{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EheA5_j_cEwc"
      },
      "source": [
        "##### Copyright 2019 The TensorFlow Probability Authors.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "YCriMWd-pRTP"
      },
      "outputs": [],
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kBQzOeY8Iaq3"
      },
      "source": [
        "# 베이지안 변환점(switchpoint) 분석\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td><a target=\"_blank\" href=\"https://www.tensorflow.org/probability/examples/Bayesian_Switchpoint_Analysis\"><img src=\"https://www.tensorflow.org/images/tf_logo_32px.png\">TensorFlow.org에서 보기</a></td>\n",
        "  <td><a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/docs-l10n/blob/master/site/ko/probability/examples/Bayesian_Switchpoint_Analysis.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\">Google Colab에서 실행하기</a></td>\n",
        "  <td><a target=\"_blank\" href=\"https://github.com/tensorflow/docs-l10n/blob/master/site/ko/probability/examples/Bayesian_Switchpoint_Analysis.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\">GitHub에서 보기</a></td>\n",
        "  <td><a href=\"https://storage.googleapis.com/tensorflow_docs/docs-l10n/site/ko/probability/examples/Bayesian_Switchpoint_Analysis.ipynb\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\">노트북 다운로드하기</a></td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5XxXGBbRgsq2"
      },
      "source": [
        "이 노트북에서는 [pymc3 설명서](https://docs.pymc.io/notebooks/getting_started.html#Case-study-2:-Coal-mining-disasters)의 베이지안 '변환점 분석' 예제를 다시 구현하고 확장합니다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_mpkdys-KrTT"
      },
      "source": [
        "## 전제 조건"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "t_Uo-kwnGqZi"
      },
      "outputs": [],
      "source": [
        "import tensorflow.compat.v2 as tf\n",
        "tf.enable_v2_behavior()\n",
        "import tensorflow_probability as tfp\n",
        "tfd = tfp.distributions\n",
        "tfb = tfp.bijectors\n",
        "import matplotlib.pyplot as plt\n",
        "plt.rcParams['figure.figsize'] = (15,8)\n",
        "%config InlineBackend.figure_format = 'retina'\n",
        "import numpy as np\n",
        "import pandas as pd"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "53lnVbvHKtH9"
      },
      "source": [
        "## 데이터세트"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "829rNEHfKyEq"
      },
      "source": [
        "데이터세트는 [여기](https://pymc-devs.github.io/pymc/tutorial.html#two-types-of-variables)에서 가져왔습니다. 이 예제 <a>floating around</a>의 다른 버전이 있지만, '누락된' 데이터가 있다는 점을 유의하세요. 이 경우 누락된 값을 대치해야 합니다. (그렇지 않으면 우도 함수가 정의되지 않으므로 모델이 초기 매개변수를 떠나지 않습니다.)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XGMvb9_DObuU"
      },
      "outputs": [
        {
          "data": {
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            "text/plain": [
              "<matplotlib.figure.Figure at 0x16e5ab366f10>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 512,
              "width": 899
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "disaster_data = np.array([ 4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,\n",
        "                           3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,\n",
        "                           2, 2, 3, 4, 2, 1, 3, 2, 2, 1, 1, 1, 1, 3, 0, 0,\n",
        "                           1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,\n",
        "                           0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,\n",
        "                           3, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,\n",
        "                           0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])\n",
        "years = np.arange(1851, 1962)\n",
        "plt.plot(years, disaster_data, 'o', markersize=8);\n",
        "plt.ylabel('Disaster count')\n",
        "plt.xlabel('Year')\n",
        "plt.title('Mining disaster data set')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "puvRMZnQLRmD"
      },
      "source": [
        "## 확률 모델"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2UA6HkV0gXvb"
      },
      "source": [
        "이 모델은 '변환점'(예: 안전 규정이 변경된 1년)과 해당 변환점 전후에 일정한(그렇지만 잠재적으로 다른) 비율로 포아송 분포 재해율을 가정합니다.\n",
