \n",
       "Z_hat[136,4]     29.362277   363.927194  1259.485075  1344.917131   2.408891   \n",
       "Z_hat[137,4]     29.363425   363.996148  1259.935871  1345.011952   2.409462   \n",
       "Z_hat[138,4]     29.364542   364.065740  1260.373821  1345.102313   2.410019   \n",
       "Z_hat[139,4]     29.365712   364.129465  1260.799309  1345.188423   2.410564   \n",
       "Z_hat[140,4]     29.366941   364.190726  1261.212711  1345.270483   2.411094   \n",
       "Z_hat[141,4]     29.368013   364.251806  1261.614387  1345.348682   2.411612   \n",
       "Z_hat[142,4]     29.369071   364.308422  1262.004687  1345.423203   2.412118   \n",
       "Z_hat[143,4]     29.370007   364.362848  1262.383952  1345.494219   2.412611   \n",
       "Z_hat[144,4]     29.370822   364.421860  1262.752508  1345.561894   2.413091   \n",
       "Z_hat[145,4]     29.371464   364.472159  1263.110673  1345.626385   2.413560   \n",
       "Z_hat[146,4]     29.372019   364.526479  1263.458756  1345.687843   2.414018   \n",
       "Z_hat[147,4]     29.372637   364.575702  1263.797052  1345.746410   2.414464   \n",
       "Z_hat[148,4]     29.373372   364.620389  1264.125852  1345.802222   2.414899   \n",
       "Z_hat[149,4]     29.374091   364.665531  1264.445434  1345.855409   2.415324   \n",
       "Z_hat[150,4]     29.374719   364.706830  1264.756069  1345.906094   2.415737   \n",
       "Z_init[1]       724.121394  1634.237542  1970.613176  1975.057103   2.431316   \n",
       "Z_init[2]         0.000000     0.000000     0.000000     0.000000        NaN   \n",
       "Z_init[3]        29.386824   365.762458  1275.878606  1346.932895   2.431316   \n",
       "Z_init[4]         0.000000     0.000000     0.000000     0.000000        NaN   \n",
       "theta[1]          5.059879    36.066159    37.692059    37.732697   2.603311   \n",
       "theta[2]         19.510625    21.276597    25.590881    37.013475   9.138017   \n",
       "theta[3]          2.493323    10.975670    16.956968    17.337714   2.697472   \n",
       "theta[4]          0.189240     0.198604     0.254465     0.441967  15.301790   \n",
       "theta[5]          0.000000     0.000000     0.000000     0.000000        NaN   \n",
       "theta[6]          0.000000     0.000000     0.000000     0.000000        NaN   \n",
       "lp__         -24584.712075 -9938.561453 -4281.189125 -4279.113187   3.185849   \n",
       "\n",
       "                  Rhat  \n",
       "t_inc         3.020099  \n",
       "t_inf         1.544864  \n",
       "r_t           3.172794  \n",
       "rho           1.460634  \n",
       "S0            3.354659  \n",
       "Z_hat[1,1]    3.354659  \n",
       "Z_hat[2,1]    3.354659  \n",
       "Z_hat[3,1]    3.354659  \n",
       "Z_hat[4,1]    3.354659  \n",
       "Z_hat[5,1]    3.354659  \n",
       "Z_hat[6,1]    3.354659  \n",
       "Z_hat[7,1]    3.354659  \n",
       "Z_hat[8,1]    3.354659  \n",
       "Z_hat[9,1]    3.354659  \n",
       "Z_hat[10,1]   3.354659  \n",
       "Z_hat[11,1]   3.354659  \n",
       "Z_hat[12,1]   3.354659  \n",
       "Z_hat[13,1]   3.354659  \n",
       "Z_hat[14,1]   3.354659  \n",
       "Z_hat[15,1]   3.354659  \n",
       "Z_hat[16,1]   3.354659  \n",
       "Z_hat[17,1]   3.354659  \n",
       "Z_hat[18,1]   3.354659  \n",
       "Z_hat[19,1]   3.354659  \n",
       "Z_hat[20,1]   3.354659  \n",
       "Z_hat[21,1]   3.354659  \n",
       "Z_hat[22,1]   3.354659  \n",
       "Z_hat[23,1]   3.354659  \n",
       "Z_hat[24,1]   3.354659  \n",
       "Z_hat[25,1]   3.354659  \n",
       "...                ...  \n",
       "Z_hat[132,4]  3.437432  \n",
       "Z_hat[133,4]  3.435244  \n",
       "Z_hat[134,4]  3.433113  \n",
       "Z_hat[135,4]  3.431038  \n",
       "Z_hat[136,4]  3.429017  \n",
       "Z_hat[137,4]  3.427049  \n",
       "Z_hat[138,4]  3.425133  \n",
       "Z_hat[139,4]  3.423266  \n",
       "Z_hat[140,4]  3.421449  \n",
       "Z_hat[141,4]  3.419680  \n",
       "Z_hat[142,4]  3.417957  \n",
       "Z_hat[143,4]  3.416279  \n",
       "Z_hat[144,4]  3.414645  \n",
       "Z_hat[145,4]  3.413054  \n",
       "Z_hat[146,4]  3.411505  \n",
       "Z_hat[147,4]  3.409997  \n",
       "Z_hat[148,4]  3.408528  \n",
       "Z_hat[149,4]  3.407098  \n",
