diff --git a/notebooks/Multi-Parameter Distributions/MPD_6_1.ipynb b/notebooks/Multi-Parameter Distributions/MPD_6_1.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..375bf09079df925e51c05faf25c636c4e6b857bf --- /dev/null +++ b/notebooks/Multi-Parameter Distributions/MPD_6_1.ipynb @@ -0,0 +1,887 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "cubic-disease", + "metadata": {}, + "source": [ + "# NMR" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "involved-buffalo", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + } + ], + "source": [ + "%matplotlib inline\n", + "import pymc as pm\n", + "import matplotlib.pyplot as plt\n", + "import scipy.stats as st\n", + "import arviz as az\n", + "import metropolis_commands as mc\n", + "import numpy as np\n", + "import pandas as pd\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")\n", + "plt.rcParams['figure.figsize'] = [5, 3]" + ] + }, + { + "cell_type": "markdown", + "id": "ea67ea3e-b07d-4fb9-8644-0cca9e5758ed", + "metadata": {}, + "source": [ + "Die magnetische Kernresonanz (NMR: nuclear magnetic resonance) ist eine leistungsstarke Technik, die zur Untersuchung von Molekülen und auch von Lebewesen wie Menschen oder Hefe verwendet wird. \n", + "\n", + "Mit NMR kann man verschiedene Arten von beobachtbaren Grössen messen, die mit unbeobachtbaren und interessanten molekularen Eigenschaften zusammenhängen. Eine dieser beobachtbaren Grössen ist bekannt als chemische Verschiebung (Signalverschiebung gegenüber einem Referenzwert). Wir können chemische Verschiebungen allerdings nur für die Kerne bestimmter Atome erhalten.\n", + "\n", + "All dies fällt in den Bereich der Quantenchemie; die Details sind für diese Diskussion irrelevant. Wir betrachten im Folgenden den Datensatz in der Datei `chemical_shifts.csv`. Darin enthalten sind 48 Werte für chemische Verschiebungen, die wir in ein `numpy`-Array laden und mit Hilfe des folgenden Codes darstellen können:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "artificial-fraud", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "<div>\n", + "<style scoped>\n", + " .dataframe tbody tr th:only-of-type {\n", + " vertical-align: middle;\n", + " }\n", + "\n", + " .dataframe tbody tr th {\n", + " vertical-align: top;\n", + " }\n", + "\n", + " .dataframe thead th {\n", + " text-align: right;\n", + " }\n", + "</style>\n", + "<table border=\"1\" class=\"dataframe\">\n", + " <thead>\n", + " <tr style=\"text-align: right;\">\n", + " <th></th>\n", + " <th>0</th>\n", + " </tr>\n", + " </thead>\n", + " <tbody>\n", + " <tr>\n", + " <th>0</th>\n", + " <td>51.06</td>\n", + " </tr>\n", + " <tr>\n", + " <th>1</th>\n", + " <td>55.12</td>\n", + " </tr>\n", + " <tr>\n", + " <th>2</th>\n", + " <td>53.73</td>\n", + " </tr>\n", + " <tr>\n", + " <th>3</th>\n", + " <td>50.24</td>\n", + " </tr>\n", + " <tr>\n", + " <th>4</th>\n", + " <td>52.05</td>\n", + " </tr>\n", + " </tbody>\n", + "</table>\n", + "</div>" + ], + "text/plain": [ + " 0\n", + "0 51.06\n", + "1 55.12\n", + "2 53.73\n", + "3 50.24\n", + "4 52.05" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.read_csv(\"./Daten/chemical_shifts.csv\",header=None)\n", + "df.head()" + ] + }, + { + "cell_type": "markdown", + "id": "48f249fc-b6de-42ec-b20d-08aaa884b4ae", + "metadata": {}, + "source": [ + "Die Daten müssen hinsichtlich der Modellierung nicht strikt normalverteilt sein, allerdings sollte die Normalverteilung eine vernünftige Annäherung an unsere Daten darstellen." