probabilistic_programming_workshop.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "probabilistic-programming-workshop.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOaACma/gDMb6adw9HJ4V1w",
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/aliizadi/probabilistic-programming-workshop/blob/main/probabilistic_programming_workshop.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IdgEywiQ6nOB"
      },
      "source": [
        "Install Everything you need with !pip"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TG4EuSAX6jRQ"
      },
      "source": [
        "!pip install numpy\n",
        "!pip install matplotlib\n",
        "!pip install pandas\n",
        "!pip install tensorflow\n",
        "!pip install tensorflow_probability\n",
        "!pip install keras\n",
        "!pip install scipy\n",
        "!pip install pymc3"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Th2uKIrC6lGj"
      },
      "source": [
        "# Coin Flip Example. Bayesian thinking"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cCj33uSRmUWK"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy import stats"
      ],
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gzv1S2MgqYsl"
      },
      "source": [
        "## normal and beta distribution"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 530
        },
        "id": "6dvLg7cRmZv_",
        "outputId": "6e1b1c8d-812d-438a-f0e7-e204e221062c"
      },
      "source": [
        "samples = stats.norm.rvs(0, 1000, size=1000)\n",
        "\n",
        "plt.hist(samples, density=True)\n",
        "\n",
        "x = np.linspace(-5, 5, 1000)\n",
        "y = stats.norm(0, 1000).pdf(x)\n",
        "plt.plot(x, y)\n",
        "\n",
        "plt.figure()\n",
        "\n",
        "a, b = 5, 5\n",
        "samples = stats.beta.rvs(a, b, size=1000)\n",
        "\n",
        "plt.hist(samples, density=True)\n",
        "\n",
        "x = np.linspace(0, 1, 1000)\n",
        "y = stats.beta(a, b).pdf(x)\n",
        "plt.plot(x, y)"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f369a4f5790>]"
            ]
          },
          "metadata": {},
          "execution_count": 2
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WEdXQF1cqeR3"
      },
      "source": [
        "## Let's flip coin and draw our belief about probability of observing heads."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qMaNGPESN-K2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "90fb5ee4-41b1-422f-fb80-5c4cad2f3708"
      },
      "source": [
        "dist = stats.beta\n",
        "\n",
        "p_success = 0.5\n",
        "n_trials = [0, 1, 2, 3, 4, 5, 8, 15, 50, 500]\n",
        "\n",
        "data = stats.bernoulli.rvs(p_success, size = 500)\n",
        "\n",
        "x = np.linspace(0, 1, 1000)\n",
        "\n",
        "for i, N in enumerate(n_trials):\n",
        "  heads = data[:N].sum()\n",
        "  y = dist.pdf(x, 1 + heads, 1 + N - heads)\n",
        "  plt.plot(x, y, label=f'N={N}, heads={heads}')\n",
        "  plt.legend()\n",
        "  plt.figure()\n",
        "\n",
        "# Bayes theorem: *P(A|X) = P(X|A).P(A)* \n",
        "# new_beta = bernoulli * beta"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Y3ZkWjfV6+drWrmkQf72mI8tTsvlw9V6r4yiLaNGrOrPzcB7TFqdyTdcIvVlZHbqtVyuu6hDOK9/vZE92gdVxlAXsmTN2lohkichZJ/YWkf4ikisim2wfT1VZN1REUkQkTUSecGRw5VpKyyt49IvNhPh78/zIzlbHqVdEhJev74KvlwePz91CeYUewqlv7BnRfwgMrWablcaYbraP5wBExBN4GxgGxAG3iEhcTcIq1/XO8t1sy8zjhVFdaFyPJvZ2Fk2D/XhmRCcS9x3ng1XpVsdRdazaojfGrAByLuK5ewJpxpg9xpgSYA4w8iKeR7m47Qdzmb5kFyO7NWdo52ZWx6m3RnePZFDHcKYuTNFDOPWMo47R9xaRzSLyvYh0si2LBA5U2SbDtuysRGS8iCSKSGJ2draDYimrlZRV8OgXW2gY4MMz13Wq/gGq1ogIL47WQzj1kSOKfgPQyhhzCfAm8PXFPIkxZqYxJsEYkxAWpje2chczlqeRfCiPl0Z3ppEesrGcHsKpn2pc9MaYPGNMge3zBYC3iIQCmUCLKptG2ZapeiItq4AZy3Yz4pLmDOmkh2ycxejukQzsEM5rP6ZyIEcnKqkPalz0ItJMRMT2eU/bcx4D1gOxItJaRHyAMcC8mr6ecg0VFYa/fLUVP28P/n6tnoN3JiLCc6M6IwJPfbNN30hVD9hzeeVsYA3QXkQyRGSciNwnIvfZNrkR2CYim4HpwBhTqQx4EFgIJAOfG2O2185uKGczNymDdek5/GV4R8KCfK2Oo84Q2dCfR4a0Z1lKNvO3HrI6jqpl4ow/zRMSEkxiYqLVMdRFOlpQzMDXfqJ90yDmjO+ltx92UuUVhlFvr+JwXhGLH+5HiL+31ZFUDYhIkjEm4Wzr9J2xyuFe+G4HhSVlvHR9Zy15J+bpUflGqmMFxfzzh51Wx1G1SIteOdTKXdl8vekg9/ePISY8yOo4qhqdI0O4q09rPv1lP0n7LubtMsoVaNErhykqLeevX22jTWgDHujf1uo4yk4PD25H8xA/nvxyK6XlFVbHUbVAi145zHs/7WF/TiEvjO6Mn7en1XGUnRr4evHsyM6kHingI73DpVvSolcOcSCnkBnL07i2awSXtw21Oo66QIM6hjOgfRjTFu8iK7/I6jjKwbTolUO8MH8HHiL89ZqOVkdRF0FEeOq6TpSUVfDK93pi1t1o0asa+yk1m4Xbj/DQwBgiQvytjqMuUuvQBtxzZWu+3JBJ4l49MetOtOhVjZSUVfDsvO20Dm3AuCtaWx1H1dCEATFEhPjx1Dfb9aZnbkSLXtXIrFXp7Dl6kqeui8PXS0/AuroAHy/+ek1HdhzK43/r9lsdRzmIFr26aIdzi5i+ZBeDOjZlQPtwq+MoB7mmSwS92zTh1YUp5JwssTqOcgAtenXRXv4+mbIKw1N60zK3IiI8O7ITBcVlvPpjitVxlANo0auLkrTvON9sOsi9V7ahZZMAq+MoB2vXNIjberVizrr97DycZ3UcVUNa9OqCGWN4/rsdhAf5cl8/fQesu5o0MJYgP29enJ+stzJ2cVr06oJ9u+UQmw6c4NGr29PA18vqOKqWNGrgw8SBsazcdZTlqTq9pyvTolcXpKi0nH98v5OOEcHcEB9ldRxVy27r1YrWoQ14cX6y3gfHhWnRqwvywaq9ZJ44xd+u6Yin3oLY7fl4efDksA6kZRUwRy+3dFla9MpuRwuKeXtZGoM6htMnRu9nU18MjmtKrzaNeX1RKrmnSq2Ooy6CPVMJzhKRLBHZdo71Y0Vki4hsFZHVInJJlXV7bcs3iYhOGeXi3liUSlFpOU8O1/vZ1Cciwt+uiePEqVLeXpZmdRx1EewZ0X8IDD3P+nSgnzGmC/A8MPOM9QOMMd3ONcWVcg2pR/KZvW4/Yy9rSduwQKvjqDrWOTKEG+Oj+GBVOvuOnbQ6jrpA1Ra9MWYFcM47HBljVhtjjtu+XAvoGTo39NKCZBr4ejFpUDuroyiLPHp1e7w9PfTuli7I0cfoxwHfV/naAD+KSJKIjD/fA0VkvIgkikhidrZeyuVMVqRmszwlm4lXxdK4gY/VcZRFmgb7Mf7KNny/7TAb9h+v/gHKaTis6EVkAJVF/+cqi68wxsQDw4AJInLluR5vjJlpjEkwxiSEhYU5KpaqoYoKwyvf7ySqkT+3X97K6jjKYnf3bUNooA+vfL9T30TlQhxS9CLSFfgPMNIYc+z0cmNMpu3PLOAroKcjXk/VnW+3HGTHoTweHdJe706pCPT1YuLAWNal57A8RX/zdhU1LnoRaQl8CdxmjEmtsryBiASd/hwYApz1yh3lnErKKnjtx1Q6RgQz4pLmVsdRTmLMpS1p1SSAf/ywU+9Z7yLsubxyNrAGaC8iGSIyTkTuE5H7bJs8BTQBZpxxGWVT4GcR2QysA+YbY36ohX1QtWT2uv3szynk8aHt8dA3RykbHy8PHh3Snp2H8/lmU6bVcZQdxBmPsyUkJJjERL3s3koni8voN3UZbcMCmTO+FyJa9Or/VFQYRr69ipyTJSx5pB9+3npYz2oiknSuy9j1nbHqrP6zMp2jBSX8eVgHLXn1Ox4ewhPDOpB54hSfrN1ndRxVDS169TtHC4qZuWI3V3dqSnzLRlbHUU6qT0wofWNDeWtZGnlFemsEZ6ZFr37nraVpnCot57GrO1gdRTm5Pw/twInCUt77abfVUdR5aNGr3ziQU8inv+zjpoQWxITrrQ7U+XWODGFkt+a8/3M6WXlFVsdR56BFr37j9UWpeIgwWW91oOz0yOD2lFcY/rVkl9VR1Dlo0atfJR/K4+tNmdzZJ5pmIX5Wx1EuomWTAG7p2ZLP1h9g/7FCq+Oos9CiV7967cdUgny9eKBfjNVRlIuZMCAGTw9h2pLU6jdWdU6LXgGwJeMEi5OPcE/fNoQEeFsdR7mYpsF+3HF5NF9vzCQtK9/qOOoMWvQKqJxUpGGAN3f2ibY6inJR9/Vri7+3J28s0mP1zkaLXrFx/3GWpWRzT982BPnpaF5dnMYNfBh3RWvmbz3Etsxcq+OoKrToFW8s3kWjAG/uuDza6ijKxY3r24YQf2/eWKTH6p2JFn09l7QvhxWp2dzbry2Bvl5Wx1EuLsTfm/FXtmHJziydnMSJaNHXc28s2kWTBj7c3lsnFVGOcVefaEIDfXh1YYrVUZSNFn09ti49h5/TjnJfv7YE+OhoXjlGgI8X9/ePYfXuY6xOO2p1HIUWfb32xqJUQgN9ubWXjuaVY429rCURIX68+mOKTjnoBLTo66k1u4+xZs8xHujfFn8fvZe4ciw/b08euiqWDftPsCwly+o49Z4WfT1kjOGNxamEB/nyx8taWh1Huak/JETRsnEAry5MpUKnHLSUXUUvIrNEJEtEzjrnq1SaLiJpIrJFROKrrLtDRHbZPu5wVHB18VbvPsa69BwmDIjRmYFUrfH29GDyoFh2HMpj4fbDVsep1+wd0X8IDD3P+mFArO1jPPAOgIg0Bp4GLgN6Ak+LiM5kYSFjDK8vSqVZsB83X9rC6jjKzY3sFkmbsAZMW7xLR/UWsqvojTErgJzzbDIS+NhUWgs0FJEI4GpgkTEmxxhzHFjE+X9gqFq2ctdRkvYdZ8JVOppXtc/TQ5g0MJaUI/l8v01H9VZx1DH6SOBAla8zbMvOtfx3RGS8iCSKSGJ2draDYqmqTo/mIxv6c1NClNVxVD1xbdfmxIQH8q8leqzeKk5zMtYYM9MYk2CMSQgLC7M6jltanprNpgMnmDAgBl8vHc2ruuHpIUwcGEvqkQLmbz1kdZx6yVFFnwlUPeAbZVt2ruWqjhljeGNRKlGN/Lmxh47mVd26pksEseGB/GvJLsp1VF/nHFX084DbbVff9AJyjTGHgIXAEBFpZDsJO8S2TNWxJclZbMnI5aGrYvDxcppf5FQ94ekhTBoUS1pWAd9tOWh1nHrHrve9i8hsoD8QKiIZVF5J4w1gjHkXWAAMB9KAQuAu27ocEXkeWG97queMMec7qatqwenr5ls2DuD6eB3NK2sM7xxB+6ZpTF+yi2u7NsfTQ6yOVG/YVfTGmFuqWW+ACedYNwuYdeHRlKP8uOMI2w/m8eofLsHbU0fzyhoetlH9A59u4NvNBxnV/azXZahaoP/r3VxFhWHa4l20Dm3AqG7NrY6j6rmhnZrRoVkQ05fsoqy8wuo49YYWvZtbuP0wyYfymDgwBi8dzSuLeXgIkwfFsufoSeZt1mP1dUX/57ux06P5NmENGHGJ/pqsnMOQuGZ0jAjWUX0d0qJ3Ywu2HSLlSD6TBsbqiS/lNE6P6vceK+TrTTqqrwta9G6q3Daajw0P5NquemxeOZchcU3p1DyYN5fqqL4uaNG7qe+2HCQtq4BJg3Q0r5yPiDB5UDv2HSvky436HsrapkXvhsrKK/jX4l20bxrE8M4RVsdR6qwGdQync2TlqL5UR/W1SoveDc3bfJA9R08yZXAsHjqaV05KRJg8sB0Hck7x5YYMq+O4NS16N1NWXsH0JbvoGBHMkLhmVsdR6rwGdgyna1QIby5N01F9LdKidzNfbcxk77FCpgzS0bxyfpXH6mPJOH6K/5eko/raokXvRkrLK3hzaRqdI4MZHNfU6jhK2WVA+3AuadGQN5emUVKmo/raoEXvRr7ckMH+nEKmDGqHiI7mlWs4ParPPHGKL5IOVP8AdcG06N1ESVnlaP6SqBCu6hBudRylLkj/dmF0b9mQt5emUVxWbnUct6NF7ybmJmWQcfwUkwfraF65HhFhyqB2HMwt4vNEPVbvaFr0bqC4rJy3lu6ie8uG9G+n0zAq19Q3NpQerRoxY1kaRaU6qnckLXo38HliBgdzi3hYR/PKhZ0e1R/KLeKz9Xqs3pG06F1cUWk5by9NI6FVI66ICbU6jlI10iemCT2jGzNjuY7qHUmL3sV9tv4Ah/N0NK/cg4gweXAsR/KKmb1uv9Vx3IZdRS8iQ0UkRUTSROSJs6x/Q0Q22T5SReRElXXlVdbNc2T4+q6otJy3l6XRs3VjerdtYnUcpRzi8rahXNa6MTOW79ZRvYNUW/Qi4gm8DQwD4oBbRCSu6jbGmCnGmG7GmG7Am8CXVVafOr3OGDPCgdnrvU9/2U9WfrGO5pXbmTK4Hdn5xXz6i47qHcGeEX1PIM0Ys8cYUwLMAUaeZ/tbgNmOCKfO7VRJOe8s383lbZvQq42O5pV76dWmCb3bNOGd5bs5VaKj+pqyp+gjgaqnwDNsy35HRFoBrYGlVRb7iUiiiKwVkVHnehERGW/bLjE7O9uOWPXbJ2v3cbSgmCmD21kdRalaMWVwO44WFPPJ2n1WR3F5jj4ZOwaYa4yp+iO4lTEmAfgjME1E2p7tgcaYmcaYBGNMQliYXgt+PoUlZbz70276xoZyaXRjq+MoVSt6tm7MFTGhvPvTbgpLyqyO49LsKfpMoEWVr6Nsy85mDGcctjHGZNr+3AMsB7pfcEr1Gx+v2cexkyVMHqSjeeXepgyO5djJEv67Rkf1NWFP0a8HYkWktYj4UFnmv7t6RkQ6AI2ANVWWNRIRX9vnoUAfYIcjgtdXBcVlvPfTbq5sF0aPVo2sjqNUrerRqjF9Y0N5b8UeThbrqP5iVVv0xpgy4EFgIZAMfG6M2S4iz4lI1atoxgBzjDGmyrKOQKKIbAaWAa8YY7Toa+DDVekcLyzlYT02r+qJKYPbkXOyhI/W7LU6isvysmcjY8wCYMEZy5464+tnzvK41UCXGuRTVeSeKmXmij0M6hhOtxYNrY6jVJ2Ib9mI/u3DmLliD7f3jibQ167aUlXoO2NdyKyf08krKtNj86remTyoHScKS/lo9V6ro7gkLXoXcaKwhFk/pzO0UzM6R4ZYHUepOtWtRUOu6hDOzBV7yCsqtTqOy9GidxEzV+yhoKRMr5tX9dbkQbHknirlw1V7rY7icrToXcCxgmI+XL2Xa7s2p32zIKvjKGWJrlENGdSxKf9ZuYfcUzqqvxBa9C7gvRV7KCotZ9LAWKujKGWpyYNiySsq44NV6VZHcSla9E4uK7+Ij9fsZVS3SGLCA62Oo5SlOkeGMCSuKe+vTCe3UEf19tKid3LvLN9Nablhoo7mlQIqr8DJLy7j/V1gQ7MAABKLSURBVJ/3WB3FZWjRO7FDuaf49Jf93BAfSXRoA6vjKOUU4poHM6xzM2at2suJwhKr47gELXonNmPZbioqDA9dpaN5paqaNCiWguIy/r1SR/X20KJ3UhnHC5mzfj83XdqCFo0DrI6jlFPp0CyYa7pG8MGqvRwtKLY6jtPTondSby1NQxAeHBBjdRSlnNKUQe0oKi1nxrLdVkdxelr0Tmjv0ZPMTcrglp4taN7Q3+o4SjmlmPBAbuwRxSdr95F54pTVcZyaFr0Ten1RKt6eHkzQ0bxS5zXJdt+nfy1OtTiJc9OidzLbD+Yyb/NB7uoTTXiwn9VxlHJqkQ39GdurJXOTMtidXWB1HKelRe9kXl2YQoi/N/f2O+uMi0qpM0wYEIOftyev/6ij+nPRonci69JzWJaSzf392xLi7211HKVcQmigL3df0Zr5Ww+xLTPX6jhOSYveSRhj+OcPOwkP8uWO3tFWx1HKpdx9ZRsaBngzdWGK1VGckl1FLyJDRSRFRNJE5ImzrL9TRLJFZJPt4+4q6+4QkV22jzscGd6dLN2ZReK+40waFIu/j6fVcZRyKcF+3tzfry0/pWbzy55jVsdxOtUWvYh4Am8Dw4A44BYRiTvLpp8ZY7rZPv5je2xj4GngMqAn8LSI6IzWZ6ioMExdmEJ0kwBuSmhhdRylXNIdl0fTNNiXfy5M4bdTVyt7RvQ9gTRjzB5jTAkwBxhp5/NfDSwyxuQYY44Di4ChFxfVfc3bfJCdh/N5eEh7vD31aJpSF8PP25OJA2NJ2necZSlZVsdxKva0SiRwoMrXGbZlZ7pBRLaIyFwROT0stfexiMh4EUkUkcTs7Gw7YrmHkrIKXl+USlxEMNd2ibA6jlIu7aaEFrRqEsDUhalUVOio/jRHDR+/BaKNMV2pHLV/dKFPYIyZaYxJMMYkhIWFOSiW8/ts/X725xTy2ND2eHiI1XGUcmnenh48PLgdyYfy+GZzptVxnIY9RZ8JVD1wHGVb9itjzDFjzOk7C/0H6GHvY+uzk8VlTF+aRs/oxvRvV39+uClVm67r2pzOkcG8ujCVotJyq+M4BXuKfj0QKyKtRcQHGAPMq7qBiFQ95jACSLZ9vhAYIiKNbCdhh9iWKSqnCMzOL+bJ4R0Q0dG8Uo7g4SH8ZXhHMk+c4gOdSBywo+iNMWXAg1QWdDLwuTFmu4g8JyIjbJtNFJHtIrIZmAjcaXtsDvA8lT8s1gPP2ZbVe4dzi5i5YjfXdo2ge0u9EEkpR7q8bSgDO4QzY1kaOSd1chJxxsuQEhISTGJiotUxatXjczfz9caDLHmkn95vXqlasOtIPldPW8HtvaN5ZkQnq+PUOhFJMsYknG2dXstngR0H8/giKYM7+0RryStVS2KbBjGmZ0s+WbuP9KMnrY5jKS36OmaM4aUFyYT4ezOhv96GWKnaNHlQLD5eHvzzh51WR7GUFn0d+yk1m5/TjjLxqlhCAvTGZUrVpvAgP+7r15bvtx0mcW/9PT2oRV+HysoreGlBMq2aBHBrr1ZWx1GqXri7b2vCg3x5cUFyvb01ghZ9HZqblEHqkQKeGNoBHy/9q1eqLgT4ePHokPZs3H+C77YcsjqOJbRt6kheUSmv/phCj1aNGNq5mdVxlKpXbugRRVxEMC8vSOZUSf17E5UWfR2ZvngXx06W8Mx1nfTNUUrVMU8P4ZkRnTiYW8Q7P+22Ok6d06KvA2lZ+Xy4ei9jLm1Bl6gQq+MoVS/1bN2YEZc0592fdnMgp9DqOHVKi76WGWN49tsd+Pt48uiQ9lbHUapee3J4BzxFeHF+cvUbuxEt+lq2aMcRVu46ysOD29Ek0NfqOErVaxEh/kwY0JYfth9mVdpRq+PUGS36WlRUWs7z83fQrmmgXk6plJO4u28bWjT259lvt1NaXmF1nDqhRV+L/r1iDwdyTvH0dZ105iilnISftyd/vyaO1CMFfLJ2n9Vx6oS2Ty05kFPI28vTGNqpGX1iQq2Oo5SqYnBcU/rGhvL6olSy8ousjlPrtOhrgTGGp77ZhocIf7/ubPOoK6WsJFJ5uWVxaQXPf+f+J2a16GvBgq2HWZaSzcOD2xHZ0N/qOEqps2gbFsiEATF8u/kgy918MnEtegfLKyrlmW+306l5MHdeHm11HKXUedzXvw1twhrw92+2ufU7ZrXoHWzqDykcKyjm5eu74KUnYJVyar5enrw0ugsHck4xfekuq+PUGruaSESGikiKiKSJyBNnWf+wiOwQkS0iskREWlVZVy4im2wf8858rDvZsP84n/yyj9t7R9M1qqHVcZRSdujVpgl/6BHFv1fsYefhPKvj1Ipqi15EPIG3gWFAHHCLiJx5hnEjkGCM6QrMBf5ZZd0pY0w328cI3FRJWQV/+XIrTYP8eGRIO6vjKKUuwF+GdyTY35snv9xKeYX73crYnhF9TyDNGLPHGFMCzAFGVt3AGLPMGHP65hFrgSjHxnR+by1LY+fhfJ4b2YkgP51QRClX0qiBD09dG8fG/SeY9XO61XEczp6ijwQOVPk6w7bsXMYB31f52k9EEkVkrYiMuoiMTm9bZi4zlqUxunskQzrpLYiVckUjuzVncFxTpv6YQlpWgdVxHMqhZwtF5FYgAZhaZXEr28zkfwSmiUjbczx2vO0HQmJ2drYjY9WqkrIKHv1iM40b+PC0XjOvlMsSEV4c3ZkAH08e+WIzZW50ewR7ij4TaFHl6yjbst8QkUHAX4ERxpji08uNMZm2P/cAy4HuZ3sRY8xMY0yCMSYhLCzM7h2w2ptLd7HzcD4vX9+FhgE+VsdRStVAeJAfz43szOYDJ/j3Svc5hGNP0a8HYkWktYj4AGOA31w9IyLdgfeoLPmsKssbiYiv7fNQoA+ww1Hhrbb5wAlmLN/NDfFRDOzY1Oo4SikHuK5rBMM6N+ONRamkHM63Oo5DVFv0xpgy4EFgIZAMfG6M2S4iz4nI6atopgKBwBdnXEbZEUgUkc3AMuAVY4xbFH1BcRkT52ykaZAvT+khG6Xchojw/KjOBPl5MWnORopKXf+NVOKMs6InJCSYxMREq2Oc18Ofb+LrjZnMGd+bnq0bWx1HKeVgS3ce4U8fJnJH71Y8O7Kz1XGqJSJJtvOhv6Nv3bwIX2/M5MsNmTx0VayWvFJu6qoOTflTn9Z8tGYfP24/bHWcGtGiv0D7jxXyt6+3kdCqEQ9dFWN1HKVULfrzsPZ0ah7M4/9vC4dyT1kd56Jp0V+AotJyJvxvAx4C08Z003vZKOXmfL08efOW7pSUVTBp9iaXnZFKm8pOxhj+9vU2tmbm8tpN3YhqFGB1JKVUHWgTFshLo7uwbm8OLy1wzXvXe1kdwFV8snYfc5MymDgwlsFxeimlUvXJqO6RbMnIZdaqdLpEhnB9vGvd5UVH9HZI3JvDs9/u4KoO4UweGGt1HKWUBZ4c3oFebRrz5Jdb2ZqRa3WcC6JFX419x05y73+TiGrkzxs3d8PDQ6yOpJSygLenB2//MZ7QQF/G/zeRI3muM9esFv15HD9Zwp0frKfcGGbdeSkh/npXSqXqsyaBvrx3Ww/yTpVy5wfryS8qtTqSXbToz6GotJx7Pk4k88Qp/n17Am3CAq2OpJRyAp0jQ5hxaw92Hcnn/k82UFLm/FfiaNGfRUlZBQ/+bwOJ+47zxk3duDRa3xSllPo//dqF8fL1Xfg57SiPzd3s9JOV6FU3Zygtr2Di7I0sTs7i+VGduaZrhNWRlFJO6A8JLcguKOafP6Tg6SFMvfESPJ30HJ4WfRVl5RU8/Plmfth+mKeujeO2Xq2qf5BSqt56oH8MZeWG1xel4iHCP2/o6pQXbGjR25wqKeeh2RtYnJzFE8M68KcrWlsdSSnlAiYOjKW8wvCvJbsoKatg6h+64uvlaXWs39CiB04UljDuo0Q27D/O8yM7cVvvaKsjKaVcyORBsfh6e/DPH1I4WlDMu7f1INiJ5o6u9ydjkw/lMfLtVWzNyGXGH+O15JVSF0xEeKB/DK/fdAnr0nO48Z3V7Ml2nnln63XRf70xk9EzVnGqpJzZ4y9jWBc98aqUunjXx0fx0Z96kp1fzIi3VrFg6yGrIwH1tOiPFhQz4dMNTP5sE12jGvLdxCvo0UovoVRK1VyfmFDmT+xLTHggD3y6gUe/2MyJwhJLM9WrY/Sl5RXMXrefaYt3UVBUxqND2nFvv7Z46+2GlVIO1LyhP5/f25tpi1N5b8Uelqdk8/jQ9lzfPdKS25vb9YoiMlREUkQkTUSeOMt6XxH5zLb+FxGJrrLuSdvyFBG52nHR7XeyuIxPf9nH4Nd/4qlvthMTHsi3D13Bg1fFaskrpWqFj5cHjw/twLwH+xDZyJ/H527h6mkrmJuUUefz0FY7Z6yIeAKpwGAgA1gP3FJ1km8ReQDoaoy5T0TGAKONMTeLSBwwG+gJNAcWA+2MMefdy5rOGWuMIfPEKTYfyGXJziMs2n6E/OIyOjUP5pEh7RjQPhwR57vWVSnlnowxLNx+hNcXpZB6pIBgPy+GdY6gf/swurVsSLNgvxp30vnmjLXn0E1PIM0Ys8f2ZHOAkcCOKtuMBJ6xfT4XeEsqU48E5hhjioF0EUmzPd+ai9mR6lz75kqOnyzleGEJhSWVP0tC/L0Z3KkpYy9rSXzLRlrwSqk6JyIM7dyMqzs15Zf0HGav28+CrYf4LPEAAA18PGnUwIfmIf58fl9vh7++PUUfCRyo8nUGcNm5tjHGlIlILtDEtnztGY+NPNuLiMh4YDxAy5Yt7cn+O7HhQXh6CMF+3rQJa0Cn5sF0iQzRKf+UUk5BROjVpgm92jShtLyCzQdOkHwoj93ZJ8k7VYqPV+10ldOcjDXGzARmQuWhm4t5jjdu7ubQTEopVVu8PT1IiG5MQh3cNNGeHx+ZQIsqX0fZlp11GxHxAkKAY3Y+VimlVC2yp+jXA7Ei0lpEfIAxwLwztpkH3GH7/EZgqak8yzsPGGO7Kqc1EAusc0x0pZRS9qj20I3tmPuDwELAE5hljNkuIs8BicaYecD7wH9tJ1tzqPxhgG27z6k8cVsGTKjuihullFKOVe3llVao6eWVSilV35zv8kq9HEUppdycFr1SSrk5LXqllHJzWvRKKeXmnPJkrIhkA/su8uGhwFEHxnEFus/ur77tL+g+X6hWxpiws61wyqKvCRFJPNeZZ3el++z+6tv+gu6zI+mhG6WUcnNa9Eop5ebcsehnWh3AArrP7q++7S/oPjuM2x2jV0op9VvuOKJXSilVhRa9Ukq5OZct+ppMWO6K7Njfh0Vkh4hsEZElItLKipyOVN0+V9nuBhExIuLyl+LZs88icpPte71dRP5X1xkdzY5/2y1FZJmIbLT9+x5uRU5HEZFZIpIlItvOsV5EZLrt72OLiMTX+EWNMS73QeXtkncDbQAfYDMQd8Y2DwDv2j4fA3xmde5a3t8BQIDt8/tdeX/t3WfbdkHACiqnrEywOncdfJ9jgY1AI9vX4VbnroN9ngncb/s8Dthrde4a7vOVQDyw7RzrhwPfAwL0An6p6Wu66oj+1wnLjTElwOkJy6saCXxk+3wuMFBcd2bwavfXGLPMGFNo+3ItlbN5uTJ7vscAzwP/AIrqMlwtsWef7wHeNsYcBzDGZNVxRkezZ58NEGz7PAQ4WIf5HM4Ys4LKeTvOZSTwsam0FmgoIhE1eU1XLfqzTVh+5qTjv5mwHDg9Ybkrsmd/qxpH5YjAlVW7z7ZfaVsYY+bXZbBaZM/3uR3QTkRWichaERlaZ+lqhz37/Axwq4hkAAuAh+ommmUu9P97tZxmcnDlGCJyK5AA9LM6S20SEQ/gdeBOi6PUNS8qD9/0p/K3thUi0sUYc8LSVLXrFuBDY8xrItKbytnsOhtjKqwO5ipcdURfkwnLXZFdk6yLyCDgr8AIY0xxHWWrLdXtcxDQGVguInupPJY5z8VPyNrzfc4A5hljSo0x6UAqlcXvquzZ53HA5wDGmDWAH5U3/3JXdv1/vxCuWvQ1mbDcFVW7vyLSHXiPypJ39eO2UM0+G2NyjTGhxphoY0w0leclRhhjXHkOSnv+XX9N5WgeEQml8lDOnroM6WD27PN+YCCAiHSksuiz6zRl3ZoH3G67+qYXkGuMOVSTJ3TJQzemBhOWuyI793cqEAh8YTvnvN8YM8Ky0DVk5z67FTv3eSEwRER2AOXAY8YYV/1N1d59fgT4t4hMofLE7J0uPGhDRGZT+cM61Hbe4WnAG8AY8y6V5yGGA2lAIXBXjV/Thf++lFJK2cFVD90opZSykxa9Ukq5OS16pZRyc1r0Sinl5rTolVLKzWnRK6WUm9OiV0opN/f/AezHfANA1NahAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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IPlDQi8SYSNNNdHuRoFPQi8QIjTNEcVR0G3WxlHygoBeJ0dk7mFAbvWr0kk8U9CIRQ8NOV1+iTTeq0Uv+GDfozexuM9thZhtiln3fzN42s9fN7BEzaxjjtZvMbL2ZrTOzNeksuEi6dfWNP0RxlGr0kk8SqdH/FDhj1LKngcPd/Ujgv4G/38/rT3b3xe7enFwRRbIjOmPU/iYdiaopK8EM3R0reWHcoHf31cCuUcuecvfoO/wlYHYGyiaSVYkOaAZQVGTUlJVoOkHJC+loo/9fwBNjrHPgKTN71cyWp+FYIhmT6KQjURrBUvLF+FWX/TCzfwQGgXvH2OQEd99iZtOBp83s7cg3hHj7Wg4sB5g7d24qxRJJSiiBaQRjaQRLyRdJ1+jN7AvA2cClPsbITu6+JfJ7B/AIsHSs/bn7ne7e7O7NTU1NyRZLJGkjE4MnWKOvq1SNXvJDUkFvZmcA3wCWuXv3GNtUm1lt9DFwOrAh3rYiQZDIxOCxaitK6exTjV6CL5HulfcDfwA+aWYtZnYFcDtQS7g5Zp2Z3RHZdqaZrYq8dAbwgpm9BrwCPO7uT2bkLETSQG30MlmNW3Vx90viLF4xxrZbgbMij98DFqVUOpEsCvUOUlFaRFlJYl90FfSSL3RnrEhEZ4Lj3ERp8hHJFwp6kYhQgiNXRmnyEckXCnqRiFDPxGv0oMlHJPgU9CIR4ZErE6/R12m8G8kTCnqRiM7exKYRjNLAZpIvFPQiEYnOLhU10nSj8W4k4BT0IhGh3oGERq6MUo1e8oWCXgQYGBqmd2CY2vKJtNFr8hHJDwp6ESY+/EHstqrRS9Ap6EXY284+ke6V1ZHJR1Sjl6BT0IsQM+nIBNroi4qMmvISzTIlgaegFyF2QLOJTdFQV1GqphsJPAW9CBOfdCQqPLCZmm4k2BT0IuwdxmAiN0yBRrCU/KCgFyF2YvCJBr0mH5HgU9CLsLeNviapphvV6CXYFPQiQKhnkOqyYoqLbEKvU9BLPlDQixAZ0GwCXSujNPmI5AMFvQgTH9AsSpOPSD5IKOjN7G4z22FmG2KWTTGzp83sncjvxjFee3lkm3fM7PJ0FVwknTr7JjbpSJQmH5F8kGiN/qfAGaOW3QD81t0PAX4beb4PM5sC3AQcAywFbhrrA0Ekl0I9E5t0JCr6mlCP2ukluBIKendfDewatfgc4J7I43uAc+O89G+Ap919l7u3A0/z8Q8MkZyb6MTgUXsHNlONXoIrlTb6Ge6+LfL4I2BGnG1mAZtjnrdEln2MmS03szVmtmbnzp0pFEtk4pJvo48OVawavQRXWi7GerjLQUrdDtz9TndvdvfmpqamdBRLJCHuHgn6VGr0CnoJrlSCfruZHQgQ+b0jzjZbgDkxz2dHlokERt/gMP1Dw9RVplKjV9ONBFcqQb8SiPaiuRx4LM42vwFON7PGyEXY0yPLRAIj1Dvxseij6lSjlzyQaPfK+4E/AJ80sxYzuwL4LvAZM3sHOC3yHDNrNrO7ANx9F/BPwB8jP9+OLBMJjL3j3Ey8Rq/JRyQfJPTOdvdLxlh1apxt1wBXxjy/G7g7qdKJZEF0dqmJDmgGmnxE8oPujJWCl8x8sbE0+YgEnYJeCt7eoJ94jT78Ok0+IsGmoJeCl+w0glEawVKCTkEvBW9kdqkkRq8ETT4iwaegl4LX2TtIkUF1WXFSr1eNXoJOQS8Fr7N3kJryEswmNulIlIJegk5BLwUv1JPcgGZRmnxEgk5BLwUv1DuYdPs8aPIRCT4FvRS88BDFyfW4AU0+IsGnoJeC19mb3KQjURrvRoJOQS8FL9Q7kNTwB1G1I7NMqUYvwaSgl4KX7KQjUZp8RIJOQS8FLTzpSKq9btR0I8GmoJeCtqd/iGGH+pR63WjyEQk2Bb0UtJEhipOYXSpKNXoJOgW9FLSOFMaij6rR5CMScAp6KWh7a/TJB70mH5GgU9BLQQuNTCOYfNBHX6+mGwkqBb0UtHS00YMmH5FgSzrozeyTZrYu5idkZteM2uYkM+uI2ebG1Isskj7RYQtS6XUDGsFSgi3paoy7/xlYDGBmxcAW4JE4mz7v7mcnexyRTAr1hMO5pjzVGn0pOzp701EkkbRLV9PNqcC77v5BmvYnkhUdPQPUlJdQUpzafwXV6CXI0hX0FwP3j7HuODN7zcyeMLOFY+3AzJab2RozW7Nz5840FUtk/8Lj3KRWmwcFvQRbykFvZmXAMuCXcVavBQ5y90XAvwKPjrUfd7/T3ZvdvbmpqSnVYokkJNQzkFLXyihNPiJBlo4a/ZnAWnffPnqFu4fcvSvyeBVQambT0nBMkbRIdeTKKE0+IkGWjqC/hDGabczsAItMxGlmSyPHa0vDMUXSItST2uxSUZp8RIIspaA3s2rgM8DDMcu+bGZfjjw9H9hgZq8BPwYudn23lQDp6BlIuQ89aPIRCbaU3uHuvgeYOmrZHTGPbwduT+UYIpmUrqab6D46NPmIBJDujJWCNTzsdPWlp+mmvkpBL8GloJeC1dk3iDtp6V7ZEPmw6OhW0EvwKOilYKVj5MqohqoyAHZ396e8L5F0U9BLwUrXODew91tBR48uxkrwKOilYKVj0pGokuIiastL2N2jGr0Ej4JeClZ0QLN0dK+E8AVZtdFLECnopWBFm27SUaMHaKgqZbd63UgAKeilYKXzYiyE2/rVvVKCSEEvBSvUM4AZ1KY4Fn1UQ2WZet1IICnopWDt7hmgvrKUoiJLy/7qq1Sjl2BS0EvBau8eGLnRKR0aKkvZ3a2hiiV4FPRSsHZ394/c6JQO9ZWlDA47e/qH0rZPkXRQ0EvBau/up7EqjTV6jXcjAaWgl4K1u3uAxrTW6DUMggSTgl4K1u7ugZFRJ9NhpEavm6YkYBT0UpD6B4fp6htMc40+HPS6aUqCRkEvBSk6Jo3a6KUQKOilIO2ONK+ks9dNw0gbvYJegiXloDezTWa23szWmdmaOOvNzH5sZhvN7HUzOzrVY4qkKhrG6Wy6qSgtoqykSCNYSuCk595vONndW8dYdyZwSOTnGODfI79FcqY90jOmIY1NN2YWHu9GNXoJmGw03ZwD/KeHvQQ0mNmBWTiuyJh2ZyDoIXx3rNroJWjSEfQOPGVmr5rZ8jjrZwGbY563RJaJ5Ex7Bppuovtr26OmGwmWdDTdnODuW8xsOvC0mb3t7qsnupPIh8RygLlz56ahWCJja+/up6y4iKqy4rTud2pNGe/s6ErrPkVSlXKN3t23RH7vAB4Blo7aZAswJ+b57Miy0fu5092b3b25qakp1WKJ7FdH5GYps/SMXBk1pbqMXarRS8CkFPRmVm1mtdHHwOnAhlGbrQQ+H+l9cyzQ4e7bUjmuSKrSPc5N1NTqMtq7+xka1giWEhypNt3MAB6J1IpKgPvc/Ukz+zKAu98BrALOAjYC3cAXUzymSMra96R3nJuoqTXluIc/SKbVlKd9/yLJSCno3f09YFGc5XfEPHbgK6kcRyTdWrv6+NTMurTvd0p1+MOjrUtBL8GhO2OlILV29TGtOhM1+kjQ7+lL+75FkqWgl4LTNzhEqHcwIzXuqdXhfeqCrASJgl4KTjSEp2Yi6Gv2Nt2IBIWCXgpOa2c4hKfVpL/pprGqDDN005QEioJeCk5rpP08EzX64iKjobKUti610UtwKOil4LR2hkO4KUO9YqbWlKuNXgJFQS8Fp22kjT79TTcQ7mKpNnoJEgW9FJzWzj4qS4upLk/XKN37mlZTpu6VEigKeik4bXv6M1abh3AXy1bV6CVAFPRScFq7+jJ61+r02nI6egboHRjK2DFEJkJBLwWntas/I10ro2bUVQCwI6TmGwkGBb0UnEzX6GfUh4N+e2dvxo4hMhEKeikog0PDtHX10VSbuaA/IFKj/6hDQS/BoKCXgrKzq49hhwMite5MmFEX/hDZHlLQSzAo6KWgRGvZ0Vp3JtRXllJeUqSgl8BQ0EtBGQn6DNbozYwD6ivYrouxEhAKeikoH4UyX6MHmFFbMXIskVxT0EtB+aijl7LiopGZoDJlRn0FOxT0EhAKeikoH4V6mVFfTmSe44yZUVvOR6FewjNpiuRW0kFvZnPM7Fkze9PM3jCz/xNnm5PMrMPM1kV+bkytuCKp2dbRm/FmGwhfA+gdGCbUO5jxY4mMJ5VRnQaB69x9rZnVAq+a2dPu/uao7Z5397NTOI5I2nzU0cuiOQ0ZP070Yu+2jh7qK0szfjyR/Um6Ru/u29x9beRxJ/AWMCtdBRNJt6FhZ+vuHmY3Vmb8WLMbqwDYvKsn48cSGU9a2ujNbB5wFPBynNXHmdlrZvaEmS3czz6Wm9kaM1uzc+fOdBRLZB/bOnoYHHbmTqnK+LHmRD5MNu/qzvixRMaTctCbWQ3wEHCNu4dGrV4LHOTui4B/BR4daz/ufqe7N7t7c1NTU6rFEvmYaO16TmPmg35KdRlVZcVsblfQS+6lFPRmVko45O9194dHr3f3kLt3RR6vAkrNbFoqxxRJVjR050zJfNONmTF3SpWabiQQUul1Y8AK4C13v22MbQ6IbIeZLY0cry3ZY4qkYvOubooMZjZkPugh3E6vphsJglR63fwV8LfAejNbF1n2D8BcAHe/Azgf+DszGwR6gItdHYslRzbv6ubA+kpKi7Nz+8icKZX8/t1W3D3j/fZF9ifpoHf3F4D9vnvd/Xbg9mSPIZJOH+7qzkqzTdTcKVV09w/R2tWf0WGRRcajO2OlILg7G3d08YmmmqwdM3qsjTu6snZMkXgU9FIQdnb1Eeod5JDp2Qv6BZFjbdypoJfcUtBLQdi4PRy2C6bXZu2YB9ZXUF1WzLuq0UuOKeilIERr1QuyWKM3MxZMr1HTjeScgl4KwsYdXdSUl4xM85ctn5hewzs7OrN6TJHRFPRSEN7e1smhM2qy3s3xLw6oZXuoj7YuzTYluaOgl0lvaNjZsLWDI2dnftTK0Y6YFT7m+i0dWT+2SJSCXia9d3d20d0/xBGz6rN+7MNn1QGwvkVBL7mjoJdJ77XNuwFYNCf7QV9bUcrBTdW8pqCXHFLQy6T3WstuqsuKmT8tez1uYi2a3cC6zbs1raDkjIJeJr3fv9vGX86fQnFRbsabOfbgKbR29ambpeSMgl4mta27e3hv5x5OWJC70bH/KnLsFza25qwMUtgU9DKpRcP1hENyF/SzG6uYN7WKF95R0EtuKOhlUnvqjY84oK6CT87I3tAH8Zz0yek8v7GVzt6BnJZDCpOCXiat9j39PPfnnSxbPDPn48EvWzyT/sFhfvPG9pyWQwqTgl4mrcfWbWFw2Fm2aGaui8JRcxqYO6WKX6zZnOuiSAFS0MukNDA0zE+ef5+j5jawcGZdrouDmfH54w7ilfd38eoH7bkujhQYBb1MSve9/CFbdvdw9ckLct5sE3XJ0rk0VpVy65NvMzysPvWSPQp6mXQ27ujk1iff5tOHNnHKX0zPdXFGVJeXcMOZf8Er7+/i7hffz3VxpICkFPRmdoaZ/dnMNprZDXHWl5vZzyPrXzazeakcT2Q861s6uOyuV6gqK+G75x0RmNp81IXNc/ibhTP451VvcfcL7+tuWcmKpCcHN7Ni4N+AzwAtwB/NbKW7vxmz2RVAu7svMLOLgVuBi1IpsEisgaFhdnT28frm3Tyx4SMeX7+N6bXl/OyKpcxsyN5E4IkyM3508VFcfd9avv3rN3lobQsXL53LX85r5KAp1VSWFee6iDIJJR30wFJgo7u/B2BmDwDnALFBfw5wc+Txg8DtZmaeoWrM2f/6PL0Dw/ssi3eouAf38bdJdF/xzs7jbBl3uwT/ZrJSlgT3F2/LxPeXwnm409k3OLKupryELx4/j6+cvIDG6rJ4BQ2EitJi7vzbZh5a28K//+5dvvXohpF1VWXFVJYWU1FaTGlx+NtI9FuJjfwx8gszI1jfWSQVjVVl/OLLx6V9v6kE/Swgtq9YC3DMWNu4+6CZdQBTgY/dImhmy4HlAHPnzk2qQAuaahgYipMIcf4nxPvPEe9r/ugl8VoCkt3X2GWL89qEj5vC/hIsYFbKEnd/H19aX1nKAfUVHDqjhiNnN1BanB+XnYqKjAua53D+ktm817qHN7aG+LBtDx09A/QMDJnnjaAAAARdSURBVNHdP8TQsI98iDl7PxRH3uEe/0Nb8lddRWlG9ptK0KeVu98J3AnQ3Nyc1Lv3/118VFrLJJJpZsYnmmr4RFNuRtaUwpBK9WcLMCfm+ezIsrjbmFkJUA+0pXBMERGZoFSC/o/AIWY238zKgIuBlaO2WQlcHnl8PvBMptrnRUQkvqSbbiJt7lcDvwGKgbvd/Q0z+zawxt1XAiuAn5nZRmAX4Q8DERHJopTa6N19FbBq1LIbYx73AhekcgwREUlNfnRREBGRpCnoRUQmOQW9iMgkp6AXEZnkLIi9Hc1sJ/BBki+fRpw7byc5nfPkV2jnCzrniTrI3ZvirQhk0KfCzNa4e3Ouy5FNOufJr9DOF3TO6aSmGxGRSU5BLyIyyU3GoL8z1wXIAZ3z5Fdo5ws657SZdG30IiKyr8lYoxcRkRgKehGRSS5vg77QJiZP4Hy/ZmZvmtnrZvZbMzsoF+VMp/HOOWa7z5mZm1ned8VL5JzN7MLIv/UbZnZftsuYbgm8t+ea2bNm9qfI+/usXJQzXczsbjPbYWYbxlhvZvbjyN/H62Z2dMoHdfe8+yE8LPK7wMFAGfAacNioba4C7og8vhj4ea7LneHzPRmoijz+u3w+30TPObJdLbAaeAloznW5s/DvfAjwJ6Ax8nx6rsudhXO+E/i7yOPDgE25LneK5/xp4GhgwxjrzwKeIDyj5rHAy6keM19r9CMTk7t7PxCdmDzWOcA9kccPAqdavElH88O45+vuz7p7d+TpS4Rn/MpnifwbA/wTcCvQm83CZUgi5/wl4N/cvR3A3XdkuYzplsg5O1AXeVwPbM1i+dLO3VcTnp9jLOcA/+lhLwENZnZgKsfM16CPNzH5rLG2cfdBIDoxeT5K5HxjXUG4RpDPxj3nyFfaOe7+eDYLlkGJ/DsfChxqZi+a2UtmdkbWSpcZiZzzzcBlZtZCeP6Lr2anaDkz0f/v4wrM5OCSHmZ2GdAM/HWuy5JJZlYE3AZ8IcdFybYSws03JxH+1rbazI5w9905LVVmXQL81N1/YGbHEZ617nB3H851wfJFvtboC21i8kTOFzM7DfhHYJm792WpbJky3jnXAocDz5nZJsJtmSvz/IJsIv/OLcBKdx9w9/eB/yYc/PkqkXO+AvgFgLv/AaggPPjXZJXQ//eJyNegL7SJycc9XzM7CvgPwiGf7+22MM45u3uHu09z93nuPo/wdYll7r4mN8VNi0Te148Srs1jZtMIN+W8l81Cplki5/whcCqAmX2KcNDvzGops2sl8PlI75tjgQ5335bKDvOy6cYLbGLyBM/3+0AN8MvINecP3X1ZzgqdogTPeVJJ8Jx/A5xuZm8CQ8DX3T1fv6kmes7XAT8xs2sJX5j9Qh5X2jCz+wl/WE+LXHe4CSgFcPc7CF+HOAvYCHQDX0z5mHn89yUiIgnI16YbERFJkIJeRGSSU9CLiExyCnoRkUlOQS8iMskp6EVEJjkFvYjIJPf/AXUcBIpE1/AeAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ItgpAg_FrQbH"
      },
      "source": [
        "# Our First Probabilistic Program (Space Shuttle Disaster)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "FnXtKeAghsxj",
        "outputId": "8516963f-69eb-473a-9fbd-dd573811d31e"
      },
      "source": [
        "!wget https://raw.githubusercontent.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/data/challenger_data.csv"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "--2021-08-27 08:20:24--  https://raw.githubusercontent.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/data/challenger_data.csv\n",
            "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.110.133, 185.199.111.133, 185.199.108.133, ...\n",
            "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.110.133|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 413 [text/plain]\n",
            "Saving to: ‘challenger_data.csv’\n",
            "\n",
            "challenger_data.csv 100%[===================>]     413  --.-KB/s    in 0s      \n",
            "\n",
            "2021-08-27 08:20:24 (12.3 MB/s) - ‘challenger_data.csv’ saved [413/413]\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9EbLLBrIOp0c"
      },
      "source": [
        "## Reading Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 834
        },
        "id": "VOh46fvixFXN",
        "outputId": "6ac2ee79-6b90-421d-9744-b2111c8ab53f"
      },
      "source": [
        "import pandas as pd\n",
        "raw_data = pd.read_csv('challenger_data.csv')\n",
        "raw_data"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>Date</th>\n",
              "      <th>Temperature</th>\n",
              "      <th>Damage Incident</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>04/12/1981</td>\n",
              "      <td>66</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>11/12/1981</td>\n",
              "      <td>70</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3/22/82</td>\n",
              "      <td>69</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>6/27/82</td>\n",
              "      <td>80</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>01/11/1982</td>\n",
