Stan modeling - HRTEM data & Call center data.ipynb

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  "metadata": {
    "colab": {
      "name": "[Hoang Tran] CS146 Assignment 3.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S0i-gAAbe7RG",
        "colab_type": "text"
      },
      "source": [
        "# Assigment 3\n",
        "\n",
        "Content: \n",
        "- Part 1 (Call center dataset, Normal likelihood with normal-inverse-gamma prior, and log-normal HRTEM data)\n",
        "- Part 2 (Stretch goal)\n",
        "\n",
        "### HCs Appendix\n",
        "- **#modeling**: All the code are based on simulations and modeling using StanCode. For the stretch goal, I created a function for measuring the prior hyper parameters given some conditions. I also modify the default Stan Model for higher convergence. \n",
        "- #heuristics: I applied Means-ends analysis to modify the default pystan default metrics (increase the adapt_delta, number of iterations) as I want higher convergence. I follow the Stan documentations on steps toward my goals (convergence), which results in the modified code."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "veqTHukZdI7_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# importing packages\n",
        "\n",
        "import pystan\n",
        "import numpy as np\n",
        "import scipy as sp\n",
        "import scipy.stats as sts\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "np.random.seed(2019)\n",
        "%matplotlib inline"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u1JeDVE_QhjI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zzgptqcGQhuO",
        "colab_type": "text"
      },
      "source": [
        "# Part 1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yywXtGdiMBMk",
        "colab_type": "text"
      },
      "source": [
        "## 1. Call center data set — exponential likelihood with a gamma prior"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tA4zbxRAeufd",
        "colab_type": "code",
        "outputId": "35f31c49-abbc-467e-b8c3-74218b64436a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        }
      },
      "source": [
        "# Load the data set containing durations between calls arriving at the call\n",
        "# center during 1 day. All values are in minutes.\n",
        "waiting_times_day = np.loadtxt('https://docs.google.com/spreadsheets/d/e/2PACX-1vTDuQCIYts48eH8mNrw60_c5H0cjRzhwxD2OLveOaN5DnelQ99s22oU2rzRyLS0Oh1iNlEatp68fdmv/pub?gid=485723753&single=true&output=csv')\n",
        "\n",
        "# Display some basic information about the data set.\n",
        "print('Size of data set:', len(waiting_times_day))\n",
        "print('First 3 values in data set:', waiting_times_day[:3])\n",
        "print('Sum of data set:', sum(waiting_times_day))\n",
        "\n",
        "# Make 24 empty lists, one per hour.\n",
        "waiting_times_per_hour = [[] for _ in range(24)]\n",
        "\n",
        "# Split the data into 24 separate series, one for each hour of the day.\n",
        "current_time = 0\n",
        "for t in waiting_times_day:\n",
        "    current_hour = int(current_time // 60)\n",
        "    current_time += t\n",
        "    waiting_times_per_hour[current_hour].append(t)"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Size of data set: 5856\n",
            "First 3 values in data set: [30.   3.4  3.2]\n",
            "Sum of data set: 1441.6838153800093\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PuuHArXyezq9",
        "colab_type": "code",
        "outputId": "a78ca572-6c92-46cb-d317-151235b0cb4d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "stan_code = \"\"\"\n",
        "\n",
        "// The data block contains all known quantities - typically the observed\n",
        "// data and any constant hyperparameters.\n",
        "data {  \n",
        "    int<lower=1> num_calls;  \n",
        "    real<lower=0> call[num_calls];  \n",
        "    real<lower=0> alpha;  // fixed prior hyperparameter\n",
        "    real<lower=0> beta;   // fixed prior hyperparameter\n",
        "}\n",
        "\n",
        "// The parameters block contains all unknown quantities - typically the\n",
        "// parameters of the model. Stan will generate samples from the posterior\n",
        "// distributions over all parameters.\n",
        "parameters {\n",
        "    real<lower=0> lambda;  \n",
        "}\n",
        "\n",
        "// The model block contains all probability distributions in the model.\n",
        "// This of this as specifying the generative model for the scenario.\n",
        "model {\n",
        "    lambda ~ gamma(alpha, beta);  // prior\n",
        "    for(i in 1:num_calls) {\n",
        "        call[i] ~ exponential(lambda);  // likelihood function\n",
        "    }\n",
        "}\n",
        "\n",
        "\"\"\"\n",
        "stan_model = pystan.StanModel(model_code=stan_code)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_6dd61ab5dd02fec5575754133ad6eead NOW.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RQG440m-nyvK",
        "colab_type": "code",
        "outputId": "cf90ebb6-41c3-447f-ba3a-4d65b283d9a7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        }
      },
      "source": [
        "input_data = {\n",
        "    'num_calls' : len(waiting_times_per_hour[13]),\n",
        "    'call': waiting_times_per_hour[13],\n",
        "    'alpha' : 1,\n",
        "    'beta' : 0.25\n",
        "}\n",
        "\n",
        "# Fit the model to the data. This will generate samples from the posterior over\n",
        "# all parameters of the model. \n",
        "stan_results = stan_model.sampling(data=input_data)\n",
        "\n",
        "print(stan_results)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Inference for Stan model: anon_model_6dd61ab5dd02fec5575754133ad6eead.\n",
            "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
            "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
            "\n",
            "         mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
            "lambda   6.35  8.2e-3   0.32   5.74   6.14   6.34   6.56   6.99   1519    1.0\n",
            "lp__   324.44    0.02   0.69 322.44 324.27 324.71 324.88 324.92   2006    1.0\n",
