infer_binomial_proportion.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "infer-binomial-proportion.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "mlTDRJk6gIg2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import pymc3\n",
        "import scipy.stats as stats\n",
        "\n",
        "plt.style.use(\"ggplot\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ptoVdabWgO-j",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "n=50\n",
        "z=10\n",
        "alpha=12\n",
        "beta=12\n",
        "alpha_post=22\n",
        "beta_post=52\n",
        "\n",
        "iterations=100000"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XLVnfb2MhP7N",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 171
        },
        "outputId": "ec63cbdb-7a1a-4c64-c1fa-c78f6f19c5d1"
      },
      "source": [
        "basic_model = pymc3.Model()\n",
        "with basic_model:\n",
        "  theta = pymc3.Beta(\"theta\", alpha=alpha, beta=beta)\n",
        "  y = pymc3.Binomial(\"y\", n=n, p=theta, observed=z)\n",
        "  start = pymc3.find_MAP()\n",
        "  step = pymc3.Metropolis()\n",
        "  trace = pymc3.sample(\n",
        "      iterations, step, start, random_seed=1, progressbar=True\n",
        "  )"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/pymc3/tuning/starting.py:61: UserWarning: find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.\n",
            "  warnings.warn('find_MAP should not be used to initialize the NUTS sampler, simply call pymc3.sample() and it will automatically initialize NUTS in a better way.')\n",
            "logp = -10.252, ||grad|| = 15: 100%|██████████| 7/7 [00:00<00:00, 1106.18it/s]\n",
            "Sequential sampling (2 chains in 1 job)\n",
            "Metropolis: [theta]\n",
            "100%|██████████| 100500/100500 [00:14<00:00, 6856.91it/s]\n",
            "100%|██████████| 100500/100500 [00:15<00:00, 6626.34it/s]\n",
            "The number of effective samples is smaller than 25% for some parameters.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WpUfHgFOh5x-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 806
        },
        "outputId": "05e9cf03-1f6b-40a2-e039-9d21f81be03d"
      },
      "source": [
        "bins = 50\n",
        "plt.hist(\n",
        "    trace[\"theta\"], bins,\n",
        "    histtype=\"step\",\n",
        "    label=\"Posterior (MCMC)\", color=\"red\"\n",
        ")\n",
        "\n",
        "x = np.linspace(0,1,100)\n",
        "\n",
        "plt.plot(\n",
        "    x, stats.beta.pdf(x, alpha, beta),\n",
        "    \"--\", label=\"Prior\", color=\"blue\"\n",
        ")\n",
        "\n",
        "plt.plot(\n",
        "    x, stats.beta.pdf(x, alpha_post, beta_post),\n",
        "    label=\"Posterior (Analytic)\", color=\"green\"\n",
        ")\n",
        "\n",
        "\n",
        "plt.legend(title=\"Parameters\", loc=\"best\")\n",
        "plt.xlabel(\"$\\\\theta$, Fairness\")\n",
        "plt.ylabel(\"Density\")\n",
        "plt.show()\n",
        "\n",
        "pymc3.traceplot(trace)\n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "error",
          "ename": "ImportError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-15-15bb240f3535>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     24\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     25\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 26\u001b[0;31m \u001b[0mpymc3\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtraceplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrace\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     27\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pymc3/plots/__init__.py\u001b[0m in \u001b[0;36mwrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     40\u001b[0m                 \u001b[0mwarnings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwarn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mold\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mold\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnew\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnew\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     41\u001b[0m                 \u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnew\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mold\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 42\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     43\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrapped\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     44\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pymc3/plots/__init__.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m     20\u001b[0m         \u001b[0;32mdef\u001b[0m \u001b[0m__call__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m             raise ImportError(\n\u001b[0;32m---> 22\u001b[0;31m                 \u001b[0;34m\"ArviZ is not installed. In order to use `{0.attr}`:\\npip install arviz\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     23\u001b[0m             )\n\u001b[1;32m     24\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mImportError\u001b[0m: ArviZ is not installed. In order to use `plot_trace`:\npip install arviz",
            "",
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0;32m\nNOTE: If your import is failing due to a missing package, you can\nmanually install dependencies using either !pip or !apt.\n\nTo view examples of installing some common dependencies, click the\n\"Open Examples\" button below.\n\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iqnnI92LitTu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 440
        },
        "outputId": "4449c1b8-29b0-407f-a99b-257ac9d692e8"
      },
      "source": [
        "!pip install arviz\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting arviz\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/d2/ed/2f9d0217fac295b3dd158195060e5350c1c9a2abcba04030a426a15fd908/arviz-0.9.0-py3-none-any.whl (1.5MB)\n",