              "      <td>68</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>04/04/1983</td>\n",
              "      <td>67</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>6/18/83</td>\n",
              "      <td>72</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>8/30/83</td>\n",
              "      <td>73</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>11/28/83</td>\n",
              "      <td>70</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>02/03/1984</td>\n",
              "      <td>57</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>04/06/1984</td>\n",
              "      <td>63</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>8/30/84</td>\n",
              "      <td>70</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>10/05/1984</td>\n",
              "      <td>78</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>11/08/1984</td>\n",
              "      <td>67</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>1/24/85</td>\n",
              "      <td>53</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>04/12/1985</td>\n",
              "      <td>67</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>4/29/85</td>\n",
              "      <td>75</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>6/17/85</td>\n",
              "      <td>70</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>7/29/85</td>\n",
              "      <td>81</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>8/27/85</td>\n",
              "      <td>76</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>10/03/1985</td>\n",
              "      <td>79</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>10/30/85</td>\n",
              "      <td>75</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>22</th>\n",
              "      <td>11/26/85</td>\n",
              "      <td>76</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>23</th>\n",
              "      <td>01/12/1986</td>\n",
              "      <td>58</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>24</th>\n",
              "      <td>1/28/86</td>\n",
              "      <td>31</td>\n",
              "      <td>Challenger Accident</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          Date  Temperature      Damage Incident\n",
              "0   04/12/1981           66                    0\n",
              "1   11/12/1981           70                    1\n",
              "2      3/22/82           69                    0\n",
              "3      6/27/82           80                  NaN\n",
              "4   01/11/1982           68                    0\n",
              "5   04/04/1983           67                    0\n",
              "6      6/18/83           72                    0\n",
              "7      8/30/83           73                    0\n",
              "8     11/28/83           70                    0\n",
              "9   02/03/1984           57                    1\n",
              "10  04/06/1984           63                    1\n",
              "11     8/30/84           70                    1\n",
              "12  10/05/1984           78                    0\n",
              "13  11/08/1984           67                    0\n",
              "14     1/24/85           53                    1\n",
              "15  04/12/1985           67                    0\n",
              "16     4/29/85           75                    0\n",
              "17     6/17/85           70                    0\n",
              "18     7/29/85           81                    0\n",
              "19     8/27/85           76                    0\n",
              "20  10/03/1985           79                    0\n",
              "21    10/30/85           75                    1\n",
              "22    11/26/85           76                    0\n",
              "23  01/12/1986           58                    1\n",
              "24     1/28/86           31  Challenger Accident"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GxSGpwSsOt5T"
      },
      "source": [
        "## Preprocessing Data (cleaning)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 228
        },
        "id": "DNjcq8MAxK70",
        "outputId": "5e39f89f-22c6-4696-fa0d-ec724bfd138a"
      },
      "source": [
        "accident_temperature = 31\n",
        "data = raw_data.dropna().iloc[:-1, :]\n",
        "data['Damage Incident'] = pd.to_numeric(data['Damage Incident']).astype(np.int64)\n",
        "plt.figure(figsize=(13, 3))\n",
        "plt.scatter(data['Temperature'], data['Damage Incident'])"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f369921cd10>"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 936x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6IbDfWC-Ox7b"
      },
      "source": [
        "## Define a function that sperate categories:\n",
        "\n",
        "Logistic:\n",
        "\n",
        "![Screenshot from 2021-08-26 16-03-16.png](data:image/png;base64,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)\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 422
        },
        "id": "YWXsdhapyp_1",
        "outputId": "ae4ff8db-1cbd-4a3f-8308-045ce7ae3cb9"
      },
      "source": [
        "plt.figure(figsize=(10, 3))\n",
        "def logistic(t, beta):\n",
        "    return 1.0 / (1.0 + np.exp(beta * t))\n",
        "\n",
        "t = np.linspace(-5, 5, 100)\n",
        "plt.plot(t, logistic(t, 1), label=r\"$\\beta = 1$\")\n",
        "plt.plot(t, logistic(t, 3), label=r\"$\\beta = 3$\")\n",
        "plt.plot(t, logistic(t, -5), label=r\"$\\beta = -5$\")\n",
        "\n",
        "plt.legend()\n",
        "\n",
        "def logistic(t, beta, alpha=0):\n",
        "    return 1.0 / (1.0 + np.exp(np.dot(beta, t) + alpha))\n",
        "\n",
        "plt.figure(figsize=(10, 3))\n",
        "plt.plot(t, logistic(t, 1, 0), label=r\"$\\beta = 1, \\alpha = 0$\")\n",
        "plt.plot(t, logistic(t, 1, -1), label=r\"$\\beta = 1, \\alpha = -1$\", ls='--')\n",
        "plt.legend()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f36991a33d0>"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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NI1j14KXcdUlPMg4f4/o31nPZ8+m8v/4w1U6P0WGeH6XgihchuqcvqSrLMTqiMyqtKeXT3Z8yNWWqJFJCiHPSYDKllDIDLwNTgf7AtUqp/qdU+y/gY631UOAa4BV/BypER9A1IpAHJvdh9UOX8syswVjNJh6Z/wMX/vd/+PvinRSUO4wO8dwFhMAv3wVnFXxyM3hcRkdUr492fUS1u5rZF8w2OhQhRBvTmJ6pkcBerfV+rbUT+BA49QFVGgirXQ8HWu/XTyHaALvVzFXDE/jq7rF8+pvRpPWM5rXv9jH2qeU89Nn37CusMDrEc9OpL1wxF7LWwdLHjY7mNA63g/d2vMfY+LH0iepjdDhCiDamMQPQ44GsOtvZwKhT6jwBfKOUuhsIBib6JTohOjilFKnJUaQmR3GwqJI3Vu3nk03ZfLQpi4n94vjtxT0YlhRpdJiNM/AqyNoA616GxBG+AeqtxIJ9CyhxlDBnwByjQxFCtEH+ulf5WuBtrXUCMA14Vyl12rmVUrcppTYppTYVFhb6qWkhOobkmGD++vOBrH7oUu6+tBcbD5bwi1fWcMMb61m/v9jo8Bpn8l99c099eS+U5xsdDQAer4e3f3ybAdEDSI2rd2ypEEKcVWOSqSNAYp3thNp9df0a+BhAa70WsAMxp55Iaz1Pa52qtU6NjY09v4iF6OBiQgK4f1JvVj94KY9M68vOvHKunreOX762lpV7CjHqDt1GsdjgytfA5YBFfzA6GgC+PfwtWeVZzBk4p23fOSmEMExjkqmNQC+lVIpSyoZvgPmCU+ocBiYAKKX64UumpOtJiGYUHGDhtvE9WPXgJTz+s/4cLqnixjc3MPPVNazZW2R0eGcW0wsu+iNs/wJ2fGl0NLzz4zt0C+vGpYmXGh2KEKKNajCZ0lq7gbuAJcAOfHft/aiU+rNS6oraag8AtyqltgIfALN1q/56LET7YbeauTkthe/+eDF//fkAcksdXPfGeq6dt47Nh0qMDq9+afdC3ED4+vdQfcywMA6UHuD7ou+Z1XsWZpPZsDiEEG2bTNopRDvjcHl4f/1hXlmxl6IKJxf3ieX3k/swIL6VzeidkwGvXwpDb/DNRWWAVzJf4bWtr7H0qqXEBccZEoMQom1o8qSdQoi2w241M2dsCul/vIQHp/Ql4/AxLn9xFfd8kEFWSZXR4f2k61AYfRdseQf2f9fizWutWXhgISM6j5BESgjRJJJMCdFOBdks/PbiHqx88BLuvKQH32zP49L/WcGfv9zO0Uqn0eH5XPwwRKbAl/f4JvVsQdtLtnOo7BDTUuSBDUKIppFkSoh2Lsxu5Q+X9WXF7y/hF0MTeHvNAcb/fTmvrNiLw2XwY2psQb7JPI8ehBV/a9GmF+5fiMVkYWI3mRZPCNE0kkwJ0UF0Drfz9FWDWHzfeEamRPH3xbuY+Ox3LPwh19jpFFLGw9AbYd2rULSnRZr0eD0sPrCYsfFjCQ9oZWPJhBBtjiRTQnQwveNCeXP2CN67ZRQhARbueG8LV89bx7YjpcYFNeFxsATC0sdapLktBVsoqC5gesr0FmlPCNG+STIlRAeV1jOGr+8Zx5NXDmBvQQU/e2kVf/x0K0UVNS0fTEgsjPsd7FoIB1Y2e3Nf7/+aQEsgFyVe1OxtCSHaP0mmhOjAzCbF9aO6seIPF3PruO7MzzjCJc+s4O3VB3B7vC0bzIV3QFgCfPMoeJuvbZfHxdJDS7k06VICLYHN1o4QouOQZEoIQZjdyiPT+rH4vvEMSYzgiS+3c/mLq9h4sAUn/bQGwoTHIHcr/PBxszWzOmc1Zc4yuYtPCOE3kkwJIU7oERvCO3NG8ur1wyirdjHrtbXc/1EmheUtdOlv4Czf/FP/+XOzTZWwcP9CIgIiGN11dLOcXwjR8ViMDkAI0boopZg6sAsX9YnlpWV7eX3lfr7dkc/D0/pxdWoiJlMzPgzYZILJT8Lb02DdyzDevw9DrnJVsTxrOVf0uAKryerXcwvRFrhcLrKzs3E4HEaH0mrZ7XYSEhKwWhv/GSHJlBCiXkE2C3+c0pdfDIvnkfnbePjfP/DZ5myevHIgfTqHNl/DyWnQ93JY9TwMuwlCOvnt1MuzluPwOJjWXS7xiY4pOzub0NBQkpOTUaoZvxi1UVpriouLyc7OJiUlpdGvk8t8Qoiz6tkplI9uu5B/XDWIfYUVTJ+7kqcX72zeCT8n/gncDlju34k8Fx5YSOfgzgztNNSv5xWirXA4HERHR0sidQZKKaKjo8+5506SKSFEg5RSzEpN5D8PXMzPh8bz6op9THk+nbX7ipunwZiekPpr2PIvKN7nl1OWO8