            "\n",
            "Samples were drawn using NUTS at Sat Oct 19 15:03:55 2019.\n",
            "For each parameter, n_eff is a crude measure of effective sample size,\n",
            "and Rhat is the potential scale reduction factor on split chains (at \n",
            "convergence, Rhat=1).\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MGO0AhuHg6JH",
        "colab_type": "text"
      },
      "source": [
        "### Posterior 98% confidence interval over λ"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XEJ_wrIWoWHY",
        "colab_type": "code",
        "outputId": "1184609d-5524-45ed-b180-87e6f805aa0b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "# extract samples from stan_results\n",
        "posterior_samples = stan_results.extract()\n",
        "print(\n",
        "    \"Posterior 98% confidence interval for lambda:\",\n",
        "    # percentile using numpy\n",
        "    np.percentile(posterior_samples['lambda'], [1, 99]))"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Posterior 98% confidence interval for lambda: [5.6352548  7.14216347]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FBpSOSo5hSfi",
        "colab_type": "text"
      },
      "source": [
        "### Histogram of posterior λ samples"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ttOZ5gWMhPN4",
        "colab_type": "code",
        "outputId": "0520c629-4625-42f0-b1df-b812eb35741a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "# Plot using matplotlib\n",
        "plt.hist(posterior_samples['lambda'], bins=50, density=True)\n",
        "plt.title('Sampled posterior probability density for lambda')\n",
        "plt.show()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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HRM9oBWz5qWr4pdFy1i87spLlm40nrdwts6hJ+UnASZVFZGZmbfMvVM3MMuTkbmaWISd3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\nGfpfkApsdyZQMO8AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1zUb4KkTh1iO",
        "colab_type": "text"
      },
      "source": [
        "### The likelihood function for the expected λ on top of the data histogram"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CNd6YVoSof2g",
        "colab_type": "code",
        "outputId": "e86fcbd7-8ce8-4e5b-c947-55a628c06837",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        }
      },
      "source": [
        "# Plot the likelihood function for the expected λ on top of the data histogram\n",
        "\n",
        "# plot the mean + the 95% uncertainty of lambda\n",
        "lambda_1 = np.mean(posterior_samples['lambda'])\n",
        "lambda_2 = np.percentile(posterior_samples['lambda'], 2.5)\n",
        "lambda_3 = np.percentile(posterior_samples['lambda'], 97.5)\n",
        "x = np.linspace(0, max(waiting_times_per_hour[13]), 200)\n",
        "y_1 = sts.expon.pdf(x, scale=1/lambda_1)\n",
        "y_2 = sts.expon.pdf(x, scale=1/lambda_2)\n",
        "y_3 = sts.expon.pdf(x, scale=1/lambda_3)\n",
        "plt.plot(x, y_1, color = \"red\")\n",
        "plt.plot(x, y_2, color = \"black\", linestyle = \"--\")\n",
        "plt.plot(x, y_3, color = \"black\", linestyle = \"--\")\n",
        "\n",
        "# histogram of data\n",
        "plt.hist(waiting_times_per_hour[13], bins=20, density=True)\n",
        "\n",
        "# title\n",
        "plt.title('The likelihood function for the expected λ (red line), \\n 95% uncertainty (dotted black line) and the data histogram')\n",
        "plt.show()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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I65r6GTPAGBo1akRaWhoL3PbwlVJKnSmgE/1ll11G/fr1+eqrr053HDIEdu+G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\nf4eklFKAJnqv6jt0KFd17Mj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ys7MZMWIE48ePxxhD//79qV+/Ps2bN6dx48bkHDxASFxd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\nPqWUGvcDtAcvcNdXacYAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rLP864FBxwnJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "McnFYSS0y1fp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KabrgZojy1lu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xScs2uJUMRzB",
        "colab_type": "text"
      },
      "source": [
        "## 2. Normal likelihood with normal-inverse-gamma prior"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uGhc2t0Vy1cg",
        "colab_type": "code",
        "outputId": "2cb23114-1e3f-467e-8a14-04d53e188ab2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "stan_code = \"\"\"\n",
        "\n",
        "// The data block contains all known quantities - typically the observed\n",
        "// data and any constant hyperparameters.\n",
        "data {  \n",
        "    int<lower=1> num_data;  // number of data\n",
        "    real ndata[num_data];  // data\n",
        "    real<lower=0> mu;  // fixed prior hyperparameter\n",
        "    real<lower=0> nu;   // fixed prior hyperparameter\n",
        "    real<lower=0> alpha;  // fixed prior hyperparameter\n",
        "    real<lower=0> beta;   // fixed prior hyperparameter\n",
        "}\n",
        "\n",
        "// The parameters block contains all unknown quantities - typically the\n",
        "// parameters of the model. Stan will generate samples from the posterior\n",
        "// distributions over all parameters.\n",
        "parameters {\n",
        "    real<lower=0> sigma;\n",
        "    real<lower=0> mean_;\n",
        "}\n",
        "\n",
        "// The model block contains all probability distributions in the model.\n",
        "// This of this as specifying the generative model for the scenario.\n",
        "model {\n",
        "    // The normal inverse gamma is: variance sampled from a inv_gamma dist.\n",
        "    // And the mean is sampled from a normal dist.\n",
        "    sigma ~ inv_gamma(alpha, beta);   // variance\n",
        "    mean_ ~ normal(mu, sqrt(sigma/nu));   // mean\n",
        "    for(i in 1:num_data) {\n",
        "        ndata[i] ~ normal(mean_, sqrt(sigma));  // likelihood function\n",
        "    }\n",
        "}\n",
        "\n",
        "\"\"\"\n",
        "\n",
        "stan_model = pystan.StanModel(model_code=stan_code)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_422b92d0cd90b5cf9ef56036ee0fbea9 NOW.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ov7GdjbNEH2M",