        "\n",
        "실제 재해 수는 고정되어 있습니다(관찰됨). 이 모델의 모든 샘플은 재난의 변환점과 '초기' 및 '후기' 비율을 모두 지정해야 합니다.\n",
        "\n",
        "[pymc3 설명서 예제](https://pymc-devs.github.io/pymc/tutorial.html)의 원본 모델은 다음과 같습니다.\n",
        "\n",
        "$$ \\begin{align*} (D_t|s,e,l)&\\sim \\text{Poisson}(r_t), \\ & ,\\quad\\text{with}; r_t = \\begin{cases}e & \\text{if}; t < s\\l &\\text{if}; t \\ge s\\end{cases} \\ s&\\sim\\text{Discrete Uniform}(t_l,,t_h) \\ e&\\sim\\text{Exponential}(r_e)\\ l&\\sim\\text{Exponential}(r_l) \\end{align*} $$\n",
        "\n",
        "그렇지만 평균 재해율 $r_t$는 변환점 $s$에서 불연속성을 가지므로 구별할 수 없습니다. 따라서 해밀턴 몬테카를로(HMC) 알고리즘에 그래디언트 신호를 제공하지 않지만 $s$ 사전 확률이 연속적이므로, HMC의 임의 행로의 대체는 이 예에서 확률 질량이 높은 영역을 찾기에 충분합니다.\n",
        "\n",
        "두 번째 모델로 *e*와 *l* 간의 [시그모이드 '변환'](https://en.wikipedia.org/wiki/Sigmoid_function)으로 원본 모델을 수정하여 전환을 미분할 수 있도록 하고, 변환점 $s$에 대한 연속 균등 분포를 사용합니다(평균 속도의 '변환'이 여러 해에 걸쳐 확장될 가능성이 있어서 이 모델이 더 실제에 가깝다고 주장할 수 있습니다). 따라서 새 모델은 다음과 같습니다.\n",
        "\n",
        "$$ \\begin{align*} (D_t|s,e,l)&\\sim\\text{Poisson}(r_t), \\ & ,\\quad \\text{with}; r_t = e + \\frac{1}{1+\\exp(s-t)}(l-e) \\ s&\\sim\\text{Uniform}(t_l,,t_h) \\ e&\\sim\\text{Exponential}(r_e)\\ l&\\sim\\text{Exponential}(r_l) \\end{align*} $$\n",
        "\n",
        "추가 정보가 없는 경우 $r_e = r_l = 1$을 사전 확률에 대한 매개변수로 가정합니다. 두 모델을 모두 실행하고 추론 결과를 비교합니다."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TGIiP8niPHxr"
      },
      "outputs": [],
      "source": [
        "def disaster_count_model(disaster_rate_fn):\n",
        "  disaster_count = tfd.JointDistributionNamed(dict(\n",
        "    e=tfd.Exponential(rate=1.),\n",
        "    l=tfd.Exponential(rate=1.),\n",
        "    s=tfd.Uniform(0., high=len(years)),\n",
        "    d_t=lambda s, l, e: tfd.Independent(\n",
        "        tfd.Poisson(rate=disaster_rate_fn(np.arange(len(years)), s, l, e)),\n",
        "        reinterpreted_batch_ndims=1)\n",
        "  ))\n",
        "  return disaster_count\n",
        "\n",
        "def disaster_rate_switch(ys, s, l, e):\n",
        "  return tf.where(ys &lt; s, e, l)\n",
        "\n",
        "def disaster_rate_sigmoid(ys, s, l, e):\n",
        "  return e + tf.sigmoid(ys - s) * (l - e)\n",
        "\n",
        "model_switch = disaster_count_model(disaster_rate_switch)\n",
        "model_sigmoid = disaster_count_model(disaster_rate_sigmoid)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KgPr-m-FSMF2"
      },
      "source": [
        "위의 코드는 JointDistributionSequential 분포를 통해 모델을 정의합니다. `disaster_rate` 함수는 `[0, ..., len(years)-1]`의 배열로 호출되어 `len(years)` 확률 변수의 벡터를 생성합니다. `switchpoint` 이전의 연도는 `early_disaster_rate`이고, 이후의 연도는 `late_disaster_rate`입니다(시그모이드 전환에 대해 modulo 연산 수행).\n",
        "\n",
        "다음은 대상 로그 확률 함수가 정상인지 확인하는 온전성 검사입니다."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "OIxZCvGeHkQd"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[-176.94559, -176.28717]\n",
            "[-371.3125, -366.8816]\n",
            "[-inf, -inf]\n"
          ]
        }
      ],
      "source": [
        "def target_log_prob_fn(model, s, e, l):\n",
        "  return model.log_prob(s=s, e=e, l=l, d_t=disaster_data)\n",
        "\n",
        "models = [model_switch, model_sigmoid]\n",
        "print([target_log_prob_fn(m, 40., 3., .9).numpy() for m in models])  # Somewhat likely result\n",
        "print([target_log_prob_fn(m, 60., 1., 5.).numpy() for m in models])  # Rather unlikely result\n",
        "print([target_log_prob_fn(m, -10., 1., 1.).numpy() for m in models]) # Impossible result"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tuzwBtQxUAES"
      },
      "source": [
        "## 베이지안 추론을 수행하는 HMC\n",
        "\n",
        "필요한 결과 수와 burn-in 스텝을 정의합니다. 코드는 대부분 [tfp.mcmc.HamiltonianMonteCarlo의 설명서](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/HamiltonianMonteCarlo)를 모델로 합니다. 코드는 적응형 스텝 크기를 사용합니다(그렇지 않으면 도출된 결과가 선택한 스텝 크기 값에 매우 민감함). chain의 초기 상태로 1의 값을 사용합니다.\n",
        "\n",
        "위의 내용만이 전부는 아닙니다. 위의 모델 정의로 돌아가면 일부 확률 분포가 실정수 선에서 잘 정의되지 않았음을 알 수 있습니다. 따라서 HMC 커널을 확률 분포가 정의된 도메인으로 실수를 변환하기 위해 순방향 bijector를 지정하는 [TransformedTransitionKernel](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc/TransformedTransitionKernel)로 래핑하여 HMC가 검사할 공간을 제약합니다(아래 코드의 코멘트를 참조하세요)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_V57TSedc8wb"