tZc2QNU5KnYFLy0Sc6Lkmkzu58/nzkE0UI0WhRwTaemTWY928ZhVfDta+v4+F//0CZw+X/xsY9AOYASH/GL6dbk7MGt3ZzSeIlfjmfEEIcJ8mUEOKcjekZw5L7xnPb+O58tPEwk579jqXb8/3bSGgcjPg1fP+RX3qn0rPTCbOFMSh2kB+CE0KIn0gyJYQ4L4E2M49M68f8O9KIDLJx6zubuPuDDEoqnf5rZMw9YLY1uXfKq72sOrKKtK5pWExy340Qwr8kmRJCNMngxAi+vHss90/qzeJtuUx+7jsWb8vzz8n91Dv1Y9GPlDhKGJcwzj9xCSGa7LHHHmPgwIH07t2befPmndc55syZQ6dOnRgwYICfozs3kkwJIZrMajZxz4ReLLhrLHFhdn7zf5u554MMjvqjl8oPvVPpR9JRKMbGj216PEKIJluyZAkZGRlkZmby2Wef8fnnn5/XeWbPns3ixYv9HN25k2RKCOE3/bqE8fmdadw/qTeLtuUy6bnvWPJjE3up/NA7lZ6dzqDYQUTaI5sWixDCLxYsWMDs2bNxuVy89NJLzJw587zOM378eKKiovwc3bmTwQNCCL863ks1qX8cD3y8ldvf3czMYQk8fkV/wuznOev4mHtg45u+3qkrXz2nlxZWFbK9eDt3D737/NoWop3605c/sj2nzK/n7N81jMd/dkGD9TZv3syIESOIjo4mOTmZ55577qTj48aNo7y8/LTXPfPMM0ycONFv8fqL9EwJIZrF8V6quy/tyeeZR5jyXDpr9had38ma0Du16sgqAMYnjD+/toUQfuX1esnOzmb27NkUFRUxfPhwnn322ZPqrFy5kszMzNOW1phIQSN7ppRSU4AXADPwhtb6qXrq/BJ4AtDAVq31dX6MUwjRBtksJh6Y3IcJ/eK4/6NMrntjPbPHJPPglL4E2szndrLz7J1Kz06nU1An+kT2OcfohWjfGtOD1Bx27dpFr169AAgMDCQtLY28vJOHA7S1nqkGkymllBl4GZgEZAMblVILtNbb69TpBTwMpGmtjyql/PcwLSFEmzckMYKv7xnH04t38vaag6TvKeT5q4cwKCGi8Sc53ju17hW46A8Q1b3Bl7g8LtbmrmVK8hSZ9VmIViIjI4Oamho8Hg9ut5v333+fuXPnnlRn5cqVBkV3fhpzmW8ksFdrvV9r7QQ+BGacUudW4GWt9VEArXWBf8MUQrR1gTYzT1xxAe/dMopqp4dfvLKGl5fvxePVjT/JmLvBZIE1Lzaq+uaCzVS6KuUSnxCtSGZmJtXV1fTo0YO0tDRuuukmBg8efF7nuvbaaxk9ejS7du0iISGBN99808/RNk5jLvPFA1l1trOBUafU6Q2glFqN71LgE1rr0+5VVErdBtwGkJSUdD7xCiHauLSeMSy+dzyPfv4D/1iyi+U7C3ju6iEkRgU1/OLQzjDkOsh4Dy56yNdbdRbp2elYTVYu7HKhn6IXQjRVRkYG7777rl/mhvrggw/8EFHT+WsAugXoBVwMXAu8rpQ6rf9eaz1Pa52qtU6NjY31U9NCiLYmPMjKi9cO5fmrh7Arr5ypL6zk083ZaN2IXqox94DXBetfa7DqyuyVjOg8giBrIxI1IUSL2LlzJ3379jU6DL9qTDJ1BEiss51Qu6+ubGCB1tqltT4A7MaXXAkhRL2UUvx8aDyL7hvHBV3D+P0nW7nrgwxKqxp4aHJ0D+h3BWx8AxylZ6x2uOwwB8sOyiU+IVqZrKwsLJb2NTNTY5KpjUAvpVSKUsoGXAMsOKXO5/h6pVBKxeC77Lffj3EKIdqphMgg3r/1Qv44pQ9LtuUx9YV01u0vPvuLxt4HNWWw6X/PWCU9Ox2A8fGSTAkhmleDyZTW2g3cBSwBdgAfa61/VEr9WSl1RW21JUCxUmo7sBz4g9a6gU9DIYTwMZsUd1zck89+O4YAq5lrX1/HP5bsxOXx1v+CrkOh+yW+O/tcjnqrpGenkxyWTGJYYr3HhRDCXxo1ZkprvVBr3Vtr3UNr/WTtvse01gtq17XW+n6tdX+t9UCt9YfNGbQQon0anBjBV3ePZdbwBF5evo+rXl3DoeLK+iuPvQ8q8mHr6QNQq1xVbMrfJJf4hBAtQmZAF0K0KsEBFv5+1WBeuX4YB4oqmfbCSv69Jfv0iikX+Xqo1swFr+ekQxvzNuLyuuTBxkKIFiHJlBCiVZo2sAuL7hvPBV3Duf/jrdz3YQbljjqD05WCsb+Dkv2w4+RhnGty1mA32xkWN6yFoxZCdESSTAkhWq34iEA+uO1CfjexNwu25jB97ioyDh/9qULfyyG6J6x6DupMq7AmZw3DOw8nwBxgQNRCiI5GkikhRKtmNinundiLj28fjcermfXaWl5dsQ+vV4PJ7Jt3Kncr7F8OwJGKIxwsO0ha1zSDIxdCdBSSTAkh2oTU5CgW3juOyy7ozNOLd/KrtzZQUOaAwddASBys9j3ba23OWgDGdB1jZLhCiA5EkikhRJsRHmjlpeuG8t+/GMimQyVMfWEly/eVwqjbfT1Tud+zJmcNcUFxdA9v+EHIQgjjPPbYYwwcOJDevXszb968c369w+Fg5MiRDB48mAsuuIDHH3+8GaJsHEmmhBBtilKKa0cm8eVdY4kNDeDm/93IM8VpaGsw7tVzWZe7jjFdx6CUMjpUIcQZLFmyhIyMDDIzM/nss8/4/PPPz/kcAQEBLFu2jK1bt5KZmcnixYtZt25dM0TbMEmmhBBtUq+4UD6/M41fje7GS+uKWWCeyLa9X1HuLGdMvFziE6I1W7BgAbNnz8blcvHSSy8xc+bMcz6HUoqQkBAAXC4XLpfLsC9R7evhOEKIDsVuNfPnGQMY0yOG5z89xs/CV6CACztfaHRoQrR+ix6CvB/8e87OA2HqUw1W27x5MyNGjCA6Oprk5GSee+65k46PGzeO8vLy0173zDPPMHHixBPbHo+H4cOHs3fvXu68805GjRrV9J/hPEjPlBCizZsyoDNv3vcLloR0op/Dxd/n/0BljdvosIQQ9fB6vWRnZzN79myKiooYPnw4zz777El1Vq5cSWZm5mlL3UQKwGw2k5mZSXZ2Nhs2bGDbtm0t+aOcID1TQoh2ITTIxSGbk1uOVlGV9X9cfsTDi9cOZUB8uNGhCdE6NaIHqTns2rWLXr16ARAYGEhaWhp5eXkn1Wlsz9RxERERXHLJJSxevJgBAwY0T+BnIcmUEKJd2JC7AS+atMh+DKhZxlc1V3LlK6t5aGo/5qQly4B0IVqJjIwMampq8Hg8uN1u3n//febOnXtSnZUrVzZ4nsLCQqxWKxEREVRXV7N06VIefPDB5gr7rOQynxCiXVids5pgazADRz+ArbqAxRPyuLhPJ/7y1XbmvL2R4ooao0MUQgCZmZlUV1fTo0cP0tLSuOmmmxg8ePA5nyc3N5dLLrmEQYMGMWLECCZNmsTll1/eDBE3THqmhBBtntaaNUfWMKrzKKy9JkHcQII3v8q8367h3fVZ/PXrHUx5YSXPXz2EtJ4xRocrRIeWkZHBu+++2+TLcYMGDSIjI8NPUTWN9EwJIdq8Q2WHyKnM8c16rhSMuRsKd6L2LOVXo5P5/I40wuwWbnhzPU8t2onL4zU6ZCE6rJ07d9K3b1+jw/ArSaaEEG3empw1AD/NLzXgFxCeCKtfAKB/1zC+vHssV6cm8tp3+7jqtbUcKq40KlwhOrSsrCwslvZ1YUySKSFEm7c2Zy2JoYkkhib6dpitMPouOLwGDvtmRA6yWXhq5iBeuX4YBwormD53FfMzslCd9b4AAB6RSURBVA2MWgjRXkgyJYRo01weFxvyNpz+YONhN0JgFKx6/qTd0wZ2YdF94+nXJZTffbSV332USbnD1YIRCyHaG0mmhBBtWmZhJlXuqtOTKVswjPoN7F4E+dtPOhQfEcgHt17I7yb25ovMI0yfu4oth4+2YNRCiPZEkikhRJuWnp2OxWRhVJd6HiMx8lawBsOauacdsphN3DuxFx/fPhqPVzPrtbXM/c8ePF7dAlELIdoTSaaEEG1aenY6qXGpBFuDTz8YFAXDb4IfPoFjh+t9fWpyFIvuG8flg7rw7NLdXDNvLdlHq5o5aiFEe9KoZEopNUUptUsptVcp9dBZ6s1USmmlVKr/QhRCiPpll2ezv3Q/4xPGn7nS6Dt95dqXz1glzG7lhWuG8tzVg9mRW87UF1ayYGuOn6MVQrRXDSZTSikz8DIwFegPXKuU6l9PvVDgXmC9v4MUQoj6pGenA5w9mQpPgEFXw+Z/QWXxWc935dAEFt4zjl6dQrjngwzu+zCD0moZnC6EOLvG9EyNBPZqrfdrrZ3Ah8CMeur9BXgacPgxPiGEOKP0I+l0C+tGt7BuZ6+Ydi+4q2HDPxs8Z1J0EB/fPpr7J/Xmy+9zmfp8Omv3nT0JE0J0bI1JpuKBrDrb2bX7TlBKDQMStdZfn+1ESqnblFKblFKbCgsLzzlYIYQ4rspVxcbcjYyLH9dw5dg+0Gc6bJgHNRUNVreYTdwzoRef/XYMAVYz172xjv9etIMat8cPkQshAB577DEGDhxI7969mTdvXou0mZyczMCBAxkyZAipqf4bkdTkAehKKRPwLPBAQ3W11vO01qla69TY2NimNi2E6MA25G3A6XWe/RJfXWN/B9VHYfPbjW5jSGIEX98zlmtHJvHP7/bz85fXsCO37PwCFkKcsGTJEjIyMsjMzOSzzz7j888/b7G2ly9fTmZmJps2bfLbORuTTB0BEutsJ9TuOy4UGACsUEodBC4EFsggdCFEc0rPTifIEkRqXCM/ahJHQMp43zQJrupGtxNks/C3Kwfy5k2pFJbXMOOl1by6Yp9MoSBEEyxYsIDZs2fjcrl46aWXmDlzptEhNUljHo6zEeillErBl0RdA1x3/KDWuhQ48Rh2pdQK4Pdaa/+lfEIIUYfWmvTsdEZ3HY3VbG38Cy96CN6eBpv+F0bfcU5tTugXxze/i+TR+T/w9OKd/GdHPs/MGkxyTD1TMgjRBjy94Wl2luz06zn7RvXlwZEPNlhv8+bNjBgxgujoaJKTk3nuuedOOj5u3DjKy8tPe90zzzzDxIkTzzs+pRSTJ09GKcXtt9/Obbfddt7nqqvBZEpr7VZK3QUsAczAW1rrH5VSfwY2aa0X+CUSIYRopN1Hd5Nflc8dCeeWEJGc5uudWv08pN4M1sBzenlUsI1Xrh/GF5k5/L8vtjH1hZU8Mr0fN4xKQil1brEI0UF5vV6ys7OZPXs2V199NbfffjvPPvss//Vf/3WizsqVK8/pnBMnTiQvL++0/U8++SQzZvx0z9yqVauIj4+noKCASZMm0bdvX8aPb+RQgbNo1GObtdYLgYWn7HvsDHUvbnJUQghxFiuP+D5oGzX4/FRN6J0C3zfbnw+NZ1T3KP746ff8v8+3sXhbLk/PHERCZNC5xyOEQRrTg9Qcdu3aRa9evQAIDAwkLS3ttEToXHumvv3220a1HR/vu3+uU6dOXHnllWzYsKHlkikhhGhN0rPT6RfVj9ig87iRpYm9U8d1CQ/knTkjeX/DYf729Q4uey6dR6b347qR0kslxNlkZGRQU1ODx+PB7Xbz/vvvM3fuyY98OteeqcaorKzE6/USGhpKZWUl33zzDY89Vm+/0DmTx8kIIdqUY45jbC3c2vi7+Opz0UNQke/rnWoCpRTXj+rGkt+NZ0hSBI/O38aNb26Qx9EIcRaZmZlUV1fTo0cP0tLSuOmmmxg8eHCzt5ufn8/YsWMZPHgwI0eOZPr06UyZMsUv55aeKSFEm7I6ZzVe7W1aMuWn3qnjEiKD+L9fjzqpl+rBqX25YVQ3TCbppRKiroyMDN59910GDBjQou12796drVu3Nsu5pWdKCNGmpGenE2WPYkBMEz+I/dQ7ddzxXqrF941nWLdIHvviR66et5a9BQ1PEipER7Jz50769u1rdBh+JcmUEKLN8Hg9rM5Zzdj4sZhUEz++6vZOncO8Uw1JjArinTkjeWbWYHbnVzDthZW8vHwvLo/Xb20I0ZZlZWVhsbSvC2OSTAkh2ozvi76ntKaUcQnncRdffU70Tr3ln/PVUkpx1fAElt4/non9O/GPJbu44qXVbM065td2hBCtgyRTQog245uD32A1WUnrmuafEyanQfeLIf0ZqPZ/otMp1M4r1w/ntRuGU1xRw89fWc3jX2yjzOHye1tCCONIMiWEaBM8Xg+LDy5mfMJ4Qm2h/jvxpL/4ntm38n/8d85TTBnQmW8fuIhfXdiNd9YdYtKz37Hwh1y0lkfSiJYnv3dndz5/PpJMCSHahE35myiqLmJayjT/nrjLIBhyHax/DY4e9O+56wizW/nTjAHMvyON6OAA7nhvC3Pe3khWiUyjIFqO3W6nuLhYEqoz0FpTXFyM3W4/p9cpo/5AU1NTtT+f2CyEaN8eX/M4Sw4uYcUvV2C3nNsHXYPKcuDF4dB7Cszyz919Z+P2eHl7zUGeXbobj1fz24t78JuLemC3mpu9bdGxuVwusrOzcTgcRofSatntdhISErBaT37up1Jqs9a63iert6/h9EKIdsnpcbL04FImJE3wfyIFENYVxtwN3z0NF94BiSP830YdFrOJW8Z1Z/qgLjz59Q6e/3YPn23J5vHLL2Bi/7hmbVt0bFarlZSUFKPDaHfkMp8QotVbdWQV5a5y/1/iq2vMPRASB988Ci3UY98lPJCXrhvG+7eMIsBi5pZ3NjHn7Y0cLKpskfaFEP4hyZQQotVbeGAhUfYoRnUZ1XyNBITAJY9C1nrY/kXztVOPMT1jWHTvOB6d1o/1+4uZ9Nx3/PfCHXLXnxBthCRTQohWrdJVyYqsFUzuNhmLqZlHJgy9ATpdAN8+Du6a5m3rFFaziVvHd2f57y/m50PimbdyP5f8YwXvrz+MxyuDhYVozSSZEkK0assOL6PGU8P07tObvzGTGSb/xXdX34bXm7+9enQKs/OPWYNZcOdYuscG88j8H5g+dyWr9xYZEo8QomGSTAkhWrWFBxbSNbgrg2Ob/6nyAPScAD0nwYr/htLslmmzHgMTwvn49tG8fN0wyh1urn9jPTe9tYEduWWGxSSEqJ8kU0KIVqvEUcLanLVMTZmKUqrlGp7+DGgvfHV/iw1Gr49SiumDuvCfBy7i0Wn9yMw6xrS5K3ng460cOea/5wkKIZpGkikhRKv1zcFv8GgP07o341189YlMhkv/H+xZAts+a9m262G3mrl1fHfS/3AJt43rzpff53DJMyt48uvtlFQ6jQ5PiA5PkikhRKu16MAiekb0pHdk75ZvfNTtEJ8Ki/4IlcUt3349woOsPDytH8t/fzGXD+rCG6sOMO7pZTz7zS5Kq+XOPyGMIsmUEKJVyqnIYUvBluadW+psTGa44kVwlMHih4yJ4QziIwJ59pdD+Oa+8VzcpxNzl+1l3NPLeHn5Xipr3EaHJ0SH06hkSik1RSm1Sym1Vyl12qeKUup+pdR2pdT3Sqn/KKW6+T9UIURH8uW+LwGYkjLFuCDi+sO4++GHj2HPUuPiOINecaG8fP0wvrp7LCOSo/jHkl2M+/tyXl6+l3KZo0qIFtNgMqWUMgMvA1OB/sC1Sqn+p1TLAFK11oOAT4G/+ztQIUTHUeOp4YOdH5DWNY3E0ERjgxn3AMT0gS/vg5pyY2M5gwHx4bw5ewT/vmMMgxLC+ceSXYx9ejnPf7ub0ipJqoRobo3pmRoJ7NVa79daO4EPgRl1K2itl2utjz/6fB2Q4N8whRAdyYJ9Cyh2FDNnwByjQwFLAMx4CcqOwLdPGB3NWQ1LiuTtm0ey4K40RqZE8fy3e0h7ehl/X7yTwvKWnYRUiI6kMclUPJBVZzu7dt+Z/BpY1JSghBAdl8fr4e1tbzMgegAjOjfvA4cbLXEkXPhb2PgGbF9gdDQNGpQQweu/SmXRveO4qHcsr363j7Snl/Hwv39gf2GF0eEJ0e749dkMSqkbgFTgojMcvw24DSApKcmfTQsh2ollWcs4XH6Y/7nof1p2bqmGTHzC99y+z++ATv0hpqfRETWoX5cwXr5+GPsLK3hj1QE+3ZzNhxsPc1n/ztx2UXeGJUUaHaIQ7YLSDUxIp5QaDTyhtb6sdvthAK31f59SbyLwInCR1rqgoYZTU1P1pk2bzjduIUQ7pLXmuq+vo8xZxoKfL8BsMhsd0smOZcE/x0NoF7jlW7AFGR3ROSksr+Ffaw7yztqDlDncDEmM4Oa0ZKYO6ILNIjd3C3E2SqnNWuvU+o415m/PRqCXUipFKWUDrgFO6udWSg0F/glc0ZhESggh6rMpfxPbirdx0wU3tb5ECiAiEWa+DgXb4avfGTo7+vmIDQ3g95f1Yc3DE3jiZ/0prXZx74eZjH16GXP/s4eiChlXJcT5aLBnCkApNQ14HjADb2mtn1RK/RnYpLVeoJT6FhgI5Na+5LDW+oqznVN6poQQp/rtt79le/F2lsxcgt1iNzqcM1vxlO/ZfZc/B6mtYJD8efJ6Nd/tLuSt1QdYuacIm9nE1IGduX5UN0YkR7auy6xCGOxsPVONSqaagyRTQoi6dpXs4qovr+Keofdw66BbjQ7n7LxeeH8WHEiHOUsgfpjRETXZ3oJy3ll7iPlbjlBe46ZXpxCuG5XEL4YmEB5kNTo8IQwnyZQQotV7eOXDLDu8jG+u+obwgHCjw2lYVYlv/BTAr7+BsK7GxuMnVU43X23N5b0Nh9madQy71cTUAV24angCo7tHYzJJb5XomCSZEkK0ajkVOUz79zSu73c9fxjxB6PDabycTHj7cgjrArMXQkis0RH51bYjpXyw4TALtuZQ7nATHxHIzOEJXDUsgaTotjX4XoimkmRKCNGq/Wntn/h8z+csmrmIzsGdjQ7n3BxcDf830zdVwk1fQWCE0RH5ncPl4Zvt+XyyKYtVe4vQGlK7RTJjSFemDexCdEiA0SEK0ewkmRJCtFob8zYyZ8kcbux/I38c8Uejwzk/e7+F96+BrkPhxvkQEGJ0RM0mt7Saf285wucZR9hTUIHZpBjXK4YZQ7oyqX9nQgL8On2hEK2GJFNCiFapylXFzAUzUUrx2RWfEWgJNDqk87d9AXwyG5LT4LpPwNqK70b0A601O/PKWbA1hwWZORw5Vo3NYmJ8r1imDujMxP5xhAfKwHXRfpwtmZKvEEIIw7yY8SLZFdm8ddlbbTuRAuh/Bfz8FZh/O3xyE8z6V7tOqJRS9OsSRr8uYfxhch+2HD7Kwh/yWLQtl2935GM1K8b0iGHKgM5M6NuJTmHt989CCOmZEkIYIqMgg5sW3cTVfa7m0QsfNToc/9n4Bnz9ACSMhGveg5BORkfUorxezdbsYyzelsfCbblklVQDMDghnAn94pjYL45+XUJlDivR5shlPiFEq+JwO5j15SycHifzZ8wnyNrO7gzb/gX8+3YIjoHrPoK4C4yOyBBaa3bll/OfHQUs3Z7P1uxjaA1dwu2M7xXLRX1iSesRI/NYiTZBkikhRKvy7KZn+d8f/5d5k+Yxuutoo8NpHjkZ8MG1UFMOM9+EPlOMjshwheU1LNuZz4pdhazaW0S5w41JwdCkSMb1iiGtZwyDEyLkOYGiVZJkSgjRanxf+D03LrqRK3teyRNjnjA6nOZVluNLqHK3wuS/wug7QS5vAeD2eMnMOsZ3uwtJ313I90dK0RoCrWZGpEQxpkc0Y3pE079LGBazJFfCeJJMCSFahSMVR7h58c14tZf5M+YTags1OqTm56zyDUrfsQB6XeZ7nl94vNFRtTrHqpysP1DC2n3FrNlXxO78CgCCbWaGdYtkRHIUqcmRDE2MJNDWCh+CLdo9SaaEEIbLqcjh5sU3U+Gq4I3Jb9Avup/RIbUcrxc2/BO+/ROYrb5eqmG/kl6qsygod7B+fwkbD5aw4UAJu/LL0RosJkX/rmEMTYxgaFIkQ5MiSIoKkgHtotlJMiWEMFRuRS43L7mZMmcZr09+nQuiO+aAbEr2w4J74OBKSLkIrpgLkclGR9UmlFa52Hy4hI0Hj5J5+Bhbs49R5fQAEBVsY2B8OIMSwhkQH87A+HC6hNslwRJ+JcmUEMIweZV5zF48m7Ka2kQqpoMmUsd5vbDlbfjmMdBeSLsHLvwt2NvAw51bEbfHy56CCjIOHyPj8FF+OFLKnoIKPF7fv2kxITb6dQmjf+1cWP26hNE9NhirjL8S50mSKSGEIfIq85izZA5HHUd5ffLrDIgZYHRIrcexLFjyMOz40pdIjb4bRt0O9jCjI2uzHC4P23PL+CG7lB+OlLI9p4y9BRU4PV4AbBYTPWJD6B0XQu+40NolhMTIIEwm6cUSZyfJlBCixa3MXsmf1v6JClcF8ybNY1DsIKNDap1yt8KKp2DXQgiMhDF3w4hbpKfKT1weL/sKK9iRW8aO3HJ25ZWzJ7+cnFLHiToBFhMpMcH0iA2he6yvTIkJJjk6WObAEidIMiWEaDFHHUd5euPTfL3/a3qE9+Bv4/5G/+j+RofV+h3Z4kuq9iwBSyD0nwHDboRuaTJQvRmUO1zsKahgT345ewsq2F9Yyb7CCg6XVOGt889iZJCVbtHBJEcHkRQdTEJkIImRQSRGBdIlPBCz9Gh1GJJMCSGandaaRQcW8dSGpyh3lnPLoFu4deCt2Mw2o0NrW3IyYPO/YNtnUFMGkSkw9AYYOAsiuxkdXbtX4/ZwuLiK/UWVHCqu5GBxla8sqiKntJq6/2RaTIquEYF0jbDTNSKQ+IjA2u1AuoTbiQuzE2a3yED4dkKSKSFEs/FqL+ty1vHO9ndYnbOaAdED+FPan+gd2dvo0No2Z5Vvbqot78KhVb59sX2h12TofRkkjvJNsyBajNPtJedYNdlHq8k6WkVWSRXZR6vJOeZb8socJ/VqAQTZzHQO8yVWncIC6BQaQKdQ33psaACxIQHEhAQQHmiVcVutnCRTQgi/K3GU8Pnez/lk1ydkV2QTGRDJrwf+mhv63YDZJJMq+lXJfti1CHYvgUNrwOuCgHBIHguJI3wPVe46BGzBRkfaobk9XvLLa3yJVanDt5T9VBaUOygoq6HG7T3ttRaTIirYRkxIANEhNqKCbUQG2YgOthEZ7NuOCLISEWgjMthKZJANu1X+nrUkSaaEEE2mtSa7IptNeZtYnbOaZYeX4fK6GB43nF/2/iUTu02US3otoaYc9q/4KbEq2efbr8y+ByrHD4PYfhDbx9eTFdpZxly1IlprymvcFJTVUFDuoKjCSXFFDUUVNRSVOymqqKG40snRKiclFU7Ka9xnPFeAxUR4oPW0JdRuIay2DLVbCbNbCbFbCAmwEFpbhtgtBNssMubrHDQ5mVJKTQFeAMzAG1rrp045HgC8AwwHioGrtdYHz3ZOSaaEaN1Ka0o5WHaQvUf3sjl/MxvzN5JXmQdAlD2KqSlTmdV7Fj0iehgcaQdXWQxHNkH2RsjaAHnfQ/XRn47bwyG6F0Qk1S6JEJ4E4Qm+RCswUpKtVqzG7eFopYujVU6OVbk4VuXkaJVvu7TaRWmVy1fWLmUOF+UON+UO12mXHOtjt5oICbAQHGAhyGYh2GYmKMBCkNVMUICZIJuZIJuFQKuZQJtv2241E2itW5qw124HWHzrAVYTdosZq1m1mzFjTUqmlFJmYDcwCcgGNgLXaq2316lzBzBIa/0bpdQ1wJVa66vPdl5JpoQwhld7qXJVUeospbi6mKLqIoqqiyiuLia/Kp8DpQc4WHaQEkfJiddE2aNIjUtlROcRjOg8gu7h3dvNB2S7ozVUFkLhTijcBQU7oHiPb16r0mzfJcK6TBYI7gQhsb4yMLJ2iQB7hK8MCAVbyE+lLdi3WAPBYpdkrBXyejWVTjflDjdlDheVNb71iho3FcfLGjeVNW4qnR5fWeOmssZDlctDVY2bKqeHKqebapcHh+v0S5ONoZSvBy3A4ku0AqwmbGYTNosZm8VEgNmEzVK7mE1YLcePK6xmU51FnbRuMSksZl9di1kxMD6cXnHN+6zPsyVTlka8fiSwV2u9v/ZkHwIzgO116swAnqhd/xR4SSmltFHXEPE9vmJTviRromGaxv+a1vcrXd/rz1RPa32i/vHt4/U1Gq/2njju1V7fttZ48a17vB682otbu09su7wuXF4Xbq8bt9eN0+ukxl1DjacGh8eB0+Ok2l1NubOcSlclla7KM/7MUfYoksOSuTjxYpLDkkkJTyElPIWk0CRJntoKpSCkk29JGX/yMa8XKvLh2GEozfIlXRUFvqWytize4+vZcpRBY/9uWALBavclVmYbWALAHAAWm680W8Bk9R07vm6y1C7mn0plri1NvuX4vuPbJxZVu9RuU7vdYEmdxK/udp3f7ZN+z099DSfXrfc1fqh3Ls7w99IEhNYuXU89GFC7nAOv1rg8Xpxu3+L2enG6NS5v7T6PF5db4/Z6cXm8uD2++i6Pxu31rXu8tdseXbvfi8flq+vWGk9tXd/ixePROL0aj9Z4vJqzZRTusZfSa9rkc/uh/KgxyVQ8kFVnOxsYdaY6Wmu3UqoUiAaK6lZSSt0G3AaQlJR0niE3zvaS7Tyy6pFmbUMIoygUZmXGbDJjNVmxmCwnSpvZRoA5ALvZjs1sIywgjLigOEJsIYRYQ06UYbYwogOjiQmMISYwhkh7JFaT3B3WrplMENbFt5z2MX4KrwccpeA45hunVVMBztqlpgJc1eCqArfDV7qqfetuJ3hqfio9Lt+6t9K37nH5ese8ntrF/dOiPb6ET3t8j9rx1pbaS6MTO9EsTJxXDuafhsE3yOgsqgNjgdadTPmN1noeMA98l/mas63RXUaz8MqFzdmEaE/O4cuhqqdyfb02x+vVrX+83oljSqFQp5UmZUIphQkTJuX7NDGbzJiUCbMyn9gnRLMxmSEoyre0BlrXLp7asjbBOp5saV27Xbfk9P0n9nFyvePbdds7476TAqs/1vOudy4kwTwuMDDS0PYbk0wdARLrbCfU7quvTrZSygKE4xuIbpggaxBB1iAjQxBCCOEvxy/tIV8kROvTmN/KjUAvpVSKUsoGXAMsOKXOAuCm2vWrgGVGjpcSQgghhGgpDfZM1Y6BugtYgu+q5Vta6x+VUn8GNmmtFwBvAu8qpfYCJfgSLiGEEEKIdq9RY6a01guBhafse6zOugOY5d/QhBBCCCFaP7n4LIQQQgjRBJJMCSGEEEI0gWHP5lNKFQKHDGm8bYrhlHm7RKsg70vrI+9J6yTvS+sj78m56aa1jq3vgGHJlDg3SqlNZ5rGXhhH3pfWR96T1knel9ZH3hP/kct8QgghhBBNIMmUEEIIIUQTSDLVdswzOgBRL3lfWh95T1oneV9aH3lP/ETGTAkhhBBCNIH0TAkhhBBCNIEkU22QUuoBpZRWSsUYHUtHp5T6h1Jqp1Lqe6XUfKVUhNExdWRKqSlKqV1Kqb1KqYeMjqejU0olKqWWK6W2K6V+VErda3RMwkcpZVZKZSilvjI6lvZAkqk2RimVCEwGDhsdiwBgKTBAaz0I2A08bHA8HZZSygy8DEwF+gPXKqX6GxtVh+cGHtBa9wcuBO6U96TVuBfYYXQQ7YUkU23Pc8AfARns1gporb/RWrtrN9cBCUbG08GNBPZqrfdrrZ3Ah8AMg2Pq0LTWuVrrLbXr5fj+8Y43NiqhlEoApgNvGB1LeyHJVBuilJoBHNFabzU6FlGvOcAio4PowOKBrDrb2cg/3K2GUioZGAqsNzYSATyP70u51+hA2guL0QGIkymlvgU613PoUeARfJf4RAs623uitf6its6j+C5pvNeSsQnRFiilQoDPgPu01mVGx9ORKaUuBwq01puVUhcbHU97IclUK6O1nljffqXUQCAF2KqUAt/lpC1KqZFa67wWDLHDOdN7cpxSajZwOTBBy1wjRjoCJNbZTqjdJwyklLLiS6Te01r/2+h4BGnAFUqpaYAdCFNK/Z/W+gaD42rTZJ6pNkopdRBI1VrLQyoNpJSaAjwLXKS1LjQ6no5MKWXBdxPABHxJ1EbgOq31j4YG1oEp3ze/fwElWuv7jI5HnKy2Z+r3WuvLjY6lrZMxU0I0zUtAKLBUKZWplHrN6IA6qtobAe4CluAb6PyxJFKGSwNuBC6t/fuRWdsjIkS7Ij1TQgghhBBNID1TQgghhBBNIMmUEEIIIUQTSDIlhBBCCNEEkkwJIYQQQjSBJFNCCCGEEE0gyZQQQgghRBNIMiWEEEII0QSSTAkhhBBCNMH/B3SHI0QTlGLcAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dxp8vAuiPaRL"
      },
      "source": [
        "## Probabilistic Model Representation\n",
        "\n",
        "![Screenshot from 2021-08-26 16-10-03.png](data:image/png;base64,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)\n",
        "\n",
        "![Screenshot from 2021-08-26 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)\n",
        "\n",
        "Posterior Probability using MCMC method."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 253
        },
        "id": "JUmoJehwzf2E",
        "outputId": "0838384c-bc3e-418b-d037-f09bc085a1fe"
      },
      "source": [
        "import pymc3 as pm\n",
        "\n",
        "temperature = data['Temperature'].values\n",
        "labels = data['Damage Incident'].values\n",
        "\n",
        "# probabilistic model\n",
        "with pm.Model() as model:\n",
        "\n",
        "  beta = pm.Normal('beta', mu=0, tau=0.001, testval=0)\n",
        "  alpha = pm.Normal('alpha', mu=0, tau=0.001, testval=0)\n",
        "\n",
        "  p = 1.0 / (1.0 + np.exp(beta * temperature + alpha))\n",
        "\n",
        "# inference \n",
        "with model:\n",
        "  observed = pm.Bernoulli('bernoulli_obs', p, observed=labels)\n",
        "\n",
        "  start = pm.find_MAP()\n",
        "  step = pm.Metropolis()\n",
        "  samples = pm.sample(120000, step=step, start=start)\n",
        "  true_samples = samples[100000::2]\n",
        "\n",
        "\n",
        "\n"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "    <div>\n",
              "        <style>\n",
              "            /* Turns off some styling */\n",
              "            progress {\n",
              "                /* gets rid of default border in Firefox and Opera. */\n",
              "                border: none;\n",
              "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
              "                background-size: auto;\n",
              "            }\n",
              "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
              "                background: #F44336;\n",
              "            }\n",
              "        </style>\n",
              "      <progress value='26' class='' max='26' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
              "      100.00% [26/26 00:00<00:00 logp = -19.024, ||grad|| = 9.9071]\n",
              "    </div>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:20: FutureWarning: In v4.0, pm.sample will return an `arviz.InferenceData` object instead of a `MultiTrace` by default. You can pass return_inferencedata=True or return_inferencedata=False to be safe and silence this warning.\n",
            "Sequential sampling (2 chains in 1 job)\n",
            "CompoundStep\n",
            ">Metropolis: [alpha]\n",