        "colab_type": "code",
        "outputId": "1dd425ce-e63a-4080-e5a4-143842cb4b76",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "data = np.array([3.54551763569501, 4.23799861761927, 4.72138425951628, -0.692265320368236, 3.04473513808788, 3.10721270732507, 3.42982225852764, 3.12153903971176, 3.60532628639808, 2.46561737557325, 1.64059465916131, 2.4621623937158, 2.76744495617481, 2.11580054750407, 5.14077208608354, 4.90288499104252, 1.43357579078348, 4.78997817363558, 1.93633438207439, 2.43698838097178, 3.95389148701877, 2.4242295507716, 2.90256268679023, 2.90931728045901, 0.658072819386888, 3.05946763895983, 3.42615331539605, 2.68842833004417, 2.35850130765166, 2.20014998540933, 4.73846511350084, 4.19839721414451, 2.11805510171691, -0.572742936038015, 0.389413982010623, 3.87846130744249, 1.34057656890858, 0.7235748351719, 5.11042369840174, 4.00747556696571, 3.18080956726965, 3.24677964069676, 5.1154659863626, 1.80276616697155, 0.305877679021404, -0.449168307882718, 4.63705561194774, 1.37783714058301, 4.9608149859515, 6.7764195802069, 1.75515522922399, 7.04457337435215, 0.625185284955128, 2.25130734369064, 2.19770178119255, 2.16858257249432, 6.25367644481438, 0.116081323476489, 2.06315857864341, 1.82409781471718, 5.15226741230987, 2.03408231293173, -1.12450854337596, 5.03511270642234, 2.03841989653263, 5.80911741751597, 2.31718128783245, 4.97575010580997, 3.34262752222776, -0.786983904253601, 0.777362359850013, 0.975825009321195, 3.76354577515958, 7.27215002907876, 1.35404089480189, 3.76567940257157, 3.48573993343334, 1.85976988586156, 1.93567061960716, 5.31071812003942, 2.96832987672751, 3.32378908637275, 2.61631960054551, 5.80897964052825, 4.95215217171488, 1.32036772796131, 3.79932542233371, 3.08108492766309, 2.6734110081666, -0.14251851138521, 2.48744375588965, 3.98463042123415, 6.32781680028, 4.0029172024315, 4.23210369459457, 1.71412938967325, 5.16492114963802, 2.53409673107906, 4.77346963973334, 3.34088878725551, 4.77681472750664, 3.81135755590976, 1.14054269983137, 1.42057452397702, 0.132142311125433, 7.12577254064672, 4.85422012781764, 4.15745720676399, 4.48763147363348, 1.56060322283629, 2.64821761542887, 1.26655351354548, 4.48497722937931, 4.3286302403783, 4.26157679512625, 4.0597558651364, 5.14051109132496, 2.5660348362221, 1.10764013818617, 0.386889523012303, 3.54150473246237, 3.57480214382351, 1.95150869584847, 2.70688970563118, 2.47971849820016, 6.50838037000679, 4.01511556826974, 1.11562740835344, 5.02637639472439, 4.38184491686864, 5.60423144047386, 2.40067408379298, 5.7849941378344, 2.37225791084559, 6.86031465910273, 4.09214858239736, 6.85994063692621, 3.62202415158781, -1.11220646958158, 3.73920971696866, 3.24533871512216, 1.28724203643002, 0.291152541773164, 0.368630935755111, 6.71607270510525, 5.42278455200833, 5.35188416119281, 2.305874586163, -1.85878097203032, 2.69877382351447, 4.84121860550417, 4.40973060799391, 5.04399320650774, 2.68632252661298, 6.06531610659912, 3.11881325011993, 3.45532087005125, 3.08442259840346, 4.43564424136733, 2.84252623135804, 1.50536798885106, 1.48868622407603, 2.07322837615663, 2.5476910210998, 5.66941808257884, 2.16731067416426, 2.49843958833905, 3.94586413879977, 0.316433764679541, -0.608937441815983, 2.5943436558557, 1.05516869528337, 2.1447601332725, 6.65846634141906, 2.1771555267834, 5.23953812029442, 3.53629759842647, 6.03263538017003, 3.85739159396599, 5.95093453004638, 1.12856987160476, 3.5559912886093, 2.21974864244489, 3.38471394882135, -1.90805399279409, 3.5113699258973, 4.49319955412346, 5.10507952638867, 1.08277895384184, 4.58403638422759, 1.37304994426824, 4.17566975753523, 3.36454182510378, 0.177136582644021, 2.91337423388405, 3.22796455457526, 2.80124198378441, 1.95189718582788, 3.37659263896246, -1.6463045238231])\n",
        "print(len(data), \"data\")"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "200 data\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "82WMFXlK7MDJ",
        "colab_type": "code",
        "outputId": "25f9aff8-0ba4-4828-d9ec-9134fa01b5ef",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        }
      },
      "source": [
        "# priors taken from the prompt\n",
        "input_data = {\n",
        "    'num_data' : len(data),\n",
        "    'ndata': data,\n",
        "    'mu' : 0,\n",
        "    'nu' : 0.054,\n",
        "    'alpha': 1.12,\n",
        "    'beta': 0.4\n",
        "}\n",
        "\n",
        "stan_results = stan_model.sampling(data=input_data)\n",
        "print(stan_results)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Inference for Stan model: anon_model_422b92d0cd90b5cf9ef56036ee0fbea9.\n",
            "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
            "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
            "\n",
            "        mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
            "sigma   3.62  6.6e-3   0.36   2.98   3.37    3.6   3.86   4.39   2932    1.0\n",
            "mean_   3.06  2.5e-3   0.13    2.8   2.97   3.06   3.15   3.32   2919    1.0\n",
            "lp__  -232.1    0.02   0.96 -234.7 -232.4 -231.8 -231.4 -231.1   1798    1.0\n",
            "\n",
            "Samples were drawn using NUTS at Sat Oct 19 15:05:08 2019.\n",
            "For each parameter, n_eff is a crude measure of effective sample size,\n",
            "and Rhat is the potential scale reduction factor on split chains (at \n",
            "convergence, Rhat=1).\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lHji0y6z98q3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# extract samplings data from stan_results\n",
        "posterior_samples = stan_results.extract()\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fTD8IBfGmLzs",
        "colab_type": "text"
      },
      "source": [
        "### 95% posterior confidence intervals for the μ and variance σ of the log-transformed data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Edwfu9AOPRFx",
        "colab_type": "code",
        "outputId": "897a83f9-51a7-407e-a1cc-5d7094109c74",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        }
      },
      "source": [
        "# sample (With replacement) 1000000 samples from posterior_samples\n",