      },
      "outputs": [],
      "source": [
        "num_results = 10000\n",
        "num_burnin_steps = 3000\n",
        "\n",
        "@tf.function(autograph=False, experimental_compile=True)\n",
        "def make_chain(target_log_prob_fn):\n",
        "   kernel = tfp.mcmc.TransformedTransitionKernel(\n",
        "       inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n",
        "          target_log_prob_fn=target_log_prob_fn,\n",
        "          step_size=0.05,\n",
        "          num_leapfrog_steps=3),\n",
        "       bijector=[\n",
        "          # The switchpoint is constrained between zero and len(years).\n",
        "          # Hence we supply a bijector that maps the real numbers (in a\n",
        "          # differentiable way) to the interval (0;len(yers))\n",
        "          tfb.Sigmoid(low=0., high=tf.cast(len(years), dtype=tf.float32)),\n",
        "          # Early and late disaster rate: The exponential distribution is\n",
        "          # defined on the positive real numbers\n",
        "          tfb.Softplus(),\n",
        "          tfb.Softplus(),\n",
        "      ])\n",
        "   kernel = tfp.mcmc.SimpleStepSizeAdaptation(\n",
        "        inner_kernel=kernel,\n",
        "        num_adaptation_steps=int(0.8*num_burnin_steps))\n",
        "\n",
        "   states = tfp.mcmc.sample_chain(\n",
        "      num_results=num_results,\n",
        "      num_burnin_steps=num_burnin_steps,\n",
        "      current_state=[\n",
        "          # The three latent variables\n",
        "          tf.ones([], name='init_switchpoint'),\n",
        "          tf.ones([], name='init_early_disaster_rate'),\n",
        "          tf.ones([], name='init_late_disaster_rate'),\n",
        "      ],\n",
        "      trace_fn=None,\n",
        "      kernel=kernel)\n",
        "   return states\n",
        "\n",
        "switch_samples = [s.numpy() for s in make_chain(\n",
        "    lambda *args: target_log_prob_fn(model_switch, *args))]\n",
        "sigmoid_samples = [s.numpy() for s in make_chain(\n",
        "    lambda *args: target_log_prob_fn(model_sigmoid, *args))]\n",
        "\n",
        "switchpoint, early_disaster_rate, late_disaster_rate = zip(\n",
        "    switch_samples, sigmoid_samples)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6QLlqXi1VHLQ"
      },
      "source": [
        "두 모델을 병렬로 실행합니다."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G22O89uhaeKS"
      },
      "source": [
        "## 결과 시각화하기\n",
        "\n",
        "결과를 초기 및 후기 재해율과, 변환점에 대한 사후 확률 분포 샘플의 히스토그램으로 시각화합니다. 히스토그램은 샘플 중앙값을 나타내는 실선과 95% 신뢰할 수 있는 구간 경계를 나타내는 점선으로 표시됩니다."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZzSxHMRaXoip"
      },
      "outputs": [
        {
          "data": {
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mjz/+GD179sTOnTsRGxuLU6dOITk5GVevXkV4eDjmzp2LXr16AbC8bk05l7FUKhUA4N13\n38VPP/1kdj1Y+p4XlYY12qUh1qoHXcqVK4d79+4ZfDopIiICKpUKycnJGDhwIBwcHFCuXDk0atQI\nP//8M1566SWdxxVO81k/RaTusDTV89qOza0Pa5zb1Dq19eeppLGkfdiivRIRERERsWOPiIiIiKzm\n0KFDyM7Oxuuvv46FCxfq3MectbxM0aVLF8ydOxeXL1/G2bNn4e3tLT8p0adPH5PTUz8JY2iKRnOm\nb1Tz9vZGQEAAAgIC5HW0fvrpJ8TFxeGbb75Bu3bt4OnpaZW6NfZcxvLy8gIAXL582fgCFwNbt0tb\n1kOFChWK7NiLi4uDJElYvXq1wSednvbgwQON85jDmM9F4Tal/ndaWpre43Jzc3H//n2tY9Wep3Zs\njfqwBlPqtCRc54tiars0xNL2Ye32SkRERETkUNwZICIiIqLnR3p6OgDgjTfe0LvPsWPHIEmSzfLg\n5uaGbt26ASh4Um/79u3Iy8vD66+/jvr165ucXr169QAUTHeYlZWlc5+4uDjzM1yIJEnw9fVFSEgI\nnJyckJOTg7NnzwKwft0aOhfw/9PdGXriRr2uV3JyMq5cuWLUeYuDpXVXVF3Ysh5q1KgBAEhJSdG7\nzz///IOyZcua1KkHAKmpqQCAMmXKmHysWmxsrN5t6g7HunXryq+pP0/Xrl3T2/kSGxsrT7Oo3l8f\ne2/H1q4PayiqTkvCdb4oprZLQ6zZPoqqWyIiIiIiY7Bjj4iIiIisxsPDAwCQlJSkc/uGDRtw48YN\nm+ejX79+EEJg586d2LhxIyRJwgcffGBWWm3btoWHhwdyc3Oxdu1are15eXlYvXq1yenm5eXp3ebs\n7CxPa6eeos+SujX1XIXPZ+hJsVatWqFKlSoAgHnz5slT1uliKB1bs7RdFlUXtqyHJk2aQAhh8Mf/\ncuXKoXTp0nq337x5E5mZmVqvJyQkyOcwhxACu3bt0tnpGBcXh/j4eADAe++9J7/epk0beHh4ID8/\nHz///LPWcSqVCsuWLQMANGvWTGMa0eexHVtSH9ZgSZ0W93VeH3PapSHmtg9z6paIiIiIyBjs2CMi\nIiIiq2ndujUkSUJSUhLmzJmDR48eAQAyMzOxatUqzJ492+wp/0xRr1491KlTBw8fPkRSUhKcnZ3R\no0cPs9Jyc3PDyJEjIYTA0qVLERYWhidPngAoeIpq3Lhx8hMsppgyZQqmTZuGw4cPazwJmJqaiilT\npuDJkydwc3NDs2bNAFhWt6aeCwBq164NIQT27t2rs1MIAJycnDBjxgwAQHR0NIYPH44zZ87I25VK\nJRITExEUFISOHTuaXEfWYmm7LKoubFkPTZs2BQCcO3dO71Nnbdu2xd27d+V2WditW7fw1VdfyU98\nFZaQkABJkuRzmEqSJDg7O2PkyJE4efIkgIJOlaioKHz66aeQJAlt2rRB48aN5WPc3d0xevRoCCEQ\nHh6OkJAQZGdnAyh4EmzSpEmIj4+Ho6MjJk6cqHG+57EdW1If1mBOnZaU67w+5rRLQ8xtH+bULRER\nERGRMbjGHhERERHpFR8fj7Zt2xrcp2vXrpg+fTqAgmkDhw4dirCwMERERCAiIgLlypVDZmYmVCoV\n2rVrh7p16yIkJMTmee/bty9mz54NSZLg5+eH8uXLm51WQEAAzp49i/379yMwMBBBQUEoVaoUHj58\nCCcnJwQHB2P8+PEmpfnkyRPs2rULkZGRkCQJZcqUQV5eHnJycgAU/Jj87bffyvm2pG5NPRcA9OrV\nC6tXr8aJEyfQsmVLeHp6wsnJCS+//DLWr18v7+fn54d58+bhq6++QkxMDPr16wdXV1e4u7vj0aNH\nUCqVAP5/SsTiYGm7NKYubFUPDRo0QLVq1ZCSkoKYmBi0bNlSa5+xY8di3759WLNmDcaMGQMAyMrK\nwrZt23DgwAHMnTtXq/3n5uYiJiYGkiQZ/eSSLl9++SUWLVqEAQMGoFSpUlCpVHj8+DEkSUL16tUR\nGBiodcyIESNw9epVbN26FcHBwVi8eDE8PDzw8OFDCCHg6OiImTNnanU4Pq/t2Nz6sAZz6rQkXef1\nMaddGmJO+zCnbomIiIiIjMGOPSIiIiLSSZIkKJVK3Lt3z+B+Tz8FM2XKFNSsWRO//vorrly5AqVS\niTp16qB379746KOPsHTpUkiSpHP9JWuuydSpUyfMnj0bANCnTx+L0nJ0dMTixYuxfv16bNy4Edeu\nXYOjoyPeeecdjBkzBg0bNgRgWv4///xzNG3aFMeOHcP169dx+/ZtqFQqVK9eHb6+vhg8eLDWGlbm\n1q0556pZsybWrFmD0NBQJCQk4N69e1CpVDo7Nt5//320aNECa9euRXR0NNLS0pCZmYkKFSqgdu3a\nePvtt9G5c2ed9WCN99yYNCxpl8bWhSX1YMh//vMfBAcHY+fOnTo79qpVq4bw8HB8//33iIqKQunS\npeHm5oauXbtixYoVOst04MABZGVloVWrVqhWrZrJeVKrXr06Nm/ejCVLluDw4cPIyMhA1apV0blz\nZ3z88cfytI2FOTg4YP78+fDz88OGDRuQmJiIzMxMVKpUCc2bN8ewYcN0rn/2vLZjc+vDGuc2p04B\n217n9R1nShrmtMuimNo+zK1bIiIiIqKiSMLQKuJERERERHZq27Zt+PLLL/Hyyy/jwIEDVu00JHqW\nbt++DT8/P3h4eODvv/+Gs7OzxWl+8skn2LdvHxYuXIiuXbuafLyfnx9u3bqFtWvXwtfX1+L8EFkD\n2yURERERvQi4xh4RERERPZd+++03SJKEvn37slOP7FqlSpXQv39/PHjwAFu2bLE4vevXryMqKgq1\na9c2q1OPiIiIiIiIig879oiIiIjoubNx40bEx8fDxcUFH374YXFnh8hiY8eOhbu7O1auXAmVSmVR\nWqGhoVCpVJg0aZKVckdERERERETPCtfYIyIiIqLnQnp6OgYMGICsrCw8ePAAkiQhICAAFStWLO6s\nEVnM09MTCxYswIULF/DPP/+gSpUqZqUjhED16tXx5Zdfws/Pz8q5JCIiIiIiIltjxx4RERERPRfy\n8/Nx69YtODg4oFq1aujXrx8CAgKKO1tEVtOxY0d07NjRojQkScKoUaOskh9OcUslEdslERERET3v\nJCGEKO5MEBEREREREREREREREZFhXGOPiIiIiIiIiIiIiIiIyA6wY4+IiIiIiIiIiIiIiIjIDrBj\nj4iIiIiIiIiIiIiIiMgOsGOPiIiIiIiIiIiIiIiIyA6wY4+IiIiIiIiIiIiIiIjIDrBjj4iIiIiI\niIiIiIiIiMgOsGOPiIiIiIiIiIiIiIiIyA6wY4+IiIiIiIiIiIiIiIjIDrBjj4iIiIiIiIiIiIiI\niMgOsGOPiIiIiIiIiIiIiIiIyA6wY4+IiIiIiIiIiIiIiIjIDrBjj4iIiIiIiIiIiIiIiMgOsGOP\niIiIiIiIiIiIiIiIyA6wY4+IiIiIiIiIiIiIiIjIDrBjj4iIiIiIiIiIiIiIiMgOsGOPiIiIiIiI\niIiIiIiIyA6wY4+IiIiIiIiIiIiIiIjIDrBjj4iIiIiIiIiIiIiIiMgOsGOPiIiIiIiIiIiIiIiI\nyA6wY4+IiIiIiIiIiIiIiIjIDrBjj4iIiIiIiIiIiIiIiMgOsGOPiIiIiIiIiIiIiIiIyA6wY4+I\niIiIiIiIiIiIiIjIDrBjj4iIiIiIiIiIiIiIiMgOsGOPiIiIiIiIiIiIiIiIyA6wY4+IiIiIiIiI\niIiIiIjIDrBjj4iIiIiIiIiIiIiIiMgOsGOPiIiIiIiIiIiIiIiIyA6wY4+IiIiIiIiIiIiIiIjI\nDrBjj4iIiIiIiIiIiIiIiMgOsGOPiIiIiIiIiIiIiIiIyA6wY4+IiIiIiIiIiIiIiIjIDrBjj4iI\niIiIiIiIiIiIiMgOsGOPiIiIiIiIiIiIiIiIyA6wY4+IiIiIiIiIiIiIiIjIDrBjj4iIiIiIiIiI\niIiIiMgOsGOPXjj+/v5QKBTYunXrMz2vn58fFAoF4uLinul5SzqFQoE6deogLS3Namla4z0eMGAA\n6tevj5s3b1otX8XNUF0X1+eCyBKG2i3btLb09HR06tQJgwcPxuDBg3Ht2rXizhIVYefOnfD398fA\ngQMxcOBAre1CCHTp0gWNGzdGRkZGMeSQiKh4vGjf85aU1xbxVklXUmNM4MWKM1+0zyk9PxhnGo8x\npn0yFGcyxrQfTsWdAXqxKJVK/PHHH9i5cycuXLiA+/fvo1SpUvDy8kK1atXQrFkztGzZEg0aNLBp\nPiRJ0vl6ZGQkUlNT0bFjRygUimd2XrI+S+p6//79OHnyJHr16oVq1apZMVcl2/PUPs+ePYv9+/cj\nISEBN27cQEZGBp48eYIKFSqgfv366NOnDzp27GjROe7evYuQkBAcPHgQ6enpKFOmDBo0aIAhQ4ag\nVatWeo8TQmDLli3YsWMHLly4gEePHsHd3R01atSAn58f/P39Ubp0aYvyZsi2bduwZcsWnD9/Hjk5\nOahYsSLatm2LgIAAVK1aVecxkZGRmDZtmsF03d3dcfLkSZ3bnjx5guDgYOzatQv37t1DlSpV8MEH\nH2DEiBF6293hw4cxcuRIDB48GNOnT9d7XkPttjjb9OPHj7FlyxYcOnQIFy9exL///gtJkuDp6Yl6\n9eqhY8eO6Ny5M1xdXTWOmzp1KrZu3YrmzZtj7dq1Vs1Tfn4+lEql1dMl2+natSu6du2K1NRUDB48\nWGu7JEkYPXo0pk6dimXLlmHGjBnFkEsiIvNZEh8+T/euxnjRylsSWfoevIhx5vPWbm0ZZ2ZlZSEm\nJgYJCQk4e/YsEhIScP/+fQDArl27UKNGDZscay3POs60ZYwJMM40FmNM+2QozmSMaT/YsUfPTEZG\nBgICApCYmCh/Caq/aK5du4bk5GQcPHgQZcuWRWxsrM3yUaVKFdSoUQMeHh5a27Zs2YLjx4+jatWq\nNunYo5JPCIFFixbBwcEBo0ePLu7sPDOGPhf2aOPGjdiwYYN8rSlVqhQcHR1x584dHDhwAFFRUejU\nqRMWLVoER0dHk9O/cOEChgwZggcPHkCSJHh4eOD+/fs4ePAgDh48iEmTJmHUqFFaxz1+/BijR49G\nTEyMnDcPDw9kZWUhISEBZ86cwe+//461a9fqDX7MlZ+fjwkTJiAqKgqSJMHR0RGlS5dGWloaNmzY\ngO3bt2PZsmVo2bKl3jScnZ1Rrlw5ndsMdUaOHTsW0dHRkCQJ7u7uuHHjBoKCgpCWloZZs2Zp7Z+b\nm4vZs2ejUqVKmDBhgt50S2q7jYqKwqxZs3D37l35fXZ3d4eDgwPS0tKQlpaGPXv2ICgoCN9//z1a\ntGghHytJUrEEikePHsWaNWuQnZ2Nu3fv4o033sCwYcPQuHFji9JdvXo1srOz4efnB29vb7i5ueGf\nf/5BXFwcTp8+jdmzZ8v7CiHQrl07zJo1CwqFAmXKlEHZsmXN+ozqEx0djdWrV+PJkyfIz89H1apV\nMXLkSKt95ycnJ2PZsmVITk6Gm5sbJEnC5MmTddbj+fPnsXz5cvlHF1dXV3z22Wcm56VHjx5YsmQJ\nNmzYgGHDhsHb29sqZSEisjVL4sOSeg9gKy9aeZ9HL2Kc+Ty2W1vGmUePHsX48eMBaHYcGRMbWHKs\npYorzrRVjAmU3LbLOPP/vQhxprXyffr0aUyfPh1//vmn0ccwxrQP7NijZ+aLL75AYmIiPDw8MG7c\nOPTs2RMvvfQSACA7OxunT5/Gvn37cPDgQZvm47vvvrNp+mTfDh06hMuXL8PX1xc1a9Ys7uw8M8/b\n56Jx48aoVasWfH198dprr8Hd3R1AwTQR4eHhWLVqFfbu3YvQ0FB8/PHHJqX95MkTjB07Fg8fPkS9\nevWwYMEC1KpVC1lZWVi6dClWr16NRYsWoX79+mjdurXGsUuXLkVMTAwcHBwwadIkDBgwAB4eHsjP\nz8eePXvwzTff4NatW5gxYwbCwsKsVR0AgO+//x5RUVFwcnLClClT0K9fP7i6uiI9PR2BgYHYtWsX\nJkyYgJ07d8LLy0tnGo0bNzZ5JF50dDSio6Ph7e2NVatWoUaNGoiPj0dAQAB+++03DBkyBNWrV9c4\nJjQ0VA6pUG1PAAAgAElEQVTMDAVTJbHdbtmyBTNmzIAQArVq1cLHH3+Mdu3ayYFqZmYmjh49ioiI\nCMTGxiIuLk4j4AIKbuCfpT/++AN79uxBcHAwSpUqhaysLEybNg0fffQRpk+fjkGDBpmddlJSEiIj\nI7FkyRKN18uWLYsVK1ZovJaamoq7d+9qBdpPBy7jx483+XMLFLw3GzduRHBwMCpXrgyVSoUJEyag\nb9++WLp0Kdq3b29ymoXFxcVh3LhxmDBhAr7//nsAwM2bNzFq1Cj8+uuvKF++vLxvVFQUPvvsMwQF\nBaFDhw4AgH379mHgwIFYt24d6tSpY/R5HR0d0bt3byxZsgQRERGYMmWKReUgInpWLIkPS+I9gC29\naOV9Hr2Icebz2G5tGWcCgJeXF+rXr4/69eujcuXKmDlz5jM51hLFEWfaMsYESmbbZZyp6UWIM62R\nb5VKha+//hqPHz826dyMMe0D19ijZ+Lq1avySJr58+dj2LBhctAGFIxyatWqFWbOnImdO3cWY07p\nRbdp0yZIkoRu3boVd1bIAr1798bgwYNRp04dOdgCgMqVK+Pzzz9Hz549IYRAZGSkyWn/+uuvSEtL\nQ6lSpRASEoJatWoBKBhJ+OWXX6Jjx44QQmDhwoVax/7555+QJAn/+c9/EBAQIAcUTk5O6Nq1K6ZO\nnQohBGJiYvDo0SMzS68tIyMD69evhyRJGD58OPz9/eUR8ZUrV8bChQtRq1YtPHr0CMuXL7faeYGC\nEXqSJCEgIECeAqZJkybo16+fXNbCbt68iZUrV6JFixZ29zm8ePEivv76awgh0L59e0RGRqJ79+4a\no089PDzw7rvv4pdffsGiRYuKfRTo3bt3sWLFCgQFBaFUqVIACtryggUL4Onpifnz5+Ps2bMWnaNc\nuXLyCNFy5crhww8/xI4dO7RGaV6/fh3A/48mVf+pVCr5z8vLS+dac0XJysrC4sWLsWzZMlSuXBkA\n4ODggPHjxyM/Px+ff/45cnJyzC7jzZs38cknn2DMmDEaAerKlStx/fp1jfV179y5gylTpqB169Zy\npx4AdOzYETVr1tQ5wrgo3bt3B1AwBZJSqTS7HEREzwrjQ3rRMM58PtgyzuzQoQMOHz6MkJAQjB8/\nXmuQqK2OtURxxZkvUowJMM7U53mPM62R74iICJw/f96s8zPGLPnYsUfPxKVLl+R/FzVSwcXFReP/\n6vXuDh06pLXvt99+C4VCAYVCgYSEBK3tkyZNgkKh0BjBoWuh28jISCgUCsTFxUEIgalTp8rpKhQK\njR/e1K5cuYJZs2ahc+fOaNy4MXx9fdGjRw/MmTMHiYmJBsv44MEDzJ8/Hx06dECDBg3w1ltvYebM\nmbhz547B43Tx8/OT837nzh3MmjULb7/9Nho2bIiuXbsiLCxMY1TOrl27MHDgQPj6+qJp06YYPXo0\nkpKSijzPnj17MGLECLRq1QoNGjRA+/bt8fnnn+PcuXMGjxNCIDw8HL169ULDhg3RqlUrjBkzBqdO\nnTKqfElJSZg2bRo6dOiAN998E76+vhgwYAB+++035OfnG5WGse7fv48DBw5AkiR07txZ5z7Pqr7N\nKbclda1vAegHDx4gMjISEyZMQJcuXdCkSRM0btwY3bp1Q2BgIG7fvq03zcJ1Zc02bw3qdVoM5V+f\nHTt2QJIk9OjRAxUrVtTaPmLECADAuXPnkJycrLHt7t27AKB3OoZ69erJ/7akk+Fpx44dQ15eHgBg\nyJAhWtsdHBzg7+8PIQR27Nhh1Zs29TSDT08t+uqrr0IIgX///Vfj9W+//RYqlcqozg1LFy639vVl\n0aJFyM3NReXKlREUFKT1ffa09957D0OHDjUr79ayZcsWdO3aVeOHCQBwc3PDe++9B5VKhXXr1ll0\njiVLluDEiROIiYlBTEwMvvnmG1SqVElrv2vXruHLL7/EqVOnkJiYiPPnz2v8derUCXPnztU7TY8h\n8fHxuHXrFr744guN19Uj5jMzM3H58mXzCghgwYIFKF26NIYNG6bx+q1bt+Dg4KCxjk54eDgyMzPh\n6+urlU7z5s1x9uxZnD592qTzv/baa1AoFMjIyMCBAwfMKwQR0TNkSXwIGL4HUKlUCAsLQ8+ePTXu\niePj4wEU3IfVqVMHaWlpWsc+i3t9c+IqQ+W1NN7SpyTHmdYo84sYZ5pbZnPr21C7ZZypzZJpEotr\nzbfiijNtGWMClsWZtri2MM7U7XmPMy3N9507d3DkyBFUqVLFrPMzxiz52LFHz1x6erpJ+zdv3hyS\nJGmMdlc7fvy4PGLB0PbmzZtrvP70TY+rqyu8vLzg7OwMSZJQpkwZeHl5yX+FR48CBT/K9ezZE7//\n/jtu3LgBSZKQn5+Py5cvY926dQYf27916xbef/99rF27FhkZGXBwcMCdO3ewceNGDBgwwKyndCRJ\nws2bN/H+++9j48aNyMrKglKpRHJyMgIDAzF37lwAQFBQECZNmoQzZ85ACIHs7GwcPHgQgwYNwo0b\nN3SmLYTAlClTMGHCBBw5cgSPHj1CqVKlcPv2bezYsQN9+/bFr7/+qvNYpVKJcePGYe7cubh06RKU\nSiVUKpV8zr179xosV0REBHr16oWtW7ciLS0NTk5OyMnJwalTp/D1119j+PDhePLkicn1pU9MTAzy\n8/NRvXp1VKhQQe9+tqxvc8ttaV2ry/W0kJAQTJs2DXv37sW1a9fg6OiIvLw8XL16FWFhYejdu7fG\nDzO60jSnzcfGxsod67o+25ZSL75t6jp2WVlZcsd927Ztde7TqFEjlClTBkBBoFOYel5yfSOm1CPW\nvLy8tG5ILamT1NRUAECZMmW0rmdq6hvPhw8fFjk4wRTq6Qdv3ryp8br62ll4esLdu3fj77//xrBh\nw4yeosjcINba15f09HQcPHgQkiRh8ODBNhkhaYvPxZkzZxASEqJzBG2tWrUghMDFixctPk+pUqVQ\ntmxZg/skJyfDz88Prq6ucHDQvEXdunUrPD099X7uiqLuKI+OjpZ/CACg8R4bWifSkCtXrmDfvn3o\n3LmzVnsMCQnB33//rdGZrw6Knp4eCABq1KgBIQSioqJMzkeTJk0ghEB0dLTJxxIRFSdT40M1XfcA\n+fn5GD16NAIDA5GUlKRxTzx48GDs2bPHqHRtca9vSVylr7zWiAGKoy4sqQ9rlPlFjDPNLbOl9a3v\nXp1xZslhj3GmrWNMwLw40xbXFsaZhj3Pcaal+Q4KCtLqcDQVY8ySjR179EwUfgrl22+/RUZGhtHH\n+vr6Qgih9eVy//59JCUlyRfIpxdUv379Ou7cuQNnZ2c0atTI4Dm6du2Kw4cPy/v997//xeHDh+W/\n33//Xd53165dmDt3LlQqFbp06YI///wT8fHxOHnyJP7++298//33GuV92pw5c1C+fHls2LABJ0+e\nxMmTJ7Fs2TKULVsWqampWnNBG2v+/Pl49dVXsW3bNsTFxeHEiRP49NNPAQDr16/HihUrEBYWhhkz\nZuD48eM4fvw4tm/fjho1auDhw4dYtGiRznRXrlyJP/74Aw4ODpg4cSJiY2MRExODgwcPokuXLlCp\nVJgzZw6OHz+udWxoaCiioqLg6OiIKVOmyCNp9u3bh9atW2P69Ol6y7Nv3z7MmTMHbm5umDx5MqKj\noxEfH4/Tp09j9erVqFmzJuLi4jBv3jyz6ksX9SheQ++fmq3q29xyW1LXhrz88ssYPXo0IiMjER8f\nj7i4OCQkJGDz5s1o164dMjIy8NlnnxlMw5I2b82Rh9nZ2bh48SK++eYb7Ny5E5IkmTyn+5UrV+SR\nsrVr19a5jyRJ8nQgV65c0dimnhpky5YtCA0NRWZmJgAgLy8PO3fuRGBgIBwcHAzOX25OnaiPUalU\nevcpPHpS34iypKQkdO/eHQ0bNkSTJk3Qo0cPzJ8/HykpKXrTbdmyJYQQWLVqFa5evQqg4LO2ceNG\nSJIkL6Kek5OD+fPno0qVKhg7dqzJZTSFLa4vsbGxctt45513bJV1ANb9XOTn5yM/P1/nNGfqNvGs\npt14++23dXZ2/fPPP1i3bp1F8/q/9dZbeOeddzB48GCNQF8dTFapUsXs9W7++usvANC5Lp6jo6PW\nD3jqH0Dc3Ny09lfnzZxpaerXrw8AOr+PiYhKGkviQ0OWLVuGv//+G05OTvjvf/+L+Ph4xMTEICoq\nCu3atcOMGTOMSscW9/qWxFX62CoGsHVdWFIflpb5RYwzLSkz48yiWSPOLAnsKc58UWJMgHGmNdhr\nnGlJvo8ePYpKlSrJS8eYizFmycaOPXomqlWrht69ewMA/v77b7Rv3x7Dhg1DcHAw9u/fbzCQU09V\ndfbsWY2p6Y4fPw4hBHr06IGyZcsiPj5eY2oKdUffm2++WeRj6sbKz89HYGAgJElC9+7dsWjRIo0L\ntJeXF7p376734iqEgIuLC8LCwvDmm28CKJia4J133sHHH38MIQR2795tcr6EEHBwcEBoaChef/11\nAAVPIY4ZMwYtW7aESqVCcHAwxo0bh0GDBsk/JtauXRuzZ8+Wnw54elqAnJwchIaGynOXjx49Wp4b\nu1KlSli4cCGaNm0KlUqFH3/8UevYn3/+GZIkYezYsRg6dKg817q3tzeWLFkizz/9NJVKhXnz5kGS\nJHz//fcICAiAp6cngIIfSVu1aoWVK1fCzc0Nmzdvlqc3tNSZM2cgSRJ8fHwM7mer+ja33JbUdVGG\nDBkiT2mrnkJBkiTUrVsXy5YtQ+3atXH58mW9X/KWtHn107iWSE9Pl0eeNWnSBL169cKvv/4KNzc3\nfPrpp+jfv79J6RWe0kXXFA+FtwkhtKZgGTJkCAYNGgQhBH744Qc0a9YMvr6+aNiwISZPnoyaNWti\n+fLl8lzmTzO3TtRTL2RlZekdFV84yNI3dcz9+/dx9epVuLu7Izc3F5cvX8Yvv/yC7t27Y8eOHTqP\nadu2LVq3bo20tDR07doVTZo0wcCBA5GVlYUPP/xQvlH96aefkJ6ejunTp+vs8LAWW11f1J24Li4u\ncseuLVjjc1FYQEAAGjZsiDFjxmhtUz9Zqp5SyFxZWVmYO3cu+vTpg48++gj+/v5aT7MCBW1FV9m+\n/vpri9uFm5sbli9fjmnTpmm8vmvXLkiShMmTJ5udtrosFStWRFRUFEaMGIEPP/wQ/v7+OqcsUZdR\nV1nVC6HfunXL5Hyonwq8cuUKsrOzTT6eiOhZsiQ+1Cc7Oxtr1qyBJEmYMGECBg0aJMeBr7zyChYv\nXmzUdFS2uNe3JK7Sx5YxgC3rwpL6sLTML2KcaUmZGWfqZ+04s7jZW5z5osSYAONMQ573ONPcfOfl\n5WHVqlUYN26c2edWY4xZsrFjj56ZOXPmYOjQoXBxcUF+fj6OHTuGkJAQjBs3Dq1bt8YHH3yA7du3\nax1XtWpVvPLKK1AqlfK0BgAQFxcHSZLQokULNG3aFI8ePcKFCxe0tutaw8ZcR48eRXp6OhwdHc16\nnFmSJPTv31/nY+IdO3YEAKSkpODx48dmpavrkXz1osnOzs4659hu2rQpXF1dkZubKy/MqhYdHY3M\nzEw4Oztj5MiRWsc6ODhg7NixEELg+PHjuHfvntaxLi4uOudad3FxwfDhw3WWJyYmBmlpafD29ta5\nviFQEEg0atQISqVS62lNc6k7bQxNjwLYrr7NLbcldW0JZ2dnubzqUahPM7fNN2/eHOfPn8e5c+cs\n+gw7ODjIU+q6uLhAkiQ4OTlh1KhRZi2MXHhwgaGbP/W2p298HBwcMG3aNEyZMgVOTk6QJAmZmZkQ\nQkCSJGRlZWl8jgqzpE5atmwJZ2dnAAWjo5+Wl5eHX375Rf5/VlaWxvZKlSphwoQJ2LFjB86cOYNj\nx47h5MmTWLFiBV5//XU8fvwYU6dO1Rt4L1++HEOHDkXlypWRl5eH6tWrY/Lkyfjqq68AFIzQDA8P\nx1tvvSW3i/DwcHTu3BkNGjRA586dsXbtWpPKrI+tri/qaTeKmgbEEtb6XBTWtGlTbNiwQWsR+czM\nTOzevRsODg4YMGCARecIDg5Gly5dsGXLFqxbtw7+/v4YMWKEztGbT1NPSfn0AujWcPToUWzatAlf\nfPGFVvlNoZ7y6tSpU7h06RJ+/vlnbNiwARMmTMAnn3yCsLAwjf3V6+3pmoZH3Y4ePHhgcj7U311C\nCL3XESKiksTc+FCfw4cPIycnB66urvD399fa7uTkZNSaQ7a417ckrtLnWcQAJS3OtLTML2KcaUmZ\nGWfqZ+04szjZa5z5IsSYAONMQ573OFMXY/K9cuVKDBw40Cqd2YwxSzan4s4AvTicnJwwZcoUBAQE\nYN++fYiNjcXZs2dx48YNCCGQkJCAL774AlFRUVrTRzRr1gw7duxAbGysfIOn/iJs3rw5/vnnH0RF\nRSE2NlaeCks9defT6+tZ4vTp0wAAHx8fg0/rGKJ+jPlphUe6PXz40OQLsL7Rf+pRQt7e3lqL1gIF\nN8QVKlRAeno6Hj58qLFNPf+5QqGQ1wx7mq+vL5ycnKBUKpGYmIi33npL49g6deronQNc3w2DugM3\nPT3d4HzR6jnzzXmyQRf1AsvGLJhri/o2t9yW1LUxrl69ioiICBw/fhypqanIzs7WeDpWkiSDi4Pb\nqs0bo2LFijh8+LD8/+vXr2PlypX46aefsGnTJqxcudKkqQkKl9scd+/exccff4yEhAT06dMHQ4cO\nxauvvoo7d+7gr7/+wtKlSzF9+nRcv34dkyZNsuhchXl6eqJ///4IDw/HunXrULp0aQwcOBAvvfQS\nLl26hAULFiA1NRXOzs7Iz8/Xmr+9TZs2aNOmjcZrzs7OeOutt9CkSRP85z//wY0bN7Bw4UKda6G4\nurpiypQpep9m/uabb+Do6IiZM2cCAJYuXYrFixejatWq6N69uzxlSXZ2ts4Rf6YoruuLvQkPD0dW\nVhb8/f2NmjZKnyZNmmDUqFEao0s7deqEdu3a4auvvkLLli3l6+bTVCoVvvvuOwQGBpp9fl1pjho1\nCo8ePcLFixcxdOhQi6dKUj9VcujQIaxfv15+3dfXFz169EBQUBDatGkjj7x/5513cPHiRZ3XzXPn\nzgGA1veDMQoH+//++6/cgUhEVFJZEh/qor6GFn4C6GnNmjUzKm/Wvte3JK7Sx9YxgFpJijMtLfOL\nGGdaUmbGmfpZO860V8UZZzLGtE+MMy07R1H5vnnzJpKSkqw29SxjzJKNT+zRM+fp6Yl+/fohKCgI\nf/31Fw4fPozZs2fLj/D/9ddfCA8P1zjm6XX2MjMzcfHiRdSsWROenp7yzaR6e0pKCm7dugVHR0er\njr5QPy5vzBQu+uhbNLXwdKFPT1VijIoVK+p8XT2tl77tAOSbq6fPq/6x0tD0Gi4uLvI80oWnzFH/\n21AHqL501SMa8/Pzce/ePb1/ubm5ADSforKEOj31iDNDbFHfppZbPfrQkrouyp9//omePXti/fr1\nSEpKwuPHj1G2bFl5dKJ6yhxDj+Tbqs2bo3r16pgzZw6GDRuGtLQ0k5+8VZcXgMEna9XbCu8PAF9+\n+SXOnj2Lfv36Yd68eXjjjTfg