            ">Metropolis: [beta]\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "    <div>\n",
              "        <style>\n",
              "            /* Turns off some styling */\n",
              "            progress {\n",
              "                /* gets rid of default border in Firefox and Opera. */\n",
              "                border: none;\n",
              "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
              "                background-size: auto;\n",
              "            }\n",
              "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
              "                background: #F44336;\n",
              "            }\n",
              "        </style>\n",
              "      <progress value='121000' class='' max='121000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
              "      100.00% [121000/121000 00:35<00:00 Sampling chain 0, 0 divergences]\n",
              "    </div>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "    <div>\n",
              "        <style>\n",
              "            /* Turns off some styling */\n",
              "            progress {\n",
              "                /* gets rid of default border in Firefox and Opera. */\n",
              "                border: none;\n",
              "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
              "                background-size: auto;\n",
              "            }\n",
              "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
              "                background: #F44336;\n",
              "            }\n",
              "        </style>\n",
              "      <progress value='121000' class='' max='121000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
              "      100.00% [121000/121000 00:33<00:00 Sampling chain 1, 0 divergences]\n",
              "    </div>\n",
              "    "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "text": [
            "Sampling 2 chains for 1_000 tune and 120_000 draw iterations (2_000 + 240_000 draws total) took 69 seconds.\n",
            "The rhat statistic is larger than 1.05 for some parameters. This indicates slight problems during sampling.\n",
            "The estimated number of effective samples is smaller than 200 for some parameters.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vvrMYX3GS3_k"
      },
      "source": [
        "## Posterior Distribution of parameters\n",
        "Parameter uncertainty because of:\n",
        "\n",
        "  1- overlap of defects-to-nondefects\n",
        "  \n",
        "  2- low sample size"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 509
        },
        "id": "gZSP9IQwehc0",
        "outputId": "8c2a08f8-a40f-4780-babe-aae96d62917e"
      },
      "source": [
        "alpha_samples = true_samples['alpha']\n",
        "beta_samples = true_samples['beta']\n",
        "\n",
        "plt.figure(figsize=(10, 3))\n",
        "plt.hist(beta_samples, label='posterior of beta', density=True)\n",
        "\n",
        "plt.figure(figsize=(10, 3))\n",
        "plt.hist(alpha_samples, label='posterior of alpha', density=True)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0.0113787 , 0.02176914, 0.05634447, 0.06924674, 0.03579693,\n",
              "        0.01327286, 0.01839259, 0.02447313, 0.01961419, 0.00422755]),\n",
              " array([-39.00797906, -35.36520836, -31.72243765, -28.07966694,\n",
              "        -24.43689624, -20.79412553, -17.15135483, -13.50858412,\n",
              "         -9.86581342,  -6.22304271,  -2.580272  ]),\n",
              " <a list of 10 Patch objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 720x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 720x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "buJ6U8dXTQ9i"
      },
      "source": [
        "## Expected Probability for each temperature"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 280
        },
        "id": "QkM1mI1Aht1M",
        "outputId": "e4061203-af1d-4474-de13-8b10b0e04552"
      },
      "source": [
        "t = np.linspace(temperature.min() - 5, temperature.max() + 5, 50).reshape(1, -1)\n",
        "p_t = logistic(t, beta_samples.reshape(-1, 1), alpha_samples.reshape(-1, 1))\n",
        "\n",
        "print(beta_samples.reshape(-1, 1).shape, t.shape) # np.dot(beta, t)\n",
        "print(p_t.shape)\n",
        "mean_prob_t = p_t.mean(axis=0)\n",
        "print(mean_prob_t.shape)\n",
        "\n",
        "plt.figure(figsize=(10, 3))\n",
        "plt.plot(t[0], mean_prob_t, label='Posterior Expected Value of damage')\n",
        "plt.scatter(data['Temperature'], data['Damage Incident'])\n",
        "plt.plot(t[0], p_t[604, :], label='random Posterior', ls='--')\n",
        "plt.legend()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(20000, 1) (1, 50)\n",
            "(20000, 50)\n",
            "(50,)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f3681403450>"
            ]
          },
          "metadata": {},
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "99FN-j6aWDs_"
      },
      "source": [
        "## Probability Distribution for each temperature\n",
        "\n",
        "How uncertain are we in different temperatures?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 228
        },
        "id": "QioKYA8MwPHy",
        "outputId": "c98f89fd-73c6-47df-afc9-67d5a3ea1ed7"
      },
      "source": [
        "from scipy.stats.mstats import mquantiles\n",
        "\n",
        "plt.figure(figsize=(10, 3))\n",
        "plt.plot(t[0], mean_prob_t, label='Posterior Expected Value of damage', ls='--')\n",
        "plt.scatter(data['Temperature'], data['Damage Incident'])\n",
        "\n",
        "quantiles = mquantiles(p_t, [0.025, 0.975], axis=0)\n",
        "plt.plot(t[0], quantiles[0], label='0.025 quantile')\n",
        "plt.plot(t[0], quantiles[1], label='0.975 quantile')\n",
        "plt.fill_between(t[0], *quantiles, alpha=0.5)\n",
        "plt.legend()"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f368134a590>"
            ]
          },
          "metadata": {},
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CBQIeNHAWNB0"
      },
      "source": [
        "## what happended at the day of Challenger Disaster?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "C26RXKyfzQmj",
        "outputId": "5213e8e8-ff53-491a-c820-db671c4de5a9"
      },
      "source": [
        "prob_31 = logistic(31, beta_samples, alpha_samples)\n",
        "plt.figure(figsize=(10, 3))\n",
        "plt.xlim(0.995, 1)\n",
        "plt.hist(prob_31, density=True, bins=1000)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
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              "        1.26205047e+00, 1.26205047e+00, 3.78615140e-01, 1.76687065e+00,\n",
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              "        1.64066561e+00, 1.26205047e+00, 7.57230280e-01, 7.57230280e-01,\n",
              "        2.39789589e+00, 2.14548579e+00, 1.51446056e+00, 2.01928075e+00,\n",
              "        7.57230280e-01, 1.13584542e+00, 1.38825551e+00, 2.52410093e+00,\n",
              "        2.65030598e+00, 1.89307570e+00, 2.14548579e+00, 1.64066561e+00,\n",
              "        3.15512617e+00, 3.02892112e+00, 4.16476654e+00, 2.14548579e+00,\n",
              "        2.27169084e+00, 3.53374131e+00, 3.53374131e+00, 4.79579177e+00,\n",
              "        3.91235645e+00, 3.28133121e+00, 4.16476654e+00, 3.78615140e+00,\n",
              "        4.41717663e+00, 5.17440691e+00, 4.16476654e+00, 5.30061196e+00,\n",
              "        5.80543215e+00, 6.43645738e+00, 6.43645738e+00, 5.42681701e+00,\n",
              "        7.44609776e+00, 8.96055832e+00, 7.82471290e+00, 9.97019869e+00,\n",
              "        8.32953308e+00, 8.07712299e+00, 1.02226088e+01, 1.09798391e+01,\n",
              "        1.32515299e+01, 1.04750189e+01, 1.66590662e+01, 1.06012239e+01,\n",
              "        1.75425015e+01, 1.99403974e+01, 1.80473217e+01, 2.24644983e+01,\n",
              "        2.63768548e+01, 3.19298768e+01, 6.96651858e+01, 1.99820450e+03]),\n",
              " array([0.60381933, 0.60421551, 0.60461169, ..., 0.99920764, 0.99960382,\n",
              "        1.        ]),\n",
              " <a list of 1000 Patch objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CnTZkQg2Wldz"
      },
      "source": [
        "# Probabilistic Regression (Posterior Probability using variational inference methods)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "b2Aiu0fNzbdZ",