        "sample_sigma = np.random.choice(posterior_samples['sigma'], 1000000)\n",
        "sample_mean_ = np.random.choice(posterior_samples['mean_'], 1000000)\n",
        "\n",
        "# compute confidence intervals\n",
        "print('95% prior confidence intervals:')\n",
        "print('x: [%.3f, %.3f]' % (\n",
        "    np.percentile(sample_mean_, 2.5),\n",
        "    np.percentile(sample_mean_, 97.5)))\n",
        "print('σ²: [%.3f, %.3f]' % (\n",
        "    np.percentile(sample_sigma, 2.5),\n",
        "    np.percentile(sample_sigma, 97.5)))"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "95% prior confidence intervals:\n",
            "x: [2.804, 3.324]\n",
            "σ²: [2.987, 4.395]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9uALii-XmCcV",
        "colab_type": "text"
      },
      "source": [
        "### Take 10 samples from your posterior over μ and σ and plot the log-normal distributions corresponding to them"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GWuTZLYsO0_V",
        "colab_type": "code",
        "outputId": "e80321d0-1525-4e15-efd8-12931cdc231e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 390
        }
      },
      "source": [
        "# take 10 samples\n",
        "sigma_items = np.random.choice(posterior_samples['sigma'], 10)\n",
        "mean__items = np.random.choice(posterior_samples['mean_'], 10)\n",
        "plt.figure(figsize=(12, 6))\n",
        "# plot histogram\n",
        "plt.hist(data, density = True)\n",
        "\n",
        "# plot 10 samples\n",
        "\n",
        "plot_x = np.linspace(-15, 15, 500)\n",
        "num_samples = 10\n",
        "for i in range(num_samples):\n",
        "    plot_y = sts.norm.pdf(plot_x, loc=mean__items[i], scale=np.sqrt(sigma_items[i]))\n",
        "    plt.plot(plot_x, plot_y)\n",
        "plt.title('%i samples from a normal-inverse-gamma prior distribution and the data histogram' % num_samples)\n",
        "plt.show()"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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TbbetQIW8fKcbL3Y/33YgKvYFfFN1y8C3JxxDurHrf/g4MXK9/wm4XUSWOd8x3wU2GGPq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\nocWn8vTA0wDoTk3OrVJVTbyeNqrTrwDwteM9AFzePIZSXp4xLpNu2Ly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ky6tka7Fk7XtL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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qPO82cM3NDbK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u1wzj_4FSCAj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eMEyDhnvSCLn",
        "colab_type": "text"
      },
      "source": [
        "## 3. Log-normal HRTEM data. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yiQLIsgCSRay",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# load data\n",
        "data = np.loadtxt('https://course-resources.minerva.kgi.edu/uploaded_files/mke/00075398-1635/hrtem.csv')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PsTlX-mhTV2P",
        "colab_type": "code",
        "outputId": "a3ca1d6e-32d0-4b28-d842-0e5eda0b83b6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "source": [
        "stan_code = \"\"\"\n",
        "\n",
        "// The data block contains all known quantities - typically the observed\n",
        "// data and any constant hyperparameters.\n",
        "data {  \n",
        "    int<lower=1> num_data;  // number of data\n",
        "    real ndata[num_data];  // data\n",
        "    real<lower=0> mu;  // fixed prior hyperparameter\n",
        "    real<lower=0> nu;   // fixed prior hyperparameter\n",
        "    real<lower=0> alpha; // fixed prior hyperparameter\n",
        "    real<lower=0> beta;  // fixed prior hyperparameter\n",
        "}\n",
        "\n",
        "// create log_data within the stancode\n",
        "transformed data {\n",
        "    real ldata[num_data];\n",
        "    for (n in 1:num_data)\n",
        "      ldata[n] <- log(ndata[n]);\n",
        "}\n",
        "// The parameters block contains all unknown quantities - typically the\n",
        "// parameters of the model. Stan will generate samples from the posterior\n",
        "// distributions over all parameters.\n",
        "parameters {\n",
        "    real<lower=0> sigma;  // variance\n",
        "    real mean_;  // mean\n",
        "}\n",
        "\n",
        "// The model block contains all probability distributions in the model.\n",
        "// This of this as specifying the generative model for the scenario.\n",
        "model {\n",
        "\n",
        "    sigma ~ inv_gamma(alpha, beta);  # variance from inv_gamma dist.\n",
        "    mean_ ~ normal(mu, sqrt(sigma/nu));  # mean from a normal dist.\n",
        "    for(i in 1:num_data) {\n",
        "        ldata[i] ~ normal(mean_, sqrt(sigma));  // likelihood function\n",
        "    }\n",
        "}\n",
        "\n",
        "\"\"\"\n",
        "\n",
        "stan_model = pystan.StanModel(model_code=stan_code)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_9b49aadd366a9743df1a60e22a1dbb22 NOW.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "myUovSHHUSpa",
        "colab_type": "code",
        "outputId": "4b7a0662-7929-4297-e041-a446053582bb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        }
      },
      "source": [
        "# prior hyperparameters from the prompt\n",
        "\n",
        "input_data = {\n",
        "    'num_data' : len(data),\n",
        "    'ndata': data,\n",
        "    'mu' : 2.3,\n",
        "    'nu' : 0.1,\n",
        "    'alpha': 2,\n",
        "    'beta': 5\n",
        "}\n",
        "\n",
        "stan_results = stan_model.sampling(data=input_data)\n",
        "print(stan_results)"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Inference for Stan model: anon_model_9b49aadd366a9743df1a60e22a1dbb22.\n",
            "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
            "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
            "\n",
            "        mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
            "sigma    0.5  5.3e-4   0.03   0.44   0.47   0.49   0.52   0.56   3545    1.0\n",
            "mean_   1.89  5.2e-4   0.03   1.83   1.87   1.89   1.91   1.95   3683    1.0\n",
            "lp__  -76.04    0.02    1.0 -78.67 -76.45 -75.74 -75.32 -75.04   1698    1.0\n",