            "\u001b[K     |████████████████████████████████| 1.5MB 2.6MB/s \n",
            "\u001b[?25hCollecting netcdf4\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/09/39/3687b2ba762a709cd97e48dfaf3ae36a78ae603ec3d1487f767ad58a7b2e/netCDF4-1.5.4-cp36-cp36m-manylinux1_x86_64.whl (4.3MB)\n",
            "\u001b[K     |████████████████████████████████| 4.3MB 13.6MB/s \n",
            "\u001b[?25hRequirement already satisfied: pandas>=0.23 in /usr/local/lib/python3.6/dist-packages (from arviz) (1.0.5)\n",
            "Requirement already satisfied: xarray>=0.11 in /usr/local/lib/python3.6/dist-packages (from arviz) (0.15.1)\n",
            "Requirement already satisfied: scipy>=0.19 in /usr/local/lib/python3.6/dist-packages (from arviz) (1.4.1)\n",
            "Requirement already satisfied: numpy>=1.12 in /usr/local/lib/python3.6/dist-packages (from arviz) (1.18.5)\n",
            "Requirement already satisfied: packaging in /usr/local/lib/python3.6/dist-packages (from arviz) (20.4)\n",
            "Requirement already satisfied: matplotlib>=3.0 in /usr/local/lib/python3.6/dist-packages (from arviz) (3.2.2)\n",
            "Collecting cftime\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/81/f4/31cb9b65f462ea960bd334c5466313cb7b8af792f272546b68b7868fccd4/cftime-1.2.1-cp36-cp36m-manylinux1_x86_64.whl (287kB)\n",
            "\u001b[K     |████████████████████████████████| 296kB 45.1MB/s \n",
            "\u001b[?25hRequirement already satisfied: python-dateutil>=2.6.1 in /usr/local/lib/python3.6/dist-packages (from pandas>=0.23->arviz) (2.8.1)\n",
            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.6/dist-packages (from pandas>=0.23->arviz) (2018.9)\n",
            "Requirement already satisfied: setuptools>=41.2 in /usr/local/lib/python3.6/dist-packages (from xarray>=0.11->arviz) (49.1.0)\n",
            "Requirement already satisfied: pyparsing>=2.0.2 in /usr/local/lib/python3.6/dist-packages (from packaging->arviz) (2.4.7)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from packaging->arviz) (1.15.0)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=3.0->arviz) (0.10.0)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=3.0->arviz) (1.2.0)\n",
            "Installing collected packages: cftime, netcdf4, arviz\n",
            "Successfully installed arviz-0.9.0 cftime-1.2.1 netcdf4-1.5.4\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h4A1RPa2jopd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 806
        },
        "outputId": "efd281d0-d27e-43be-a09a-d6a70160856b"
      },
      "source": [
        "\n",
        "bins = 50\n",
        "plt.hist(\n",
        "    trace[\"theta\"], bins,\n",
        "    histtype=\"step\",\n",
        "    label=\"Posterior (MCMC)\", color=\"red\"\n",
        ")\n",
        "\n",
        "x = np.linspace(0,1,100)\n",
        "\n",
        "plt.plot(\n",
        "    x, stats.beta.pdf(x, alpha, beta),\n",
        "    \"--\", label=\"Prior\", color=\"blue\"\n",
        ")\n",
        "\n",
        "plt.plot(\n",
        "    x, stats.beta.pdf(x, alpha_post, beta_post),\n",
        "    label=\"Posterior (Analytic)\", color=\"green\"\n",
        ")\n",
        "\n",
        "\n",
        "plt.legend(title=\"Parameters\", loc=\"best\")\n",
        "plt.xlabel(\"$\\\\theta$, Fairness\")\n",
        "plt.ylabel(\"Density\")\n",
        "plt.show()\n",
        "\n",
        "pymc3.traceplot(trace)\n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "error",
          "ename": "ImportError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-16-014257127d35>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     25\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     26\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 27\u001b[0;31m \u001b[0mpymc3\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtraceplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrace\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     28\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pymc3/plots/__init__.py\u001b[0m in \u001b[0;36mwrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     40\u001b[0m                 \u001b[0mwarnings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwarn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mold\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mold\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnew\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnew\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     41\u001b[0m                 \u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnew\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mold\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 42\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     43\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrapped\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     44\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pymc3/plots/__init__.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m     20\u001b[0m         \u001b[0;32mdef\u001b[0m \u001b[0m__call__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m             raise ImportError(\n\u001b[0;32m---> 22\u001b[0;31m                 \u001b[0;34m\"ArviZ is not installed. In order to use `{0.attr}`:\\npip install arviz\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     23\u001b[0m             )\n\u001b[1;32m     24\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mImportError\u001b[0m: ArviZ is not installed. In order to use `plot_trace`:\npip install arviz",
            "",