        "outputId": "bfddd657-fc71-4143-a44c-91fc6acb8061"
      },
      "source": [
        "w0 = 0.125\n",
        "b0 = 5.\n",
        "x_range = [-20, 60]\n",
        "\n",
        "def load_dataset(n=150, n_tst=150):\n",
        "  np.random.seed(43)\n",
        "  def s(x):\n",
        "    g = (x - x_range[0]) / (x_range[1] - x_range[0])\n",
        "    return 3 * (0.25 + g**2.)\n",
        "  x = (x_range[1] - x_range[0]) * np.random.rand(n) + x_range[0]\n",
        "  eps = np.random.randn(n) * s(x)\n",
        "  y = (w0 * x * (1. + np.sin(x)) + b0) + eps\n",
        "  x = x[..., np.newaxis]\n",
        "  x_tst = np.linspace(*x_range, num=n_tst).astype(np.float32)\n",
        "  x_tst = x_tst[..., np.newaxis]\n",
        "  return y, x, x_tst\n",
        "\n",
        "y, x, x_test = load_dataset()\n",
        "\n",
        "plt.scatter(x, y)\n",
        "print(f'y: {y.shape}, x: {x.shape}, x_test: {x_test.shape}')"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "y: (150,), x: (150, 1), x_test: (150, 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": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F14V1ILFWdh9"
      },
      "source": [
        "# Simple Linear Regression"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "S0L3agxR61YT",
        "outputId": "b5be3995-0a86-4789-a700-798110c59179"
      },
      "source": [
        "import tensorflow as tf\n",
        "\n",
        "model = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(1)\n",
        "])\n",
        "\n",
        "model.compile(optimizer=tf.optimizers.Adam(learning_rate=0.01),\n",
        "              loss=lambda y_true, y_hat: tf.reduce_mean(tf.square(y_true - y_hat)))\n",
        "\n",
        "model.fit(x, y, epochs=500, verbose=False)\n",
        "\n",
        "y_hats = model(x_test)\n",
        "\n",
        "print(f'y_hats: {y_hats.shape}')\n",
        "\n",
        "plt.scatter(x, y, label='train')\n",
        "plt.plot(x_test, y_hats, label='test', c='r')\n",
        "plt.legend()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "y_hats: (150, 1)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f363136aa50>"
            ]
          },
          "metadata": {},
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G9vjecfsWhOs"
      },
      "source": [
        "# Linear Regression with Normal output distribution"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p-oogmjT-Pwi",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "outputId": "7a4a2c5f-488b-4d96-f656-95c16ebc73f1"
      },
      "source": [
        "import tensorflow_probability as tfp\n",
        "\n",
        "model = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(1),\n",
        "  tfp.layers.DistributionLambda(\n",
        "      lambda mean: tfp.distributions.Normal(loc=mean, scale=1))\n",
        "])\n",
        "\n",
        "\n",
        "model.compile(optimizer=tf.optimizers.Adam(learning_rate=0.01),\n",
        "              loss=lambda y_true, y_dist: -y_dist.log_prob(y_true))\n",
        "\n",
        "\n",
        "model.fit(x, y, epochs=500, verbose=False)\n",
        "\n",
        "y_hats = model(x_test)\n",
        "\n",
        "\n",
        "print(f'y_hats: {y_hats.shape}')\n",
        "\n",
        "plt.scatter(x, y, label='train')\n",
        "plt.plot(x_test, y_hats.mean(), label='test', c='r')\n",
        "plt.legend()"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "y_hats: (150, 1)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f362f46eb10>"
            ]
          },
          "metadata": {},
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UjOw2FnpWrLg"
      },
      "source": [
        "# Learn Variability"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U4o5NCXt-Pxn",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "outputId": "aebdf887-06c2-4b6a-d7cd-7fa705e945f4"
      },
      "source": [
        "model = tf.keras.Sequential([\n",
        "  tf.keras.layers.Dense(2),\n",
        "  tfp.layers.DistributionLambda(\n",
        "      lambda t: tfp.distributions.Normal(loc=t[..., :1],\n",
        "                                         scale=1 + tf.math.softplus(t[..., 1:])),\n",
        "      )\n",
        "])\n",
        "\n",
        "\n",
        "model.compile(optimizer=tf.optimizers.Adam(learning_rate=0.05),\n",
        "              loss=lambda y_true, y_dist: -y_dist.log_prob(y_true))\n",
        "\n",
        "model.fit(x, y, epochs=500, verbose=False)\n",
        "\n",
        "y_hats = model(x_test)\n",
        "\n",
        "mean = y_hats.mean()\n",
        "std = y_hats.stddev()\n",
        "\n",
        "print(f'y_hats: {y_hats.shape}')\n",
        "\n",
        "plt.scatter(x, y, label='train')\n",
        "plt.plot(x_test, mean - 2 * std, label='mean - 2 * std', c='r')\n",
        "plt.plot(x_test, mean, label='mean', c='r')\n",
        "plt.plot(x_test, mean + 2 * std, label='mean + 2 * std', c='r')\n",
        "\n",
        "plt.legend()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "y_hats: (150, 1)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f362fc0bed0>"
            ]
          },
          "metadata": {},
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fcJcp7c2d0S9"
      },
      "source": [
        "# Learn Parameter Variability\n",
        "![Screenshot from 2021-08-26 21-11-48.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ghyk7Afk61Zd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "7d8f65c5-d26e-4d8f-c29c-c345a801d165"
      },
      "source": [
        "def Q(kernel_size, bias_size=0, dtype=None):\n",
        "  n = kernel_size + bias_size\n",
        "  return tf.keras.Sequential([\n",
        "      tfp.layers.VariableLayer(2 * n, dtype=dtype),\n",
        "      tfp.layers.DistributionLambda(lambda t: tfp.distributions.Independent(\n",
        "          tfp.distributions.Normal(loc=t[..., :n],\n",
        "                     scale=0.001 + tf.nn.softplus(t[..., n:])),\n",
        "          reinterpreted_batch_ndims=1)),\n",
        "  ])\n",
        "\n",
        "def P(kernel_size, bias_size=0, dtype=None):\n",
        "  n = kernel_size + bias_size\n",
        "  return tf.keras.Sequential([\n",
        "      tfp.layers.VariableLayer(n, dtype=dtype),\n",
        "      tfp.layers.DistributionLambda(lambda t: tfp.distributions.Independent(\n",
        "          tfp.distributions.Normal(loc=t, scale=1),\n",
        "          reinterpreted_batch_ndims=1)),\n",
        "  ])\n",
        "\n",
        "model = tf.keras.Sequential([\n",
        "  tfp.layers.DenseVariational(1, Q, P, kl_weight=1/x.shape[0]),\n",
        "  tfp.layers.DistributionLambda(\n",
        "        lambda mean: tfp.distributions.Normal(loc=mean, scale=1)\n",
        "        )\n",
        "])\n",
        "\n",
        "\n",
        "model.compile(optimizer=tf.optimizers.Adam(learning_rate=0.01),\n",
        "              loss=lambda y_true, y_dist: -y_dist.log_prob(y_true))\n",
        "\n",
        "model.fit(x, y, epochs=1000, verbose=False)\n",
        "\n",
        "y_hats_samples = [model(x_test) for i in range(20)]\n",
        "\n",
        "plt.scatter(x, y, label='train')\n",
        "\n",
        "for i, y_hats in enumerate(y_hats_samples): \n",
        "  plt.plot(x_test, y_hats.mean(), c='r', linewidth=0.5)\n",
        "\n",
        "plt.legend()"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f36308f5c10>"
            ]
          },
          "metadata": {},
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YXA_ueJDeani"
      },
      "source": [
        "# Bijectors"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "KfM1RYMHL0YI",
        "outputId": "10016805-1482-4ffa-bc61-dbf53656b2fa"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "log_bijector = tfp.bijectors.Log()\n",
        "log_normal = log_bijector(tfp.distributions.Normal(1, 0.5))\n",
        "\n",
        "samples = log_normal.sample(1000)\n",
        "xs = np.linspace(-3, 2, 200)\n",
        "\n",
        "plt.hist(samples, density=True)\n",
        "plt.plot(xs, log_normal.prob(xs))"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7efe05920b10>]"
            ]
          },
          "metadata": {},
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3SiB2rlXPm6x"
      },
      "source": [
        "# Variational Inference using normalizing flow\n",
        "Example:\n",
        "https://www.tensorflow.org/probability/examples/Variational_Inference_and_Joint_Distributions"
      ]
    }
  ]
}