            "\n",
            "Samples were drawn using NUTS at Sat Oct 19 15:06:21 2019.\n",
            "For each parameter, n_eff is a crude measure of effective sample size,\n",
            "and Rhat is the potential scale reduction factor on split chains (at \n",
            "convergence, Rhat=1).\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tIoJjHfoU93E",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# extract samples from stan_results\n",
        "posterior_samples = stan_results.extract()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IdidPH9rofGG",
        "colab_type": "text"
      },
      "source": [
        "### 95% posterior confidence intervals for the μ and variance σ of the log-transformed data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zj-oy00dVENO",
        "colab_type": "code",
        "outputId": "dc96aa7b-1384-4395-ee75-9408ad6c770c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        }
      },
      "source": [
        "# random sample (With replacement) from the posterior samples\n",
        "sample_sigma = np.random.choice(posterior_samples['sigma'], 1000000)\n",
        "sample_mean_ = np.random.choice(posterior_samples['mean_'], 1000000)\n",
        "\n",
        "# compute percentile\n",
        "print('95% prior confidence intervals:')\n",
        "print('x: [%.3f, %.3f]' % (\n",
        "    np.percentile(sample_mean_, 2.5),\n",
        "    np.percentile(sample_mean_, 97.5)))\n",
        "print('σ²: [%.3f, %.3f]' % (\n",
        "    np.percentile(sample_sigma, 2.5),\n",
        "    np.percentile(sample_sigma, 97.5)))"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "95% prior confidence intervals:\n",
            "x: [1.832, 1.954]\n",
            "σ²: [0.437, 0.562]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zq3Q9emZozAD",
        "colab_type": "text"
      },
      "source": [
        "### Take 10 samples from your posterior over μ and σ and plot the log-normal distributions corresponding to them"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SkoNI1YoVCSd",
        "colab_type": "code",
        "outputId": "ade6fcc8-7f35-46a2-9850-4bdb9557fe2a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 390
        }
      },
      "source": [
        "sigma_items = np.random.choice(posterior_samples['sigma'], 10)\n",
        "mean__items = np.random.choice(posterior_samples['mean_'], 10)\n",
        "\n",
        "\n",
        "plt.figure(figsize=(12, 6))\n",
        "\n",
        "#plot histogram\n",
        "plt.hist(np.log(data), bins=np.linspace(0, 3.5, 15), density = True)\n",
        "\n",
        "# plot the lines\n",
        "plot_x = np.linspace(0, 3.5, 200)\n",
        "num_samples = 10\n",
        "for i in range(num_samples):\n",
        "    plot_y = sts.norm.pdf(plot_x, loc=mean__items[i], scale=np.sqrt(sigma_items[i]))\n",
        "    plt.plot(plot_x, plot_y)\n",
        "plt.title('%i samples from a normal-inverse-gamma prior distribution with the log(data) histogram' % num_samples)\n",
        "plt.show()"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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IK7tfecxl1h0s496PtpBXUc8tZydxz8Tu+Ji1bhOVlZUsXbqUbdu24WO1EeOf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\nQgDw/wHErf6zt+rPDgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cuHbz_8AVnTh",
        "colab_type": "code",
        "outputId": "d96479c9-58b1-41c0-b43e-cac1e075fde9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 390
        }
      },
      "source": [
        "plt.figure(figsize=(12,6))\n",
        "\n",
        "# plot histogram\n",
        "plt.hist(data, density = True)\n",
        "\n",
        "# plot the line\n",
        "plot_x = np.linspace(0, 30, 200)\n",
        "num_samples = 10\n",
        "for i in range(num_samples):\n",
        "    plot_y = sts.lognorm.pdf(plot_x, np.sqrt(sigma_items[i]), scale=np.exp(mean__items[i]))\n",
        "    plt.plot(plot_x, plot_y)\n",
        "plt.plot(plot_x, plot_y)\n",
        "plt.title('%i samples from a normal-inverse-gamma prior distribution with the real data histogram' % num_samples)\n",
        "plt.show()"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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JaDXb3cJ4IKeIiy+7kMDAQOYunkPbwdUc2FVLZvSb7HGJo/3ie9mxYelhZSQG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\nfl0Tj4879QglP3jVd51mdAQhhBCDlNxhHiCCzlRSgglSXUGyYz4ayKa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eT3lJ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\nSar4AYAKHZ3IxNcOAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "109FlQbcVFEn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SU0C9LhDWX9J",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2SLoXSIyWYGf",
        "colab_type": "text"
      },
      "source": [
        "# Part 2: Stretch goal"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DMAXtljs5IX5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "data = np.loadtxt('https://course-resources.minerva.kgi.edu/uploaded_files/mke/00075398-1635/hrtem.csv')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KJf9eYCjtunw",
        "colab_type": "text"
      },
      "source": [
        "## Reasoning: \n",
        "**Prior distribution:** We think this data can be a combination of 2 normal distribution. Call the mean and variance of both distribution ${\\chi}_1, {\\sigma}_1$ and ${\\chi}_2, {\\sigma}_2$\n",
        "\n",
        "The error margins given below represent 1 standard deviation from the mean of the parameter: \n",
        "\n",
        "We suspect that\n",
        "- ${\\chi}_1$ is approximately 5 ± 1\n",
        "- ${\\sigma}_1$ is approximately 2 ± 1\n",
        "- ${\\chi}_2$ is approximately 11 ± 2\n",
        "- ${\\sigma}_2$ is approximately 4 ± 2\n",
        "- ${\\chi}_1, {\\sigma}_1$ is sampled from the normal-inverse-gamma distribution with parameters - ${\\alpha}_1, \\beta_1, \\mu_1, \\nu_1$\n",
        "- ${\\chi}_2, {\\sigma}_2$ is sampled from the normal-inverse-gamma distribution with parameters - ${\\alpha}_2, \\beta_2, \\mu_2, \\nu_2$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L_hKKYipzHYY",
        "colab_type": "text"
      },
      "source": [