5uaGatWqISAgAN9++y0AYNWqVXrXHzDXF198AT8/PwDAihUr0L59\ne9SvXx99+vRBTEwMPvroI3mRd30/sOji4eGB0aNHQwiB06dPyz9cGCsyMhLHjx/HqFGjULVqVfz7\n778ICQnBK6+8gq1bt2L+/PnYuHEjvLy8sHz5co0Fqc1hq+uL+jpoTodMSXPlyhWEhITAz88PU6dO\ntSitDz74QOeUMS1atEBmZiY2bdqk99h9+/YhIyOjyHVyTeHg4IBVq1Zhw4YNiI6OxpkzZ9CxY0cc\nOXLE7DTV3xm6foBt1qwZ8vPzNe5r/P394eHhofFjEFDwBN+JEycAaF87jKGeGgswfH0iIippzIkP\ndVHfgxQ1XboxrH2vb0lcpY8tY4DCSlKcaWmZX8Q405IyM840nqVxpj0riXHm8xJjAowz9XkR4syn\nGZPvoKAgq15/GGOWbHxij4qdp6cn+vbtiw4dOqBHjx64d+8eNm/erDF9irrjLiEhAbm5uYiLi4NK\npZJfV48gU3fsqZ/mq1+/vlVHZ1n6tI69Ut98PCvqhZffffdd/PTTT8/svOXKlcO9e/eK7YapuMqt\nT0ZGBmbOnAmlUolu3bphxIgR8PHxkYNKAPjxxx+xfPlyu/tsDBo0CGvWrJGnm6hbt65RxxUOam/f\nvo3XXntN5363b9+GJEka+1+5cgVHjhyBJEk6p7IBgJ49e2LevHl48OABDhw4gNq1axtfqCK4uLhg\n2bJl2L17N7Zv346kpCSoVCrUrFkT/fr1w9tvv42mTZsCgN5y6dOwYUMABdfI1NTUIqcZUnv06BGC\ngoJQvXp1BAQEAACOHDmCvLw8dOvWTR4ZXKFCBfTo0QNhYWE4cuQIunbtalL+CrPV50w9Ijc3NxfJ\nyck2Xf/AlnJycvDZZ5/h7bffxsKFC7VG1VpL+fLlIYTA0aNHMWrUKJ37hIeHo3HjxlZd66Gw0qVL\nY+HChWjXrh3GjBmDiIgIeY0WU5QvXx45OTk6R9h7eXkBgMZaD56enggKCsKnn36KP//8E926dcPj\nx48xb9489OrVC+fPnzf4o50+hb+7Ci/cTkRkb4yJD3Ux5n7UVt8pxnrWcVVJxzjT9kpajAkwznze\nlLQ483mKMQHGmaZ6nuLMpxWV771796JevXoWPYzyNMaYJRuf2KMSo0KFCvDz84MQAteuXdPYVqNG\nDXh5eSEvLw8nT56U189TT7Pp4OCApk2b4uHDh7h06ZJN1tcD/n90XGpqqlXTLanUj62npaXp3Sc3\nN1ce3VT4MXf1vw1NnaFvm/qHUGs/sVQU9U1icXXsmVtuS+rakEOHDiE7Oxu1a9fGwoULUbduXY1g\nC4DdzrFdeGSpen0sY9SsWVO+idL3PgkhkJycDAAa06+oF70GII9Y1EU9tYGtrjOdO3fGkiVLsHv3\nbuzduxcrVqxAhw4dkJiYKI/AUgdQxnp6yhxjBQUFISMjAzNmzJBH1qampkKSJK06evXVVyGEMHg9\nMoatri/NmzeXy66e997eCCEwefJk1K1bF8HBwXBysmz81//+9z988MEHWk+mFabv2nT37l3ExcXh\n1VdftSgPRfH09MSbb76JvLw8BAcHm5WGOsDRNUWVeoTjP//8o/F6+/btsXnzZhw6dAgDBw7ExIkT\n0bdvX7zyyisAYFbgV3hdPmM714mISjJD8aEutrontgZL4qqi0iyJ5S2KufVhaZlfxDjTkjIzzjSd\nuXHm86CkxJnPU4wJMM7U5UWJMwsrKt85OTn47bffrL7uKWPMko0de1SiqKdb0DVFhXo9hNjYWJ3r\n5+nabmrHnnrEiL5RYeqbkEuXLpXYIMma1PNdX7t2TW95Y2Nj5ektCs+Prf73+fPntRZIVlO/T09T\nP1aenJys0Rlia+qRTykpKc/snIWZW25L6tqQ9PR0AMAbb7yhd59jx44V+8hncxR+j02Z8q506dLy\nWg7R0dE69zl9+rQ8d36rVq3k1wuPSDMUOKi36ZtaxlY2b94MoGDqClOfFjpz5oz8b2NHhyUkJGDj\nxo1499130a5dO63tT548Mfh/c9nq+lK5cmW0b98eQghERETo/SyWZPPnz4eXlxfmzZun8bm+ePGi\nWemtW7cOCQkJiIiI0NqmDhD0TcejfsLNmB82jREWFob+/fvLU10W9sorr0AIgVOnTpmVtvoaqf7c\nF6a+n9BVzlq1auG7777D+vXrERISgjfffBPp6emQJEnj2mEs9WCAMmXKmPXEHxFRSWQoPnya+smY\nCxcu6J3m7Pjx49bLnAksiauKStPaMcCzYG59WFrmFzHOtKTMjDNNZ26c+Tx7lnHm8xZjAowzdXlR\n4szCisr3qVOnkJGRgeHDh2Pw4MHyn7+/P9LT03H37l35taSkJKPPyxizZGPHHj0TKSkpuHnzpsF9\nHj9+jH379gEoWET7aep19g4cOIBz587htddek0fFAAWdfEII/PHHH0hJSYGjo6P8uL+x1KPt9Y2k\na9WqFSpXrgylUokFCxaYlLY9atOmDTw8PJCfn4+ff/5Za7tKpcKyZcsAFHSsvvTSS/K2tm3bwsPD\nA7m5uVi7dq3WsXl5eVi9erXO87Zq1Uq+aZs3b548rYEu1hz12KRJEwghcPbsWaulaQpzy21JXRui\n/jzo+9LfsGFDiRyFaKje1FatWgUAZq3D2b17dwghsH37dnndzcLUn5X69etrTDVS+Lr2+++/60w7\nKipKHp1q6mhGS5w8eRKbN2+GJEkYPXq0ScdmZmYiNDQUQEGejRnFJYTA119/DVdXV0yfPl1jm7e3\nN4QQSExM1Hj9zJkzkCQJ3t7eJuXvaba8vkycOBEuLi74559/8NlnnxU5vdSuXbuwZs0ak85hK7/9\n9hsePnyI2bNna20zd4RhhQoV4O7ujm7dumltU/+Ip+/JNPWT96asw2HIjz/+iNOnT+usb/WPv4UX\nBjdFy5YtIYSQ19YoTB14Pz0NU0ZGhs41X06ePIly5cqhU6dOJucjISEBQMF3GRFRSWeN+PBpbdq0\ngbu7O548eYJ169ZpbVcqlfjll1/My7CFLImr9LFVDPAsmFsflpb5RYwzLSkz40xNto4zn0fPMs58\nXmNMgHHm016UOLOwovLdqlUrREZGYu3atRp/4eHhUCqV8PLykl97/fXXjT4vY8ySjR179ExcvnwZ\n7733Hj755BPs2rVL48evnJwcREVFYeDAgUhJSdG7/pT66bvz589rrK+nVr9+fbi7u+Ps2bOQJAkK\nhcLkJ15q164NIQT27t2LzMxMre1OTk6YMmUKhBDYsWMHJk6ciKtXr8rb79y5g99//x1z5swx6bwl\nlbu7u7xYcXh4OEJCQuTFq9PT0zFp0iTEx8fD0dEREydO1DjWzc0NI0eOhBACS5cuRVhYmDwaKiUl\nBai+z74AACAASURBVOPGjZNH6j3NyckJM2bMAFDwVNTw4cM1RmoplUokJiYiKCgIHTt2tFp51R3B\n586dK5a5/M0ttyV1bUjr1q0hSRKSkpIwZ84c+WmUzMxMrFq1CrNnz7bZo/ixsbFQKBRQKBQmjwK9\ndesW+vTpg82bN2uUWwiBCxcu4LPPPsOmTZsgSRL8/f21bowiIyOhUChQp04dnU/W9e/fH1WqVEFm\nZiZGjRolj8jLysrCggULsHfvXkiShMmTJ2scV7VqVbRp0wZCCPzyyy/44Ycf5AXps7OzsWXLFkyb\nNk3eV70AuTXqBABiYmIQFhaGmzdvyoHGw4cPER4ejpEjR0KpVOLDDz/UelIoNTUVH374ITZt2oRb\nt27Jr+fl5eHQoUMYMGAArl27BkdHR60y67N+/XokJiZi/PjxePnllzW2tWrVCs7Ozti9e7c8tcbB\ngwexd+9euLi4mPUkU2G2vL4oFArMmjULkiThf//7H3r37o1t27ZpTF+RmZmJPXv2wN/fH5MmTTJp\nxKWlbUCfw4cPIzY2FrNnz4ZSqdT4O3HihMaUQkDBqMSPPvqoyNGo7dq1w4IFC9CjRw+tbUePHoWj\noyM++OADnceqRwYWtU7ub7/9pneEZGGVKlWCm5sbunTporXt8uXLkCQJb7/9tsbrxpazY8eOKF26\nNM6fP6+1LSEhAZIk4f3335dfO336NNq1a4exY8dq7Hvv3j0cOHAAQ4YM0Vik3Fjqc5k