       "Z_hat[150,4]  3.405706  \n",
       "Z_init[1]     3.354659  \n",
       "Z_init[2]          NaN  \n",
       "Z_init[3]     3.354659  \n",
       "Z_init[4]          NaN  \n",
       "theta[1]      3.020099  \n",
       "theta[2]      1.544864  \n",
       "theta[3]      3.172794  \n",
       "theta[4]      1.460634  \n",
       "theta[5]           NaN  \n",
       "theta[6]           NaN  \n",
       "lp__          2.328114  \n",
       "\n",
       "[616 rows x 10 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_trace(param, param_name='parameter'):\n",
    "  \"\"\"Plot the trace and posterior of a parameter.\"\"\"\n",
    "  \n",
    "  # Summary statistics\n",
    "  mean = np.mean(param)\n",
    "  median = np.median(param)\n",
    "  cred_min, cred_max = np.percentile(param, 2.5), np.percentile(param, 97.5)\n",
    "  \n",
    "  # Plotting\n",
    "  plt.subplot(2,1,1)\n",
    "  plt.plot(param)\n",
    "  plt.xlabel('samples')\n",
    "  plt.ylabel(param_name)\n",
    "  plt.axhline(mean, color='r', lw=2, linestyle='--')\n",
    "  plt.axhline(median, color='c', lw=2, linestyle='--')\n",
    "  plt.axhline(cred_min, linestyle=':', color='k', alpha=0.2)\n",
    "  plt.axhline(cred_max, linestyle=':', color='k', alpha=0.2)\n",
    "  plt.title('Trace and Posterior Distribution for {}'.format(param_name))\n",
    "\n",
    "  plt.subplot(2,1,2)\n",
    "  plt.hist(param, 30, density=True); sns.kdeplot(param, shade=True)\n",
    "  plt.xlabel(param_name)\n",
    "  plt.ylabel('density')\n",
    "  plt.axvline(mean, color='r', lw=2, linestyle='--',label='mean')\n",
    "  plt.axvline(median, color='c', lw=2, linestyle='--',label='median')\n",
    "  plt.axvline(cred_min, linestyle=':', color='k', alpha=0.2, label='95% CI')\n",
    "  plt.axvline(cred_max, linestyle=':', color='k', alpha=0.2)\n",
    "  \n",
    "  plt.gcf().tight_layout()\n",
    "  plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\henri\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.figure();\n",
    "#plot_trace(p_obs_hat, param_name='p_obs')\n",
    "plt.figure();\n",
    "plot_trace(t_inc_hat, param_name='t_inc')\n",
    "plt.figure();\n",
    "plot_trace(r_t_hat, param_name='r_t')\n",
    "plt.figure();\n",
    "plot_trace(rho_hat, param_name='rho')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Very simple older model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_Z( T, p_inf, N, Z_0= 1):\n",
    "    Z = np.zeros(T,dtype=int)\n",
    "    Z[0] = Z_0;\n",
    "    for t in range(1, T):\n",
    "        Z[t] =  Z[t - 1]+np.random.binomial(N-Z[t-1], p_inf, 1) # one try    \n",
    "    return Z;\n",
    "\n",
    "def sample_X(T,Z, p_obs):\n",
    "    X = np.zeros(T,dtype=int)\n",
    "    for t in range(0, T):\n",
    "        X[t] =  Z[t] +np.random.negative_binomial(Z[t], p_obs, size=1) \n",
    "    return X;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Parameters to be inferred\n",
    "p_inf   = 0.001\n",
    "p_obs   = 0.7\n",
    "\n",
    "# sample from a data generator\n",
    "Z = sample_Z( T, p_inf, N, Z_0= 10)\n",
    "X = sample_X( T, Z, p_obs)\n",
    "print(Z)\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(Z, color =\"red\")\n",
    "plt.plot(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Put our data in a dictionary\n",
    "data = {'N': N, 'T': T, 'X': X, 'Z':Z}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Train the model and generate samples\n",
    "fit = sm.sampling(data=data, iter=1000, chains=4, warmup=500, thin=1, seed=101)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "summary_dict = fit.summary()\n",
    "df = pd.DataFrame(summary_dict['summary'], \n",
    "                  columns=summary_dict['summary_colnames'], \n",
    "                  index=summary_dict['summary_rownames'])\n",
    "\n",
    "alpha_mean, beta_mean = df['mean']['p_inf'], df['mean']['p_obs']\n",
    "\n",
    "# Extracting traces\n",
    "p_inf_f = fit['p_inf']\n",
    "p_obs_f = fit['p_obs']\n",
    "lp = fit['lp__']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_trace(p_obs_f, param_name='parameter')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
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}