        "### A function to find the hyperparameters \n",
        "\n",
        "As $\\chi, \\sigma$ follows a normal-inverse-gamma distribution of $({\\alpha}, \\beta, \\mu, \\nu)$: \n",
        "\n",
        "$\\chi$ has the mean $a$ and standard deviation $b$; $\\sigma$ has the mean $c$ and standard deviation $d$\n",
        "\n",
        "$mean(\\chi) = a$\n",
        "\n",
        "$\\Rightarrow \\mu = a  \\qquad (1)$\n",
        "\n",
        "$var(\\chi) = b^2 \\qquad$ (because $b$ is the standard deviation)  \n",
        "\n",
        "$\\Rightarrow \\frac{\\beta}{(\\alpha-1)\\nu} = b^2  \\qquad (2)$ \n",
        "\n",
        "$mean(\\sigma) = c$\n",
        "\n",
        "$\\Rightarrow \\frac{\\beta}{\\alpha-1} = c  \\qquad (3)$\n",
        "\n",
        "$var(\\sigma) = d^2  \\qquad$ (because $d$ is the standard deviation) \n",
        "\n",
        "$\\Rightarrow \\frac{\\beta^2}{(\\alpha-1)^2(\\alpha-2)} = d^2 \\qquad (4)$\n",
        "\n",
        "$$$$\n",
        "\n",
        "From $(1)\\Rightarrow \\mu = a$\n",
        "\n",
        "From $(2),(3) \\Rightarrow \\nu = \\frac{c}{b^2}$\n",
        "\n",
        "From $(3),(4) \\Rightarrow \\alpha = \\frac{c^2}{d^2} + 2$\n",
        "\n",
        "From $(3) \\Rightarrow \\beta = c*(\\alpha-1)$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6EFCfR73QAQJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def find_para(a,b,c,d):\n",
        "  mu = a\n",
        "  nu = c/b**2\n",
        "  alpha = c**2/d**2 + 2\n",
        "  beta = c*(alpha-1)\n",
        "  return alpha, beta, mu, nu"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QXdjOB3duN_H",
        "colab_type": "code",
        "outputId": "3d846196-fef9-4c42-bb6e-e6225877af3c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 372
        }
      },
      "source": [
        "stan_code = \"\"\"\n",
        "\n",
        "// The data block contains all known quantities - typically the observed\n",
        "// data and any constant hyperparameters.\n",
        "data {  \n",
        "    int<lower=1> num_data;  \n",
        "    real ndata[num_data]; \n",
        "    real<lower=0> mu_1;  \n",
        "    real<lower=0> nu_1;  \n",
        "    real<lower=0> alpha_1;  \n",
        "    real<lower=0> beta_1;   \n",
        "    real<lower=0> mu_2;\n",
        "    real<lower=0> nu_2;\n",
        "    real<lower=0> alpha_2;  \n",
        "    real<lower=0> beta_2;   \n",
        "}\n",
        "// The parameters block contains all unknown quantities - typically the\n",
        "// parameters of the model. Stan will generate samples from the posterior\n",
        "// distributions over all parameters.\n",
        "parameters {\n",
        "    real <lower = 0, upper = 1> p;\n",
        "    real<lower=0> mean_1;\n",
        "    real<lower=0> sigma_1;\n",
        "    real<lower=0> mean_2;\n",
        "    real<lower=0> sigma_2;\n",
        "}\n",
        "\n",
        "// The model block contains all probability distributions in the model.\n",
        "// This of this as specifying the generative model for the scenario.\n",
        "\n",
        "\n",
        "model {\n",
        "    p ~ uniform(0,1);\n",
        "    sigma_1 ~ inv_gamma(alpha_1, beta_1); \n",
        "    mean_1 ~ normal(mu_1, sqrt(sigma_1/nu_1));\n",
        "    sigma_2 ~ inv_gamma(alpha_2, beta_2); \n",
        "    mean_2 ~ normal(mu_2, sqrt(sigma_2/nu_2));\n",
        "    for (i in 1:num_data){\n",
        "      target += p*normal_lpdf(ndata[i] | mean_1, sqrt(sigma_1)) + (1-p)*normal_lpdf(ndata[i] | mean_2, sqrt(sigma_2));\n",
        "    }\n",
        "    \n",
        "}\n",
        "\"\"\"\n",
        "\n",
        "input_data = {\n",
        "    'num_data' : len(data),\n",
        "    'ndata': data,\n",
        "    'alpha_1' : find_para(5,1,2,1)[0],\n",
        "    'beta_1' : find_para(5,1,2,1)[1],\n",
        "    'mu_1' : find_para(5,1,2,1)[2],\n",
        "    'nu_1' : find_para(5,1,2,1)[3],\n",
        "    'alpha_2' : find_para(11,2,4,2)[0],\n",
        "    'beta_2' : find_para(11,2,4,2)[1],\n",
        "    'mu_2' : find_para(11,2,4,2)[2],\n",
        "    'nu_2' : find_para(11,2,4,2)[3],\n",
        "}\n",
        "\n",
        "control = {}\n",
        "control['max_treedepth'] = 20\n",
        "control['adapt_delta'] = 0.99\n",
        "stan_model = pystan.stan(model_code=stan_code, data = input_data, iter=10000, chains=10, warmup=2000, control = control)\n",
        "\n",
        "stan_model"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING:pystan:DeprecationWarning: pystan.stan was deprecated in version 2.17 and will be removed in version 3.0. Compile and use a Stan program in separate steps.\n",
            "INFO:pystan:COMPILING THE C++ CODE FOR MODEL anon_model_ab6fb997c407dffab853a98c07f04768 NOW.\n",
            "WARNING:pystan:13 of 80000 iterations ended with a divergence (0.0163 %).\n",
            "WARNING:pystan:Try running with adapt_delta larger than 0.99 to remove the divergences.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Inference for Stan model: anon_model_ab6fb997c407dffab853a98c07f04768.\n",
              "10 chains, each with iter=10000; warmup=2000; thin=1; \n",
              "post-warmup draws per chain=8000, total post-warmup draws=80000.\n",
              "\n",
              "          mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
              "p       6.0e-3  3.3e-3   0.07 6.4e-6 7.8e-5 2.0e-4 4.7e-4 2.5e-3    485   1.04\n",
              "mean_1    5.27    0.01   1.16   3.06   4.54   5.24   5.97   7.78  10237    1.0\n",
              "sigma_1   2.88    0.09   2.74    1.0   1.66   2.27   3.23   7.89    889   1.02\n",
              "mean_2    8.31  5.3e-3   0.29   7.82   8.14    8.3   8.47   8.79   2986   1.01\n",
              "sigma_2  29.18    0.08   2.46  25.78  27.99  29.19  30.47  33.12   1069   1.02\n",
              "lp__     -1598    0.01   1.73  -1602  -1599  -1597  -1596  -1595  18791    1.0\n",
              "\n",
              "Samples were drawn using NUTS at Sat Oct 19 15:47:22 2019.\n",
              "For each parameter, n_eff is a crude measure of effective sample size,\n",
              "and Rhat is the potential scale reduction factor on split chains (at \n",
              "convergence, Rhat=1)."