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0;32m\nNOTE: If your import is failing due to a missing package, you can\nmanually install dependencies using either !pip or !apt.\n\nTo view examples of installing some common dependencies, click the\n\"Open Examples\" button below.\n\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uctgsTbMjyAW",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import arviz"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jk0bVPwtkJm5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "b3264dcf-eeb3-4745-b197-5ec9d6f5164a"
      },
      "source": [
        "!pip install arviz\n",
        "\n",
        "bins = 50\n",
        "plt.hist(\n",
        "    trace[\"theta\"], bins,\n",
        "    histtype=\"step\",\n",
        "    label=\"Posterior (MCMC)\", color=\"red\"\n",
        ")\n",
        "\n",
        "x = np.linspace(0,1,100)\n",
        "\n",
        "plt.plot(\n",
        "    x, stats.beta.pdf(x, alpha, beta),\n",
        "    \"--\", label=\"Prior\", color=\"blue\"\n",
        ")\n",
        "\n",
        "plt.plot(\n",
        "    x, stats.beta.pdf(x, alpha_post, beta_post),\n",
        "    label=\"Posterior (Analytic)\", color=\"green\"\n",
        ")\n",
        "\n",
        "\n",
        "plt.legend(title=\"Parameters\", loc=\"best\")\n",
        "plt.xlabel(\"$\\\\theta$, Fairness\")\n",
        "plt.ylabel(\"Density\")\n",
        "plt.show()\n",
        "\n",
        "pymc3.traceplot(trace)\n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: arviz in /usr/local/lib/python3.6/dist-packages (0.9.0)\n",
            "Requirement already satisfied: xarray>=0.11 in /usr/local/lib/python3.6/dist-packages (from arviz) (0.15.1)\n",
            "Requirement already satisfied: pandas>=0.23 in /usr/local/lib/python3.6/dist-packages (from arviz) (1.0.5)\n",
            "Requirement already satisfied: scipy>=0.19 in /usr/local/lib/python3.6/dist-packages (from arviz) (1.4.1)\n",
            "Requirement already satisfied: packaging in /usr/local/lib/python3.6/dist-packages (from arviz) (20.4)\n",
            "Requirement already satisfied: matplotlib>=3.0 in /usr/local/lib/python3.6/dist-packages (from arviz) (3.2.2)\n",
            "Requirement already satisfied: netcdf4 in /usr/local/lib/python3.6/dist-packages (from arviz) (1.5.4)\n",
            "Requirement already satisfied: numpy>=1.12 in /usr/local/lib/python3.6/dist-packages (from arviz) (1.18.5)\n",
            "Requirement already satisfied: setuptools>=41.2 in /usr/local/lib/python3.6/dist-packages (from xarray>=0.11->arviz) (49.1.0)\n",
            "Requirement already satisfied: pytz>=2017.2 in /usr/local/lib/python3.6/dist-packages (from pandas>=0.23->arviz) (2018.9)\n",
            "Requirement already satisfied: python-dateutil>=2.6.1 in /usr/local/lib/python3.6/dist-packages (from pandas>=0.23->arviz) (2.8.1)\n",
            "Requirement already satisfied: pyparsing>=2.0.2 in /usr/local/lib/python3.6/dist-packages (from packaging->arviz) (2.4.7)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from packaging->arviz) (1.15.0)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=3.0->arviz) (0.10.0)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib>=3.0->arviz) (1.2.0)\n",
            "Requirement already satisfied: cftime in /usr/local/lib/python3.6/dist-packages (from netcdf4->arviz) (1.2.1)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "error",
          "ename": "ImportError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mImportError\u001b[0m                               Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-20-a539aa87afd9>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     26\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     27\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 28\u001b[0;31m \u001b[0mpymc3\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtraceplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrace\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     29\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pymc3/plots/__init__.py\u001b[0m in \u001b[0;36mwrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     40\u001b[0m                 \u001b[0mwarnings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwarn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mold\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mold\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnew\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnew\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     41\u001b[0m                 \u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnew\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mold\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 42\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     43\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrapped\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     44\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pymc3/plots/__init__.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m     20\u001b[0m         \u001b[0;32mdef\u001b[0m \u001b[0m__call__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m             raise ImportError(\n\u001b[0;32m---> 22\u001b[0;31m                 \u001b[0;34m\"ArviZ is not installed. In order to use `{0.attr}`:\\npip install arviz\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     23\u001b[0m             )\n\u001b[1;32m     24\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mImportError\u001b[0m: ArviZ is not installed. In order to use `plot_trace`:\npip install arviz",
            "",
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0;32m\nNOTE: If your import is failing due to a missing package, you can\nmanually install dependencies using either !pip or !apt.\n\nTo view examples of installing some common dependencies, click the\n\"Open Examples\" button below.\n\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "le4kfVVPkPti",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}