6qImIqDhY\nIz58WunSpTF06FAIIRAcHIyIiAj5njgtLQ2ffPJJsS2pYElcpY+tYoBnwdz6sLTML2KcaUmZGWdq\nsnWcCQD//vuv/Fc4hnj06JHGNl3tyNxjn5c483mNMQHGmU97UeJMc/JtbYwxSzbLJrV9wWzZsgWp\nqanw9vZGnz59ijs7dsXJyQkqlQr79u3D3r17ARRcjJydneWbOEmS4OTkhAkTJuj8onvjjTdQvnx5\n3L9/H5IkoUWLFhrbHR0d0aRJE0RHR5u9vl6vXr2wevVqnDhxAi1btoSnpyecnJzw8ssvY/369QCA\nrl274vbt2/j++++xe/du/PXXXyhVqhRUKpU8b3jhKUJNJYTAX3/9ZfV5kc01YsQIXL16FVu3bkVw\ncDAWL14MDw8PPHz4EEIIODo6YubMmTov8gEBATh79iz279+PwMBABAUFoVSpUnj48CGcnJwQHByM\n8ePH6zyvn58f5s2bh6+++goxMTHo168fXF1d4e7ujkePHkGpVAKAVRfcbdCgAapVq4aUlBTExMSg\nZcuWVkvbWOaW29i6NqV91ahRA0OHDkVYWBgiIiIQERGBcuXKITMzEyqVCu3atUPdunUREhJik7oA\nTFuvrbBz587hv//9L4CCNa5KlSqFrKwseWSbJEno06cPvvjiC5PTdnV1xbJlyzBs2DCcP39eXoA7\nOzsbKpUKDg4OmDx5ss7gIDAwEMOGDcOVK1cQGhqK0NBQlC5dWr7pliQJFStWxOLFi/XOO29unaSl\npSEwMBCBgYFwcnJCqVKl8OjRIwghIEkSPvjgA3z11Vc6jz19+jROnz4tl9/d3R2ZmZnIz8+HJElw\nd3dHjx49EBMTg5SUFIPfkffu3UNwcDBq166NoUOHam339PTE6NGjsXTpUowcORJubm54/PgxJEnC\nxIkTrbJgsy2vL3379kWFChXw1VdfITk5GV9++SWAgql4JEnSeK+rVq1q1nXGmtMSXb58GRMnTkRm\nZiZ27typc5+nR7z++OOPePz4MTZs2KC1rbD33nsP48ePR8OGDVGpUiX59cTERJw/fx7jx4/XO1pQ\n3emt/hzouwdbvnw50tPTERQUhF9//VVvXoYPH46jR4+ic+fOGq+fOHECN2/exMsvv4xx48aZVU4P\nDw+MHj0aP//8s0Ybzc3NxZ49e+Dr64uuXbvK++fk5EClUmn84KBSqTBz5kw0aNDA5NHM6nPFxMRA\nkiS89957Jh//ouM9PtkS25du1ogPdRk7diwSEhIQHR2NOXPmIDAwEKVLl8aDBw/g7OyMRYsWyfGH\neu2lZ8WSuEqfgIAA7NmzB+fOnTM53ipu5taHJTEm8GLGmZaU2cvr/9i7++Aqqztx4N8LJAsoWJGA\nGJSash2hqFAJL7r+Wl+otiwrpNAqFOtLi7XDzuyObDvYVqV2dbcDrrajM7K7datgxrGFMnRlEbU6\nnW5KiF0qQ2CpfRHB8iKCSGAbDPf3h8OtMTfhkuRy73Pz+cw4ffo85/s8h+Tk5Jx873nO4Dj//PPj\n97//fbe1MfPM9mWbQ6bT6fjc5z7X6twLL7zQ5tWUXYmNKNw8c+PGjZFKpdqdZ377298+4d/YSn2O\nGWGe+X65zjOzjcE+OM9sTzHMM98v13q3F3e8nzq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            "text/plain": [
              "<matplotlib.figure.Figure at 0x16e5a763a050>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 526,
              "width": 891
            },
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
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P0aRJE6P2xRhTXmyQo0IzZcoUxMfHw9XVFePGjcP777+PypUrAwAyMzNx7tw5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\nF2v2MmzatClEUcSFCxeslqYpzD1uS8r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            "text/plain": [
              "<matplotlib.figure.Figure at 0x16e58dedaf90>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 526,
              "width": 882
            },
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
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mBgwYAF9fXzRv3hwajQYajUaZN/TmzZtG9zXVo1VuxKxbt67Ss7AoSZKUhmtznzdr7iGm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\ngLJgbX2oLfPjGGuqKTNjTePKOtYs7zjVXKypJm2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            "text/plain": [
              "<matplotlib.figure.Figure at 0x16e58d4a7e10>"
            ]
          },
          "metadata": {
            "image/png": {
              "height": 526,
              "width": 896
            },
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "def _desc(v):\n",
        "  return '(median: {}; 95%ile CI: $[{}, {}]$)'.format(\n",
        "      *np.round(np.percentile(v, [50, 2.5, 97.5]), 2))\n",
        "\n",
        "for t, v in [\n",
        "    ('Early disaster rate ($e$) posterior samples', early_disaster_rate),\n",
        "    ('Late disaster rate ($l$) posterior samples', late_disaster_rate),\n",
        "    ('Switch point ($s$) posterior samples', years[0] + switchpoint),\n",
        "]:\n",
        "  fig, ax = plt.subplots(nrows=1, ncols=2, sharex=True)\n",
        "  for (m, i) in (('Switch', 0), ('Sigmoid', 1)):\n",
        "    a = ax[i]\n",
        "    a.hist(v[i], bins=50)\n",
        "    a.axvline(x=np.percentile(v[i], 50), color='k')\n",
        "    a.axvline(x=np.percentile(v[i], 2.5), color='k', ls='dashed', alpha=.5)\n",
        "    a.axvline(x=np.percentile(v[i], 97.5), color='k', ls='dashed', alpha=.5)\n",
        "    a.set_title(m + ' model ' + _desc(v[i]))\n",
        "  fig.suptitle(t)\n",
        "  plt.show()"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "Bayesian_Switchpoint_Analysis.ipynb",
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
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