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "26ZYAk_mOIt_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "posterior_samples = stan_model.extract()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nAJS9u0nOP-_",
        "colab_type": "text"
      },
      "source": [
        "### Confidence Intervals and plot the histogram of parameters p"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i5yFBshvOQH6",
        "colab_type": "code",
        "outputId": "765a596c-a615-4675-da37-44e050230c8a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 426
        }
      },
      "source": [
        "# compute percentile\n",
        "plt.figure(figsize=(12,6))\n",
        "print('95% prior confidence intervals:')\n",
        "print('p: [%.3f, %.3f]' % (\n",
        "    np.percentile(posterior_samples['p'], 2.5),\n",
        "    np.percentile(posterior_samples['p'], 97.5)))\n",
        "\n",
        "plt.hist(posterior_samples['p'])\n",
        "plt.title(\"Histogram of parameter p\")\n",
        "plt.show()"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "95% prior confidence intervals:\n",
            "p: [0.000, 0.003]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3w49nMXjCyCHAJ9pLkiRJWjCmDNVVdcYkm06aYGwBZ09ynA3Ahgnq24Djp+pD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\nJ0O1JEmS1MlQLUmSJHX6/+Tau9DZ0SupAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N7gRCZnHOQoY",
        "colab_type": "text"
      },
      "source": [
        "### Confidence Intervals and plot the histogram of parameters $\\chi_1$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gwMByG4QOQxz",
        "colab_type": "code",
        "outputId": "49ea65be-0562-4943-f218-93aaa13c6ddc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 426
        }
      },
      "source": [
        "# compute percentile\n",
        "plt.figure(figsize=(12,6))\n",
        "print('95% prior confidence intervals:')\n",
        "print('χ1: [%.3f, %.3f]' % (\n",
        "    np.percentile(posterior_samples['mean_1'], 2.5),\n",
        "    np.percentile(posterior_samples['mean_1'], 97.5)))\n",
        "\n",
        "plt.hist(posterior_samples['mean_1'])\n",
        "plt.title(\"Histogram of parameter χ1\")\n",
        "plt.show()"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "95% prior confidence intervals:\n",
            "χ1: [3.061, 7.777]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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lyeGj7UqSJEmaut0iWANHAuur6u6qehq4Elg24p4kSZKkKdtdPnlxAbBhaHkj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\ntSRJktSBwVqSJEnq4P8DZ8+5GHwsUZMAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tjMrfoEVOQ6g",
        "colab_type": "text"
      },
      "source": [
        "### Confidence Intervals and plot the histogram of parameters $\\sigma_1$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xop6_n67ORPW",
        "colab_type": "code",
        "outputId": "b9453bb4-5a1a-463c-c1b1-dcf52783e9e4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 426
        }
      },
      "source": [
        "# compute percentile\n",
        "print('95% prior confidence intervals:')\n",
        "print('σ1: [%.3f, %.3f]' % (\n",
        "    np.percentile(posterior_samples['sigma_1'], 2.5),\n",
        "    np.percentile(posterior_samples['sigma_1'], 97.5)))\n",
        "plt.figure(figsize=(12,6))\n",
        "plt.hist(posterior_samples['sigma_1'])\n",
        "plt.title(\"Histogram of parameter σ1\")\n",
        "plt.show()"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "95% prior confidence intervals:\n",
            "σ1: [1.000, 7.890]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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jmS/TP44ANlfV7QBJLgbWALfMaa8kSVpgnL4mzY35EqqXAVuG1rcCR85RX6Sn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\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bv4P07wMORJH",
        "colab_type": "text"
      },
      "source": [
        "### Confidence Intervals and plot the histogram of parameters $\\chi_2$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lZVUGIYyOREf",
        "colab_type": "code",
        "outputId": "a0501037-6f3f-4290-e2b8-109fc01edfe7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 426
        }
      },
      "source": [
        "# compute percentile\n",
        "print('95% prior confidence intervals:')\n",
        "print('χ2: [%.3f, %.3f]' % (\n",
        "    np.percentile(posterior_samples['mean_2'], 2.5),\n",
        "    np.percentile(posterior_samples['mean_2'], 97.5)))\n",
        "plt.figure(figsize=(12,6))\n",
        "plt.hist(posterior_samples['mean_2'])\n",
        "plt.title(\"Histogram of parameter χ2\")\n",
        "plt.show()"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "95% prior confidence intervals:\n",
            "χ2: [7.824, 8.789]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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kOWy8XUmSJEmjmRGhGjga2FhVt1bVD4FLgOVj7kmSJEkayZxxN9AsADYNrW8G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\nGaolSZKkToZqSZIkqZOhWpIkSer0/wCriOfOLolIWQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oB0HqApbP2pf",
        "colab_type": "text"
      },
      "source": [
        "### Confidence Intervals and plot the histogram of parameters $\\sigma_2$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m8KC9JqbP248",
        "colab_type": "code",
        "outputId": "aff6eb59-0c3a-45f1-daaf-c30046ad0dad",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 426
        }
      },
      "source": [
        "# compute percentile\n",
        "print('95% prior confidence intervals:')\n",
        "print('σ2: [%.3f, %.3f]' % (\n",
        "    np.percentile(posterior_samples['sigma_2'], 2.5),\n",
        "    np.percentile(posterior_samples['sigma_2'], 97.5)))\n",
        "plt.figure(figsize=(12,6))\n",
        "plt.hist(posterior_samples['sigma_2'])\n",
        "plt.title(\"Histogram of parameter σ2\")\n",
        "plt.show()"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "95% prior confidence intervals:\n",
            "σ2: [25.782, 33.121]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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NAACThGoAAJgkVAMAwCShGgAAJgnVAAAwSagGAIBJQjUAAEwSqgEAYJJQDQAAk4RqAACY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\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0G4mCluTOJjC",
        "colab_type": "text"
      },
      "source": [
        "### Plot the likelihood function on top of the data histogram "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xteEtb6euSJQ",
        "colab_type": "code",
        "outputId": "f1bcd23f-4d73-4e5a-cd2d-a78d4d623f4e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 390
        }
      },
      "source": [
        "# Plot the likelihood function on top of the data histogram\n",
        "# 10 random parameters samples of this distribution\n",
        "p_items = np.random.choice(posterior_samples['p'], 10)\n",
        "mean_1_items = np.random.choice(posterior_samples['mean_1'], 10)\n",
        "sigma_1_items = np.random.choice(posterior_samples['sigma_1'], 10)\n",
        "mean_2_items = np.random.choice(posterior_samples['mean_2'], 10)\n",
        "sigma_2_items = np.random.choice(posterior_samples['sigma_2'], 10)\n",
        "\n",
        "# The average parameters values\n",
        "p_mean = np.mean(posterior_samples['p'])\n",
        "mean_1_mean = np.mean(posterior_samples['mean_1'])\n",
        "sigma_1_mean = np.mean(posterior_samples['sigma_1'])\n",
        "mean_2_mean = np.mean(posterior_samples['mean_2'])\n",
        "sigma_2_mean = np.mean(posterior_samples['sigma_2'])\n",
        "plt.figure(figsize=(12,6))\n",
        "# plot histogram\n",
        "plt.hist(data, bins=20, density=True)\n",
        "\n",
        "# plot the other lines:\n",
        "x = np.linspace(0, 30, 200)\n",
        "y = (p_mean)*sts.norm.pdf(x, loc = mean_1_mean, scale = np.sqrt(sigma_1_mean)) + (1-p_mean)*sts.norm.pdf(x, loc = mean_2_mean, scale = np.sqrt(sigma_2_mean))\n",
        "plt.plot(x, y, color = \"red\")\n",
        "\n",
        "for i in range(10):  \n",
        "  y = (p_items[i])*sts.norm.pdf(x, loc = mean_1_items[i], scale = np.sqrt(sigma_1_items[i])) + (1-p_items[i])*sts.norm.pdf(x, loc = mean_2_items[i], scale = np.sqrt(sigma_2_items[i]))\n",
        "  plt.plot(x, y, color = \"black\", linestyle = \"--\")\n",
        "\n",
        "plt.title(\"The likelihood function (10 samples likelihood: black dotted line, and the likelihood on the average of parameters) on top of the data histogram\")\n",
        "plt.show()"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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IFBjffvstL7/8MnfccUeevtwkM1asWMFdd92VL8/niYiIiGSVEjkRKRAOHjxI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\nqJgUHHpQX2cAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ovPLD7Mn1EtQ",
        "colab_type": "text"
      },
      "source": [
        "## Comments: \n",
        "\n",
        "For the original StanModel, it diverges a lot. To fix that, I changed the number of iterations to 10000, increase the chains length, and most important, the adapt_delta (from 0.8 to 0.99), which allow the stan diagnostic to be reliable. The diagnostic of the modified stan model is reliable but not extremely, with parameters ($p, \\sigma_1, \\sigma_2$) with lown\\_eff (crude measure of effective sample size) (there are 3 parameters have n_eff > 1000 but not all. The remaining parameters still have n_eff > 100, which is decently good). The Rhat are in range [0.9,1.1], which indicates the majority samples converges. However, the Rhat of $p, \\sigma_1, \\sigma_2$ are slightly further away from 1 than $\\chi_1, \\chi_2$ , which indicates higher chance for divergence. \n",
        "\n",
        "When we look at the histogram, while $\\chi_1, \\chi_2$ have only 1 peak, the $p, \\sigma_1, \\sigma_2$ are bimodel (2 peaks), which also indicates possible divergence. And this is confirmed again with the final plot, which we can see among the convergenced lines (black dotted lines near the red lines), there are outliers (the one peaked at 3).\n",
        "\n",
        "Overall, the diagnostic shows that it does converge to some extent, which show that the modified versions worked better. However, complete convergence is not guaranteed and the results is not completely reliable.\n",
        "\n",
        "These models (where if the mode is $\\theta' = (p', \\mu_1', \\mu_2', \\sigma_1', \\sigma_2')$, it can also be equivalent to $\\theta'' = (1-p', \\mu_2', \\mu_1', \\sigma_2', \\sigma_1')$). Models like this can mess up sampling-based tools like Stan, which is proven through the graphs. \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kNyQ4i0ocnjh",
        "colab_type": "text"
      },
      "source": [
        "#### Additional Comments: \n",
        "(only to note to myself to ask this question once the assignments are finalized)\n",
        "Unsure of having too many parameters, or because the model is tricky, but this stan_code is affected by priors. Usually the choice of priors does not affect much of the posterior (especially when we have many data points (500 points). For this case, choosing different priors can affect the convergence."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RQgUWXg050em",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}