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "identified-danger", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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NREREROQkTLaJiIiIiJyEyTYRERERkZMw2SYiIiIichIm20RERERETsJkm4iIiIjISZhsExERERE5CZNtIiIiIiInYbJNREREROQkTLaJiIiIiJyEyTYRERERkZMw2SYiIiIichIm20RERERETsJkm4iIiIjISZhsExERERE5CZNtIiIiIiInYbJNREREROQkTLaJiIiIiJyEyTYRERERkZMw2SYiIiIichIm20RERERETsJkm4iIiIjISZhsExERERE5CZNtIiIiIiInYbJNREREROQkTLaJiIiIiJyEyTYRERERkZMw2SYiIiIichIm20RERERETsJkm4iIiIjISZhsExERERE5CZNtIiIiIiInYbJNREREROQkTLaJiIiIiJyEyTYRERERkZMw2SYiIiIichIm20RERERETsJkm4iIiIjISZhsExERERE5CZNtIiIiIiInYbJNREREROQkTLaJiIiIiJyEyTYRERERkZPIXB1ASTZv3oyEhAScPn0aubm58PPzQ4cOHfDmm28iICAAADBv3jx88803xT7j999/R/369csrZCIiIiIiABU42RZFER9++CESExPRsGFDREREwMvLCzdv3sTBgweRmppqTrbzjRo1CkFBQUWeVb169fIKm4iIiIjIrMIm27/88gsSExMRHR2N9957D1KptNB1vV5f5DWjRo1C9+7dyytEIiIiIiKrKmTNdl5eHr799ls0aNAA7777bpFEGwBksgr7ewIREREREYAKurK9e/duZGVlYfTo0TAajdi0aRMuX74MHx8f9OzZE40aNbL4uoMHD+L48eOQSCRo3LgxwsLC4OXlVc7RExERERGZVMhk+48//gAASCQSREZG4vLly+ZrEokEsbGxmDlzZpHXzZs3r9DX1atXx7vvvouRI0dafb8aNWpAIqmQi/wO4+vr6+oQqALj/KCScI6QNZwfZE1Vnx8VMtm+c+cOACAuLg6tW7fG8uXL0axZM5w5cwbvv/8+Fi5ciAYNGiA6OhoA0LJlS8yePRvdunVD3bp1cevWLWzfvh1ff/013n77bfj4+GDAgAHFvl9WVla5fC5X8fX1RWZmpqvDoAqK84NKwjlC1nB+kDXuPj9s+UWiQi7niqIIAJDL5fj2228RGhoKLy8vdOnSBV999RUkEgkWLVpkvn/QoEF45pln0KBBAyiVStSvXx8xMTH46quvAABffvmlKz4GEREREVVxFTLZ9vb2BgC0bdsW/v7+ha4FBwejQYMGuHr1KrKzs60+JywsDA0bNsRff/2FnJwcp8VLRERERGRJhUy2mzZtCgDw8fGxeD1/PC8vr8Rn5S/vP3z40EHRERERERHZpkIm2/m9si9evFjkmk6nw9WrV+Hp6YlatWpZfU5ubi7OnTsHT0/PKl+cT0RERETlr0Im2w0bNkR4eDiuXLmC5cuXF7q2YMECZGdnY+DAgZDJZMjJycGlS5eKPCMvLw/vv/8+Hjx4gKFDh7IvNxERERGVO0HM341YwVy9ehUTJkzAnTt30LdvXzRt2hSnT5/Gvn37EBQUhMTERPj5+eH69esYOHAg2rVrh2bNmqFOnTq4c+cO9u7dixs3biA4OBi//PKL1ZVtd94lC7j/TmAqG84PKgnnCFnD+UHWuPv8sKVyosIu9zZs2BArV67E119/jV27dmHPnj2oU6cOVCoVXnnlFdSuXRsAULNmTURHR+PEiRPYsWMHsrOzoVQq0axZM0yaNAkxMTHw8PBw8achIiIioqqowq5slyd3/o0LcP/fKqlsOD+oJJwjZA3nB1nj7vOj0vbZJiIiIiJyB0y2iYiIiIichMk2EREREZGTMNkmIiIiInISJttERERERE7CZJuIiIiIyEmYbBMREREROQmTbSIiIiIiJ2GyTURERETkJEy2iYiIiIichMk2EREREZGTyFwdABERERGVH4MBSEmRISNDgL+/iLAwPaRSV0flvphsExEREVURa9bIMWuWJ9LSHhc3BAYaMWdOLiIjdS6MzH2xjISIiIioClizRo7YWC+kpQmFxtPTBcTGemHNGrmLInNvTLaJiIiI3JzBAMya5QlRBIDCybYomr5+5x1PGAzlH5u7Y7JNRERE5OZSUmSPSkcEi9dFUUBqqgQpKawwdjQm20RERERuLiPDcpJt731kOybbRERERG7O31906H1kOybbRERERG4uLEyPwEAjBMFyMi0IIoKCjAgL05dzZO6PyTYRERGRm5NKgTlzcgGgSMKd//Xs2bnst+0ETLaJiIiIqoDISB3i4h4gIKBwsh0YKCIu7gH7bDsJt5wSERERVRGRkTpERGTxBMlyxGSbiIiIqAqRSoHwcNZmlxeWkRAREREROQmTbSIiIiIiJ2GyTURERETkJEy2iYiIiIichMk2EREREZGTMNkmIiIiInISJttERERERE7CZJuIiIiIyEmYbBMREREROQmTbSIiIiIiJ2GyTURERETkJEy2iYiIiIicRGbPix4+fIjMzEzUrFkTnp6e5vGsrCz88MMPOHfuHAICAjB16lQ0bNjQYcESEREREVUmdiXb8+fPx48//ojly5ejbdu2AACtVotx48bh6tWrEEURALBx40YkJSWhbt26jouYiIiIiKiSsKuMZN++fWjYsKE50QaApKQkXLlyBd27d8dPP/2ESZMmITMzE3FxcY6KlYiIiIioUrEr2U5PT0ejRo0KjW3duhWCIGDOnDno1asX3n33XTRu3Bi7du1ySKBERERERJWNXcl2VlYWfHx8zF+LoogjR44gJCQEAQEB5vGWLVsiPT297FESEREREVVCdiXbfn5+SE1NNX996tQpZGVloWvXroXuEwShbNEREREREVVidiXbLVu2xIkTJ7Blyxbk5ORg/vz5EAQB/fr1K3TflStXuDmSiIiIiKosu7qRPPfcc9i+fTtmzJgBwFRG0qpVK/To0cN8z+3bt3H27FkMHz7cMZESEREREVUydq1sd+rUCd988w06d+6Mpk2bIioqCt999x0kksePW7t2Lby8vPDUU085LFgiIiIiospEEPObYldhmZmZrg7BqXx9fd3+M5L9OD+oJJwjZA3nB1nj7vPD19e3xHt4XDsRERERkZPYVbOdLzMzE8nJyThx4gTu3buHHj164PnnnwcAnDt3DlevXkXPnj1RrVo1hwRLRERERFSZ2J1s//bbb3jvvfeQm5sLURQhCEKhziMZGRl49dVXMXfuXIwYMcIhwRIRERERVSZ2lZEcPXoUb7zxBmQyGWbOnInly5fjydLvsLAw+Pj4YPPmzQ4JlIiIiIiosrFrZft///sfBEHAwoUL0aZNG4v3SKVStG7dGufOnStTgERERERElZXdK9sdO3YsNtHOV6dOHdy8edOuwIiIiIiIKju7ku2HDx/a1OokOzvbnscTEREREbkFu5Jtf39/nD9/3uo9oiji3LlzqF+/vl2BERERERFVdnYl20899RQuXbqEdevWFXvP8uXLkZ6ejr59+9obGxERERFRpWbXBsnp06dj7dq1mDlzJk6fPo1BgwYBMJWXnD59Gps3b8aPP/6IWrVqITY21pHxEhERERFVGnYf13706FHMmDEDt2/fhiAIha6JoojatWtj/vz5aN++vUMCdSZ3PkYUcP+jUqlsOD+oJJwjZA3nB1nj7vPDlj2Mdh9q07FjR2zYsAErVqzA3r17kZqaCqPRiHr16qFnz56YMGECfHx87H08EREREVGlV6bj2r29vREbG8tSESIiIiIiC+zaIElERERERCWza2U7LS2tVPcHBgba8zZERERERJWaXcl2//79i2yKLI4gCDh9+rQ9b0NEREREVKnZlWx37drV4rgoikhPT0d6ejqMRiM6dOgAuVxepgCJiIiIiCoru5LtxYsXW71+6dIlvPfeexBFET/++KNdgRERERERVXZO2SDZpEkTzJs3DxcuXMDXX3/tjLcgIiIioqpOp4Ns1y4IqamujqRYTutGUqtWLYSGhmL9+vXOegsiIiIiqoIkZ8+i2vvvo0bbtvAZMQJe06e7OqRilanPdklEUcTt27ed+RZEREREVBVkZ0Px669QqtWQHTpkHjbWrQvt5MkuDMw6pyXbp0+fxsGDB9n2j4iIiIjsI4qQ7d0LhVoNRVIShIcPTcMyGXRDhkCrUkE3YABQgRty2JVsf/PNN8Vey83NxeXLl7Fz504YDAZMmDDB7uAAYPPmzUhISMDp06eRm5sLPz8/dOjQAW+++SYCAgLM9+Xk5GDevHnYtGkTbt26hbp162LIkCF49dVX4eXlVaYYiIiIiKj8CGlpUC5dCoVaDemlS+ZxQ4sW0MTEQDt+PMS6dV0Yoe3sTrYFQYAoisXeU61aNbzwwguYMmWKXYGJoogPP/wQiYmJaNiwISIiIuDl5YWbN2/i4MGDSE1NNSfbubm5iImJwZkzZxAeHo7hw4fjzJkzWLhwIQ4ePAi1Wg2lUmlXHERERERUDjQayDdsMJWJbN0KwWgEAIje3tCOHg2NSgVDly6AjWe9VBR2Jdtz5swp9ppcLoefnx/atWsHT09PuwP75ZdfkJiYiOjoaLz33nuQSqWFruv1evP//vHHH3HmzBk8//zzeOONN8zjn332GX744QfExcXhhRdesDsWIiIiInIOyenTUMbHQ7FsGSR375rHdT17QqtSQRsVBVTiKgVBtLY87SJ5eXno3bs3qlevjg0bNkAmK/53AlEU0bt3b+Tk5GDPnj2FEvzc3Fz06tULtWvXxpYtW4p9RmZmpkPjr2h8fX3d/jOS/Tg/qCScI2QN5wdZU9z8ELKyIF+50rSKffSoedwYEADNxInQTpwIY7Nm5RmqXXx9fUu8x6ndSOy1e/duZGVlYfTo0TAajdi0aRMuX74MHx8f9OzZE40aNTLfe/nyZdy8eRPh4eFFVtI9PT3RqVMn7N69G+np6YVqvImIiIioHBmNkO3eDUV8PBRr10LIywMAiHI5dEOHQhMTA32/foCVRdbKqEJ+mj/++AMAIJFIEBkZicuXL5uvSSQSxMbGYubMmQCAK1euAAAaN25s8VmNGzfG7t27cfny5WKT7Ro1akAicVrL8QrBlt+8qOri/KCScI6QNZwfZI3v/ftAXBywaBFQIKdD27bAtGkQVCoo/PygcFWATmZTsj1gwAC730AQBKslHJbcuXMHABAXF4fWrVtj+fLlaNasGc6cOYP3338fCxcuRIMGDRAdHY379+8DALy9vS0+K388Jyen2PfLysoqVXyVDf/ER9ZwflBJOEfIGs4PsigvD/L16+GdmAhxyxYIj6qWRR8faMeMMW127Njx8WbHSjqHHFZGklrOR2Dml5HL5XJ8++238Pf3BwB06dIFX331FUaMGIFFixYhOjq6XOMiIiIiouJJT5ww9cRevhySe/cAAAIAXe/eps2Ow4cDZWigURnZlGyfPXvW2XEUkr8a3bZtW3OinS84OBgNGjTAlStXkJ2dDR8fHwDFr1znjxe38k1ERERE9hMyM6FYsQIKtRqyEyfM48agIEimTkXW6NEwFthvV9VUyJrtpk2bAoA5kX5S/nheXp55s2TBuu6C8seLq+kmIiIiolIyGCDbsQNKtRrydesgaLUAAFGhgG74cGhUKuj79IFvnTowVtISEUepkMl29+7dAQAXL14sck2n0+Hq1avw9PRErVq14Ofnh7p16+LIkSPIzc0t0vrvyJEjqF+/PjuREBEREZWR5MoVKBISoFiyBNLr183j+rZtoY2JgXbsWIjcMFuIQ1pwZGdnIz09HWlpaRb/U1oNGzZEeHg4rly5guXLlxe6tmDBAmRnZ2PgwIGQyWQQBAFjx45Fbm4u5s+fX+je+fPnIzc3F+PGjSvT5yMiIiKqsh4+hGL5cniPHIkaHTui2qefQnr9Oow1ayLv+eeRvX077u/cCc306Uy0LbD7UJtbt27hyy+/xNatW3HvUQG8xTcQBJw+fbrUz7969SomTJiAO3fuoG/fvmjatClOnz6Nffv2ISgoCImJifDz8wNgWsGeOHEizp49i/DwcLRu3RqnT5/G7t270a5dO8THx8PDw6PY93L3XdTcKU7WcH5QSThHyBrODzclipAeO2ba7LhiBSTZ2aZhQYC+Tx9oVCrohg8HrORXgPvPD1u6kdiVbN+8eRNjxozBzZs34e/vD71ejzt37qBDhw64fv06bt++DUEQ0KFDB8hkMixevNiuD5Ceno6vv/4au3btwr1791CnTh30798fr7zyCmrXrl3o3vv372PevHnYtGkTbt++DT8/PwwdOhSvvPJKiZsj3XkSAO4/0alsOD+oJJwjZA3nh3sR7tyBYtky02bHAoulhoYNoY2ONp3s2KCBzc9z9/nhtGT7n//8J5YsWYLXXnsNL7/8MmbNmoXVq1fjzJkzAICDBw/io48+Qo0aNbBo0SIolcrSR1+O3HkSAO4/0alsOD+oJJwjZA3nhxswGCDbutW02fG33yDodAAAUamENjISWpUK+qeeAuw4ANDd54fTjmvftWsX6tevj5dfftni9a5du2LhwoUYOnQo5s+fj7///e/2vA0REREROYnk4kUoEhKgXLIEkvR087i+Y0dTmcjo0RBr1nRdgG7CrmQ7IyMDffv2NX+df9S5VquFQmE6bNPf3x/du3fHb7/9xmSbiIiIqCJ48ACKNWugUKsh37PHPGysVQvasWOhValgaNvWhQG6H7uS7SdroKtXrw7AlIQ3KFDHo1AokJGRUYbwiIiIiKhMRBHSQ4egVKuhWLUKwqMD/0SJBPr+/U2r2EOHAhW87LeysivZDggIKNTSr0WLFgCAHTt2ICYmBgDw8OFDHDlyxNwxhIiIiIjKj3DzJhTLlkGpVkP655/mcUPjxtCqVNBMmAAxKMiFEVYNdiXbPXr0wC+//IK7d++iVq1a6N+/P6pVq4ZPPvkEN27cgL+/P5KTk3Hnzh1MnDjR0TETERERkSV6PeRbtpjKRDZuhKDXAwDEatWgHTHCtNkxLMyuzY5kH7uS7aioKNy4cQPnz59Ht27dULNmTfzrX//CrFmz8OOPP0IQBIiiiBYtWrBem4iIiMjJJOfOQZmQAMXSpZAUKOHVd+4MjUoF7ejRwKOyXypfNrX++89//oORI0ciJCTE6n1paWnYsWMHsrOz0bhxY/Tv3x9yudxhwTqLO7ekAdy/7Q6VDecHlYRzhKzh/HChnBwoVq+GUq2GbP9+87CxTh1ox4+HJjoaxlatXBig+88Ph/XZbtmyJQRBQIsWLTBixAg8/fTT8Pf3d0iQFYE7TwLA/Sc6lQ3nB5WEc4Ss4fwoZ6II6f79ps2Oq1dDePDANCyRQDdoELQqFXSDBwOPusO5mrvPD4cl2x999BE2bNiAe/fuQRAESCQSdO/eHVFRURg8eDA8PT0dErCruPMkANx/olPZcH5QSThHyBrOj/Ih3LgBRWKiabPj+fPmcUPz5qYykXHjIAYEuDBCy9x9fjj0BEm9Xo+dO3ciKSkJ27dvh0ajgSAI8PDwwIABAxAVFYXw8HBzz+3KxJ0nAeD+E53KhvODSsI5QtZwfjiRTgf5pk2mzY6bN0MwGAAAopcXtCNGQBMTA0P37oAguDjQ4rn7/HDace05OTnYuHEjkpOTcfDgQRiNRgiCgNq1a2P48OGIiopCmzZt7AraFdx5EgDuP9GpbDg/qCScI2QN54fjSc6eNZWJLFsGya1b5nF9t27QxMRAO2IE4OPjwght5+7zw2nJdkEZGRlYu3YtkpOT8eejHo6CIKBp06YYMWIEIiMjEVAB/6xRkDtPAsD9JzqVDecHlYRzhKzh/HCQ7Gwofv3VtNnx0CHzsLFuXWgnTDBtdgwOdmGA9nH3+VEuyXZB58+fx+rVq7F+/XqkpaWZ67v/+OMPR72FU7jzJADcf6JT2XB+UEk4R8gazo8yEEXIUlKgiI+HIikJwsOHpmGpFLohQ0ybHQcOBCpBZ7fiuPv8sCXZtqvPdnGaN2+O5557DgEBAfjmm2+QmZkJo9HoyLcgIiIiqtSEtDQoly6FQq2G9NIl87ihRQtTmci4cRDdqOtbVeeQZFur1eL3339HcnIydu/eDb1eD1EUUaNGDURERDjiLYiIiIgqL40G8g0bTGUiW7dCeLQYKXp7QztypGmzY9euFXqzI9mnTMl2SkoKkpOTsXnzZjx48ACiKEKhUGDQoEGIiopCnz59KsWhNkRERETOIDl9Gsr4eNNmx7t3zeO6nj2hVamgjYoCvLxcGCE5W6mT7bNnzyI5ORnr1q3DzZs3IYoiBEFAp06dMGLECAwbNgw+lWSHLBEREZGjCVlZkK9caVrFPnrUPG4MCIBmwgRoo6NhbNbMhRFSebIp2b5x4waSk5OxZs0anH/USF0URTRu3NjccaR+/fpODZSIiIiowjIaIdu927TZce1aCHl5AABRLodu6FBoYmKg79cPkDl0uxxVAjZ9x/v37w9RFCGKImrVqoWIiAhERUUhNDTU2fERERERVVjC9etQJiRAkZAA6dWr5nFDq1amzY5jx0KsU8eFEZKr2ZRsy2QyDBgwACNGjMBTTz0FqVTq7LiIiIiIKqa8PMjXrTOViezYAeFRF2XRxwfaMWOgUalg6NiRmx0JgI3J9t69e+Ht7e3sWIiIiIgqLOmJE1Co1VAsXw7JvXvmcV3v3qbNjsOHA56erguQKiSbkm0m2kRERFQVCZmZUCxfDoVaDdnJk+ZxY1AQNBMnQqtSwdiokQsjpIqOVfpEREREBRkMkO3YAaVaDfm6dRC0WgCAqFBAN3w4NCoV9H36ACyrJRsw2SYiIiICILl8GYqEBCiXLIEkNdU8rm/bFtqYGGjHjIFYq5YLI6TKiMk2ERERVV0PH0Kxdi0UajXkO3eah401a0I7diy0KhUM7L5GZcBkm4iIiKoWUYT06FFTmcjKlZBkZ5uGBQH6Pn2gUamgGz4c8PBwcaDkDphsExERUZUg3L79eLPj6dPmcUPDhtBGR0M7cSKMDRq4MEJyR0y2iYiIyH3p9ZBt2wZlfDzkGzZA0OkAAKJSCW1kJLQxMdCHhwMSSbGPMBiAlBQZMjIE+PuLCAvTO2RvpLOeSxWLTcl2Wlpamd4kMDCwTK8nIiIiKg3JxYuPNzump5vH9R07mspERo+GWLNmic9Zs0aOWbM8kZb2OBkPDDRizpxcREbq7I7PWc+lisfm49oFO09BEgQBpwv8qYaIiIjIKR48gCI52bTZce9e87CxVi3TZseYGBjatLH5cWvWyBEb64VHB0SapacLiI31QlzcA7sSY2c9lyomm5Ltrl27FhnT6XQ4duwYAKBGjRrm1eu0tDRkZWVBEAS0b98ecrnccdESERERFSSKkB46BGV8PBS//gohJ8c0LJFA37+/aRV76FBAqSzVYw0GYNYsz0cJceEFR1EUIAgi3nnHExERWaUq/XDWc6nisinZXrx4caGvc3Jy8Oyzz6JFixZ466238NRTTxW6vnv3bnz66afQ6XT48ccfHRctEREREQDh5k0oEhOhVKsh/esv87ihSRNoVSpoxo+HGBRk9/NTUmSFSjyeJIoCUlMFpKTIEB6ud/lzqeKya4PkV199hWvXrmHDhg2oZaG5e3h4OFq3bo2hQ4fiyy+/xHvvvVfmQImIiKiK0+sh37IFivh4yDdtgqA3JaNitWrQjhgBrUoFfViY1c2OtsrIsK181tb7nP1cqrjsSrY3b96MHj16WEy089WqVQs9evTA5s2bmWwTERGR3SR//QVlQgIUiYmQZGSYx/WdO0MTEwPtqFFA9eoOfU9/f7Hkm0pxn7OfSxWXXcn23bt3odeX/KcNvV6PzMxMe96CiIiIqrL796FISoJSrYZs/37zsLFOHWjHj4cmOhrGVq2c9vZhYXoEBhqRni5AFIuuMguCiMBAU7u+ivBcqrjsSraDgoKQkpKC9PR0BAQEWLwnPT0dKSkpCCpDvRQRERFVIaII6f79ps2OSUkQHjwwDUsk0A0aBG1MDHSDBwPl0HxBKgXmzMlFbKwXBEEslBgLgmnVefbs3FJvYnTWc6nisquoacyYMXj48CFiYmKwevVqaDQa8zWtVovVq1cjJiYGeXl5GDNmjMOCJSIiIvcj3LgB5VdfoXr37qgeEQFlQgKEBw9gaN4cuR9+iKyTJ/FgyRLTEerl2OUsMlKHuLgHCAgoXNIRGCiWqT2fs55LFZMgik92eSyZ0WjEG2+8gfXr15v7b+fXb9+9excAIIoihg4dii+++AISB2xUcCZ3L3Xx9fV1+89I9uP8oJJwjpA1ds8PrRbyTZtMPbG3bIFgMAAARC8vaEeOhEalgqF7d8DOcz4ciSdI2s/df374+vqWeI9dyXa+9evXIyEhAcePH4fu0fGncrkc7du3x8SJEzF8+HB7H12u3HkSAO4/0alsOD+oJJwjZE1p54fk7Fko1WrTZsfbt83j+u7doVGpoB0xAvDxcUao5ALu/vPDlmTbrprtfBEREYiIiIBer8e9e/cAADVr1oRMVqbHEhERkTvJzobi11+hjI+H7PBh87Cxbl1oJ0yARqWCsUULFwZI5DwOyYplMhnq1KnjiEcRERGROxBFyPbuhUKtNm12fPjQNCyTQTdkCLQqFXQDBpRrDTaRK5Qp2dbr9di+fTtOnjyJzMxMhIaGmjdEZmRkIDMzE82bN+dKNxERURUhpKZCuXQpFAkJkF66ZB43BAebykTGj4dYt64LIyQqX3ZnwYcOHcJbb72F9PR0iKIIQRCg0+nMyfaxY8fw+uuv46uvvsLgwYMdFjARERFVMBoN5Bs2mMpEtm2DYDQCAERvb2hHjzZtduzSpUJsdiQqb3Yl2+fPn8fzzz8PnU6HmJgYdO7cGa+//nqhe/r16wcPDw9s3LiRyTYREZEbkv7xB7BiBWosXgzJo25kAKDr2RNalQraqCjAy8uFERK5nl3J9vz586HRaLBgwQKEh4dbvEehUKBNmzY4c+ZMmQIkIiKiikPIyoJ85UrTKvaxYwBMh3YYAwKgmTgR2okTYWzWzKUx5qsKrfWo4rMr2d6/fz9CQ0OLTbTz+fv74+zZs3YFRkRERBWE0QjZrl2mzY5r10LIywMAiHI5hKgo3B83Dvr+/VGRMtk1a+SYNcsTaWmPz/oIDDRizpxcHhpD5cquZDs7Oxv16tUr8b7c3Fzo9Xp73oKIiIhcTHLtGhQJCabNjteumccNrVpBExMD7dixqNmiBfQVrI/ymjVyxMZ64cmTRNLTBcTGevGURipXdiXbtWvXxtWrV0u87+LFizYl5URERFRB5OVBvm4dlGo1ZDt2QHiUsRqrV4d2zBhoVSoYOnSosJsdDQZg1izPR4l24RhFUYAgiHjnHU9ERGRVpIV4cmN2Jds9evRAUlIS9u3bhx49eli8Z/Pmzbhy5QpUKlWZAiQiIiLnk544YSoTWb4ckkcH1QGArndv02bH4cMBT0/XBWijlBRZodKRJ4migNRUASkpMoSH86/v5Hx2JdvPP/881q9fj1deeQX/93//h0GDBpmvZWVlYfPmzfjkk09QrVo1xMbGOipWIiIiciDh7l0oVqyAQq2G7ORJ87gxKAia6Ghoo6NhbNTIhRGWXkaGbSvutt5HVFaCKD5Z0WSbLVu24M0330Teo00ST1Iqlfj8888xYMCAMgVYHjIrWK2Zo/n6+rr9ZyT7cX5QSThH3IzBANmOHVDGx0O+fj0ErRYAICoU0A0fDk10NPR9+9q82dHW+WFPZxB7XrN7twxRUT4lxpOcfJ8r2+XA3X9++Pr6lniP3YfaDBw4EGvXrkVcXBz27t2L1NRUGI1G1KtXDz179sTUqVPRsGFDex9PREREDiS5fBmKhAQolyyBJDXVPK5v1w7amBhox4yBaEPiYA97OoPY200kLEyPwEAj0tMFiGLR1WtBEBEYaErcicqDXSvbv//+O2QyGfr06eOMmMqdO//GBbj/b5VUNpwfVBLOkUrs4UMo1q6FIj4e8l27zMPGmjWhHTvWtNkxNLRMb1HS/CjcGeRx8isIpvTDUmcQe15j6fUACiXctr6eHMfdf37YsrJtV7LdqlUr9OrVCz/++KNdgVU07jwJAPef6FQ2nB9UEs6RSkYUIT16FEq1GvKVKyHJzjYNCwL0fftCo1JBFxEBeHg45O2szQ+DAWjfvgbS0gQ82RkEeLzKfOzY484g9rzGEksr40FBRsyezT7b5cndf344rYykVq1aqFGjhj0vJSIiIicQbt+GYtkyKNVqSAuc3mxo2BDa6GjTyY4NGpRrTPZ0BnFUN5HISB0iIrJ4giS5nF3Jdrdu3XDixAmIogihgvbZJCIicnt6PWTbtpk2O27YAEFnWrEVlUpoIyOhjYmBPjwckBSfvDqTPZ1BHNlNRCoFN0GSy9mVbP/tb3/DmDFjMHv2bLzxxhtQKpWOjouIiIiKIbl4EQq1GsqlSyFJTzeP6zt2NJWJjB4NsWZN1wX4iL+/bZWqBe+z5zVEFZldyfbatWvRp08fxMfHY/369QgLC0NgYCAUCkWRewVBwCuvvFLmQImIiKq0Bw+gSE6GQq2GfO9e87CxVq3Hmx3bti23cPLb8uXkAN7eMoslGvZ0BmE3EXI3dm2QbNmyJQRBgC0vFQQBZwrUjlVE7ly4D7j/5gQqG84PKgnniAuJIqSHDkEZHw/Fr79CyMkxDUsk0Pfvb1rFHjoUKOe/MJemLZ89nUHYTcR9uPvPD6d1I/n1119Ldf+oUaNK+xblyp0nAeD+E53KhvODSsI5Uv6EmzehSEw0bXb86y/zuKFxY2hVKmgmTIAYFOSS2Oxt5VfaziDsJuIe3P3nh9OSbXfjzpMAcP+JTmXD+UEl4RwpJ3o95Fu2mMpENm6EoDeVSYjVqkE7YgS0KhX0YWFO3exY0omNZWnLV14nSFLF4u4/P5x6giQRERGVneTcOSjVaigSEyHJyDCP6zt3hiYmBtpRo4Dq1Z0ehy2lIWVpy2dPZxB2EyF3UKZkW6/XY/v27Th58iQyMzMRGhqKMWPGAAAyMjKQmZmJ5s2bQyZjTk9ERGR2/z4USUlQqtWQ7d9vHjbWqQPt+PHQREfD2KpVuYVTuDTksfR0AbGxXubSEEe25SOqKuzOgg8dOoS33noL6enp5n7bOp3OnGwfO3YMr7/+Or766isMHjzYYQETERFVSqII6f79ps2OSUkQHjwwDUsk0A0aBG1MDHSDBgEWOns5k8EAzJrlWaQG2xSyAEEQ8c47noiIyGJbPiI72JVsnz9/Hs8//zx0Oh1iYmLQuXNnvP7664Xu6devHzw8PLBx40Ym20REVGUJN2483ux4/rx53NCsmalMZNw4iAEBLouvNKUhbMtHVHp2Jdvz58+HRqPBggULEB4ebvEehUKBNm3aVPi2f0RERA6n1UK+aZNps+OWLRAMBgCA6OUF7ciR0KhUMHTvDpThFGZbNw+WdF9pSkOkUmDOnFzExnpBEESLbflmz87lJkaiAuxKtvfv34/Q0NBiE+18/v7+OHv2rF2BERERVTaSM2dMmx2XLYPk9m3zuL57d2hUKmhHjAB8fMr8Prb2ubblvtKWhkRG6hAX9+DRcx8n24GBItvyEVlgV7KdnZ2NevXqlXhfbm4u9Hr7/pTUv39/pKamWrzWrVs3LF682Pz1qlWrMGvWrGKf9csvv6B79+52xUFERGRVdjYUq1aZNjsePmweNvr7QzthgmmzY4sWDns7Wzcz2nqfPaUhkZE6RERkPTpB0gfe3vfZlo+oGHYl27Vr18bVq1dLvO/ixYs2JeXF8fHxwbPPPltkPKiYRv4DBgxAKwu7t4u7n4iIyC6iCNnevVCo1abNjg8fmoZlMuiGDIFWpYJu4EDAQjcuW8o/irvH1s2MQ4Zk2bzp0d7SkPy2fL6+QGYma7SJimNXst2jRw8kJSVh37596NGjh8V7Nm/ejCtXrkClUtkdXPXq1TFjxgyb7x84cCBGjx5t9/sRERFZI6SmQpmYCIVaDemlS+ZxQ3Dw482OdesW+3pbyjqs3ePrK9q0mfGnn5Sl6ofN0hAi57Er2X7++eexfv16vPLKK/i///s/DBo0yHwtKysLmzdvxieffIJq1aohNjbWUbESERGVP40G8g0bTGUiW7dCMBoBAKK3N7SjR5s2O3bpUuJmR1vKOgBYveeFFzQ2hXzpkm2nTBbcHFmwNIQnNhI5jl3JdrNmzfDFF1/gzTffxMcff4yPP/4YgiBg9erVWL16NQBAqVTi888/R4MGDewOTqvVYtWqVbh58ya8vb3Rrl07tG/fvtj7T58+jXv37kGv16N+/foICwuz6RhNIiKiJ0n/+AOK+Hgoli+H5O5d87iuZ09oVSpoo6IALy+bnmVL+cesWZ6Pvi7+nhUrbOvB3aSJ0ab7ntwcyRMbiRxPEMUnf3+2XWpqKuLi4rB3716kpqbCaDSiXr166NmzJ6ZOnYqGDRvaHVhxGyTbtWuHL774otCzi9sg6eHhgVdeeQXTp0+3+l5GoxESiW2rAERE5Mbu3QOWLAF++gkosNkRgYFAbKzpP3Zsdty+HejXzzEh+vkBt2+jyOo3YFpcr18fOH8eaNYMSE21ft+lS+DKNZGTlSnZdqZvvvkGnTt3RnBwMDw9PXH58mUsWrQISUlJCAoKQnJyMry9vQEABw4cwF9//YXw8HDUq1cPWVlZSElJwRdffIGMjAy89957mDRpUrHvlZmZWV4fyyV8fX3d/jOS/Tg/qCRuP0eMRsh27TJtdly7FkJeHgBAlMuhGzYMGpUK+v79y5SVrlwpx/PPezsk3Jdeeojvv/cwxWhhM+OT3UhKuq+s3H5+UJm4+/ywpYKiwibbxXnrrbeQlJSEt99+G1OmTLF677lz5/DMM8+gWrVq2LNnD2QWdoUDTLapauP8oJK46xyRXLsGRUICFAkJkF67Zh43tGpl2uw4dizEOnVK/VxLnURSUmSIiip7f20ASE6+j8xMocgmyqAgY5HNjJY2W1q6ryzcdX6QY7j7/LAl2barZtuVxo8fj6SkJBw5cqTEZLtFixbo3Lkz9u7diwsXLiAkJKScoiQiogopLw/ydetMmx137IDwaL3JWL06tGPGQKtSwdChg9XNjtZa9xXXSeTf/84tsZd1QIApFlv6XUulsGkzIzc9ErmeTcm2pd7VthIEAadPn7b79U/K/w0iNze3VPc/fNQDlYiIqh7piROmMpHlyyG5d888ruvd27TZ8emngWrVSnyOtbZ8QPGdRKZO9cKrr+bhm288iu1lXfAZtvS7tnUzIzc9ErmWTcl2QECAxfG0tDTz/65evToA0+mS+QIDA8sSm0UnTpwAYNtBNQaDAadOnXJaLEREVHEJd+9CsWIFFGo1ZCdPmseNQUHQREdDGx0NY6NGNj/PWuu+Z5/1gq+vaLWTyKpVSixc+ADvvmu9lzX7XRO5F5uS7a1btxb6WqfT4bXXXoNer8fLL7+Mp59+2rxZMScnB+vWrcP8+fMREhKCefPmlTqoCxcuIDAwENWeWGW4cOECPvvsMwBAZGSkefzUqVNo27ZtoXsNBgM+++wzXLlyBd27d0ddK4cMEBGRmzAYINuxA0q1GvJ16yBotQAAUaGAbvhwaGJioO/du9SbHUtq3QeIyMws+RCZ2rVFHD9uvayDpR9E7sWumu3vv/8e+/btQ3JycpE+2t7e3hg/fjx69uyJyMhIfPvtt/jb3/5WquevX78eixYtQteuXc1J9+XLl7Fz507odDq88MIL6Nq1q/n+Z555BiEhIQgJCYG/vz+ysrJw4MABXL58GfXq1cO///1vez4mERFVEpLLl6FISIByyRJICrSN1YeGmspExoyBaOO5C8VtcLR2IuOTCXhxMjIEm8o6WPpB5D7sSraTk5PRvXt3qwfWNGjQAD169MCaNWtKnWx3794dFy5cwJkzZ3Do0CHk5eXB19cXvXv3RnR0NMLDwwvdP3XqVBw7dgx79+5FVlYW5HI5GjZsiJdeeglTpkxBjRo17PmYRERUkT18CMWaNVCo1ZDv2mUeNtasCe3YsabNjqGhpXpkcTXZUVFah4T85CEyROT+7Eq2MzIybNo0qVAocPPmzVI/v1u3bujWrZvN98+cObPU70FERJWQKEJ69KipTGTlSkge7RMSBQH6vn2hUamgi4gAPDxK/WhrNdnff6+0NUBYWuUu2EmEiKoWu5JtPz8/7N+/H9nZ2eaNkU/KysrC/v37UceOHqVEREQFCbdvQ7FsGZRqNaRnzpjHDQ0bQhsdDU10NMT69e1+vi012RKJaQNkcW35fH1FZGaa7i2pkwgRVR12nVH+9NNPIysrC1OmTMHBgweLXD906BCmTZuG7OzsQhsZiYiIbKbXQ7Z5M7wmT0aNNm3g+d57kJ45A9HDA5qxY3F/9WpkHzmCvLfeKlOiDaBATXZxtdcCjEYBovg4eTZfefT1f/+bi7i4B+Z+2fkCA0WHndZIRJWPXSvbL7/8Mg4dOoTDhw9j8uTJqF27trm1XlpaGu7cuQNRFNGpUye8/PLLDg2YiIjcm+TCBdNmx6VLIUlPN4/rO3UylYmMHg3RwXtxMjJs2+D40kt5SEpSWm3Lx04iRFSQXcm2UqlEXFwcFi1ahCVLliA9PR23b982Xw8ICMDEiRMxZcoUyOVyhwVLRERuKicHiuRk02bHlBTzsLFWLWjHjoVm0iQYW7d2yFtZ6jZi68bFYcP0+Ne/8qwm0+wkQkQF2X1cu1wux/Tp0zF9+nSkp6ebN0L6+fnxABkiIiqZKEJ68CCUajUUv/4KISfHNCyRQD9ggGkVe+hQQKEo1WOddZx6waPSmUwTka3sSra7deuG4OBgxMfHAzCtZBd3yiQREVFBws2bUCxdatrseO6cedzQtCm0KhU048dDtHPRxpnHqXODIxHZw65kW6/Xw9/f39GxEBGRu9LpIN+yxVQmsnEjBIMBACB6ekIbFQVtTAz0YWGA8DjJtbZCbena+vXlc5w6EVFp2JVst2jRwq7+2UREVLVI/voLyoQEKBITIcnIMI/ru3SBRqWCdtQowEIL2ZJWqJ+8FhBgRF4eyuU4dSKi0rAr2Y6JicHMmTNx6NAhdOnSxdExERFRZXb/PhRJSVCq1ZDt328eNtapA+24cdCoVDBaORjN2uEyzz7rZfE16ekCrB+Z7tjj1ImIbGVXst25c2eMGTMGzz33HMaMGYP+/fsjICAASqXlE7a4YZKIyM2JIqT790MZHw9FUhKEBw9MwxIJdIMGQRsTA92gQSVudrTlcBmTJ5Nn25LpkvA4dSJyNLuS7f79+0MQBIiiCLVaDbVaXey9giDg9OnTdgdIREQVl5CeDkViommz44UL5nFD8+amMpFx4yCWYgP948Nlin3HMkQL8Dh1IipvdiXbXbt2dXQcRERUWWi1kG/aBEV8PORbtkAwGgEAopcXtCNGQBMTA0P37oU2O9rK1sNlSovHqRORq9iVbC9evNjRcRARUQUnOXPG1BN72TJIChxkpuvRA1qVCtoRIwBv7zK9h2PKOAqvXhc8Th3I31zJbiNEVD7sPtSGiIiqgOxsYNky+CxYANmRI+Zho78/tBMmQBMdDWOLFg57u7AwvdXDZYqv2X68eu3hAR6nTkQVRpmS7WvXriEzMxMA4OvriwYNGjgkKCIiciGjEbK9e6GIj4dizRrg4UPIAIgyGXRDh0IbHQ3dwIGAzPHrNVIpMGdOLmJjvSweLpPfoaS4g2f++99cREToeJw6EVUYpf5JeeLECSxatAh79uzB/fv3C13z8fFBeHg4YmNjERoa6rAgiYjI+YTUVCiXLIEiIQHSy5cfX2jVCrkTJ5o2O9at67D3K+7QmshIHeLiHhRb7gGUXArCZJqIKgpBFJ/sZFq8//znP/j5559hfLQZRi6Xo0aNGgCArKws6HSmH3ISiQTPPvssZs6c6YSQHS9/dd5d+fr6uv1nJPtxflRxGg3kv/1m6om9dSuER/+XIHp7Qzt6NDQxMag+cCAy792z6/HFJdTWDq3JT5hLe4IkS0Fcgz9DyBp3nx++vr4l3mPzyvacOXPw888/Q6lUIjo6GlFRUQgODob00U83g8GAc+fOITk5GQkJCYiLi4PBYMA777xj/ycgIiKnkJ46ZSoTWb4ckgL/R6jr1cu02TEyEvB6dICMHV1FgOIT6mee0eCbbzwsHloTG+uFuLgHiIzUWS33YCkIEVUWNq1sHzt2DBMmTEBAQAB+/PFHNGvWzOr9Fy9exNSpU5GRkYGlS5eiffv2DgvYGdz5Ny7A/X+rpLLh/Kg6hHv3oFi5Eor4eMiOHzePGwMCoImOhnbiRBibNi3yupLmiKVV5vXrC54CWTBZL/h/OcX3uz52LIsr1ZUEf4aQNe4+Pxy2sr106VIIgoDPP/+8xEQbAJo2bYovvvgC0dHRlSLZJiJyW0YjZDt3QqlWQ752LQSNBgAgyuXQDR0KTUwM9P37w97M1tLqdUCAEXl5sHgKZEmH0oiigNRUASkpMq5cE5FbsCnZPnjwIEJCQtCpUyebH9ypUye0bNkS+/fvtzs4IiKyj+TaNSgSEkybHa9dM4/rW7eGNiYG2rFjIdaubfPzSl69fiw9XUBZT3p01uE2RETlzaZk+/bt2+jQoUOpH960aVP8/vvvpX4dERHZIS8P8nXrTJsdd+wwb3Y0Vq8O7Zgx0KpUMHToUGwNdnGbDletAmbMqOGw1WtbOOZwGyIi17Mp2VYqlXj48GGpH56XlweFQlHq1xERke2kx49DoVabNjtmZZnHdX36QBsdDe3TTwPVqll9hvXNjChywIwjVq8tya/ZDgtjCQkRuQebku0GDRrg6NGjMBgM5u4jJTEYDDh69CgPuiEicgLh7l0oVqyAQq2G7ORJ87gxKMi02TE6GsZGjYq8rjTlIGlpAubN88h/xycjKEP0pjcSBFg8mGb27FxujiQit2FTst23b1/Mnz8fP/zwA1588UWbHvzjjz/i3r17UKlUZQqQiIgeMRgg277dtNlx/XoIWi0AQFQooBs+3LTZsXfvYjc7Onozo23EQs/JT6hffTUPK1cqrR5MQ0TkDmxq/ZeVlYVBgwYhJycHr776Kl544YViV7gNBgMWLFiAr7/+GtWrV8emTZvMB99UVO7ckgZw/7Y7VDacHxWf5PJlKBISoFyyBJLUVPO4PjTUVCYydizEEtpPrVljrRWfc8pBfH1FeHigUHIfFGQ0J9Q8mMY98GcIWePu88OW1n82nyCZkpKC6dOnQ6/Xo27duhg6dCjatm2LWrVqAQDu3r2LU6dOYePGjcjIyIBMJsOCBQsQFhZWtk9RDtx5EgDuP9GpbDg/KqjcXCjWroVCrYZ81y7zsLFmTWjHjYM2OhqG0FCbHmUwAO3b13i0iuyMLh+WV6/j4h4gIkLHhNrN8WcIWePu88OhyTYAnDhxAm+//TYuXrwIwcJu9vxHNW3aFP/5z3/Qrl27UoTrOu48CQD3n+hUNpwfFYgoQnr0KJRqNRQrVkC4f980LAjQ9+0LjUoFXUQE4OFRwoMK271bhqgoH4eHa8vqNbk//gwha9x9fjj0uHYACA0Nxfr167Fjxw7s2LEDZ8+exb179wAANWvWRMuWLdGnTx/07t3bYjJORERFCbdvQ7FsGZRqNaRnzpjHDQ0bQqtSQTNxIsT69W1+3pPlGabOIfYyrVoLgmhxM+N//5vL1WsiIitKlWzn69OnD/r06ePoWIiIqg69HrJt26BcvBjyjRsh6EyrwKKHB7SRkciLjsFOoQ8ybknhf1lEWEDhBLa4emdLmyBr1zbaGJTlcpA33gDUatHqZkae9khEZJldyTYREdlHcuGCabPj0qWQpKebxzNbdIJ8ugr6MaORvLMOZr1StOf1nDmm5NZ6T2yPIi387twRkN9uz1LNduFykKIJ9eTJ3njrrSyuXhMR2aFUNdvuyp1riQD3r5eisuH8KAcPHkCRlGTa7JiSYh6+K6mNn42TsAhTcBKhFhJmyy3zLF1/nEw/OV74enG9ra1tZuQcIWs4P8gad58fDt8g6a7ceRIA7j/RqWw4P5xEFCE9eNC02fHXXyHk5JiGJRKkth2I1088j2REQgdlwRcV+N+WE2aJBDAai7testq1jbhzp3SbGTlHyBrOD7LG3eeHwzdIEhGRdUJGBhSJiabNjufOmccNTZpAq1Lh4djx6D6sNdJgqQ1fSQm08CjRtt/s2bkICBBZDkJEVE6YbBMRlZVOB/mWLaYykY0bIRgMAADR0xOayBE40n4STtcJh389wHipcJu88hYQIHIzIxFROWKyTURkJ8lff5nKRBITIbl50zyu79IFmpgYJHuMxRv/qoe0xMfJdc2aZVyatpMgiAgMNK1kExFR+WGyTURkxZMt9nq2y4RH8moo4+MhO3jQfN9DHz+kDpyI2m9MBFqFPHE8+mP37pWt57VEAohi4U2OBa8DxW+CnD07lyUjRETljMk2EVVpxfWrBgr2rBYQjt2YioWoJiyDp5gLADBKpNisiMD8vGlYfz8C+l/lCNxvxL//nYt33/W00DEk/+vi2/CVlDC/8oqpG0lxh8y8+moeVq5UWu2JTURE5YfJNhG5NduS6aL9rAFg1rNZmIR5mIpFCMajzY4icBYh+LPnJLy4dypu5NVDwaQ5PV3AlClesL7ZMf+a5UNkSkqYu3QxmH8JsHT9gw/y2BObiKiCYOs/sPUfVW3uPD9KSqYfl3k8TloV0GA41uIF+UIM1G2AFKYa6xx4YSkmYCGmIgU9IJEIVlrwicWMF+bra0RmpuU2fNZ+SQCs/xLhaO48R6jsOD/IGnefH2z9R0RVVnE10+npAp591gu+vmKhRLs1/sBULMQkLEZd3AIeVVzsQjgWYiqWYywewNv8HOst+Gyry1648AGkUlhMmKVS60egl3SdiIgqBibbRFSpWVrhBYBZsyzXTJvqnEVkZkpQHVkYj0RMw0/ojgPme9IQgJ/xLBZhCs4huAzRWV7hzu8MEh7O8g4iInfHZJuIKq3iykQmT9YU28tagBG9sRNTsRBjsAKeeAgA0EGGNYjEIkzBbxgGg4N+PBa3kZGdQYiIqgYm20TkULbWEttyX0mbG4srE5k716PI+9XHNTyLnzEFi9AMF83jf6A1fsI0xCMGt1D3iVcVV3ttvQVf/sr1//t/pq4k7AxCRFR1MdkmIoextiGxYHJpy33W7omI0JVYJgKYNjtGIRlTsRBDsBGSR+PZ8MESTMRCTMEBdC/yDEEQ4esrIjPT9Cx7WvDlJ9RPP53FziBERFUYu5GA3UioarNlftiyCl14pblo8hkX9wCRkTqb7gMsdwrJv2fmzDzMnVut2HhDcRxTsRAxiEdt3DWPb0NfLMIUrMQz8KhV7VEybbmfdX4cTyb8BTuGWPqFoOB1d8GfIWQN5wdZ4+7zw5ZuJEy2wWSbqraS5octq9AGA9C+fY1H5RLFl1UcPpyFTp2s3xcQYPqRZO2emjXFQi3zAKAmMjERSzAVC9EFh83j1xGEOMQiDrG4gOalSqbzP1tFacHnKvwZQtZwfpA17j4/2PqPiMrEWl10bKyXebU6JUVW7IZEwLRynJoq4KeflCXeV7C+ubh78lekBRjRD9swDT9hNFbBAxoAgBZyJGEEcsaq8MHu4bieLje//sma6YgI62UebMFHRERlwWSbiCwyGKy3zxMEEe+844mIiCxkZNjWV/rSpeIT7dJoiCt4yWMRJuTFoTGumMdPoB1+wjQkIBrKoNo4Nj8LkcgpUzJNRERUFky2icgiW1erU1Jk8Pe3rRqtSROrJ8FY5YGHGInVmIqFGIDfIckzvec91EACorEIU3AIXSA8yvvjZj8wJ9VMpomIyFWYbBNVUfm1xjk5gLe3rMiKr62r1RkZAkaO1CEw0Ij0dMFqK7xp0zT49lsPq/fl12yb7gE64QimYiGikQBf3DPfq+3dB/tbT0Zs0nhcTPcyjwcGut8GRSIiqryYbBNVQUU3PfoU2fRo62q1v78IqRSYMycXsbFeVlvhKRQl3zdnTi6UOXew9xXTKnZ7nDDfcwUNEYdYtPtsLPpNDUJbAPs/1iIlxejWGxSJiKjyYjcSsBsJVS22tujL7zBS0mr1sWNZhQ6asaUVnqX7GgTqsHDiWvQ+/zPkv/0GQasFAORBidUYiZ8wDWcD++Hfc/K4al3O+DOErOH8IGvcfX6w9Z+N3HkSAO4/0cl2trboy0+g8xNzoPhe1E8mvqU9QTL35CV0PB6PZrvVkKalma/r27dH3kQVdjcYh+u5tblq7UL8GULWcH6QNe4+P9j6j4gKKc2mx/BwPSIjdYiLe/BoFdq2I8dt6u6Rm4tqa9ZgqFoN+e7d5mFjzZrQjhsHrUoFQ7t2AIDuALqDK9lERFQ5MdkmchO2rCiXZtNjvshIXYm9qG0iipAeOQKlWg3FypUQ7t83DQsC9H36QBMTA11EBODhUcoHExERVVxMtoncgC2nPAKl2/RYUFl6UQu3b0OxbBmU8fGQnj1rHjc0agRtdDQ0EydCrF/frmcTERFVdEy2iSo5W095BICwML1NLfrCwsrYl1qvh2zrVijj4yHfsAGC3vQ80cMD2shIaGNioO/VC5A45pAbIiKiiorJNlElVppTHqVS2Nyiz95NiJILF6BISIBy6VJI0tPN4/pOnaBRqaAbPRpijRr2PZyIiKgSYrJNVImVdsMjALs2PVr14AEUSUlQqNWQp6SYh421a0M7diw0MTEwtm5dumcSERG5CSbbRJWYPRsegcKbHnNyfODtfb90mx5FEdKDB02bHX/9FUJOjmlYIoF+wADTKvbQoYBCUZqPQ0RE5HaYbBNVQLb2qrZ3wyPweNOjry+QmWlbjbaQkQFFYiKUajWk5849jrdpU2hVKmjGj4cYGGjTs4iIiKoCJttEFYytnUWActrwqNNBvmULFPHxkG/aBMFgAACInp7QjhgBrUoFfVgYINi2yk5ERFSVMNkmcgJbV6afVJrOIoBzNzxK/vwTyoQEKBITIbl50zyu79oVGpUK2pEjgerVS/9gIiKiKoTJNpGDlWZluqDSdhbJ59ANj/fvQ/Hrr1Cq1ZAdPGgeNvr5QTt+PDTR0TC2bGn784iIiKo4JttEDlTalemC7Okskq9MpzyKImQpKVDEx0ORlAQhN9c0LJVCN3gwtCoVdIMGAXK5DQ8jIiKigphsEzmIvSvT+eztLJKvtKc8CunpUC5dCixZAp/z583jhhYtTGUi48dD9Pe3+XlERERUVIVNtvv374/U1FSL17p164bFixcXGtNqtViwYAGSk5ORnp6OGjVqoF+/fnj99ddRu3bt8giZqriyrEwDZessYjOtFvKNG009sbdsgWA0mmLz9oZ25EhoVCoYunXjZkciIiIHqbDJNgD4+Pjg2WefLTIeFBRU6Guj0YiXXnoJu3fvRocOHTB48GBcuXIFy5cvR0pKCpYtW4ZatWqVV9hURZV1ZdqZnUUkZ86YemIvWwbJ7dvmcV2PHpBPn457AwcC3t6lfi4RERFZV6GT7erVq2PGjBkl3vfrr79i9+7dePrpp/HZZ59BeLQqt2TJEnz00Uf48ssv8a9//cvZ4VIVV9aVaYd3FsnOhmLVKijj4yE7csQ8bKxXD5oJE6CNjoaxeXP4mhpt2/hQIiIiKo3i/+ZdiSxfvhwA8I9//MOcaAPAhAkT0KBBA6xZswZ5eXmuCo+qiPyV6fzE+EmCICIoyGh1ZTq/s0hAQOFnBAaKVjdXmhmNkO3eDc+XXkLNVq3g9Y9/QHbkCESZDNqnn8b9pUuRdeIE8j74AMbmzUv9GYmIiKh0KvTKtlarxapVq3Dz5k14e3ujXbt2aN++faF7NBoNjh8/jiZNmhQpLxEEAT179kRiYiJOnTqFLl26lGf4VAnZ2x8bcNzKtD2dRYTUVCiXLIEiIQHSy5cff56QEGhiYqAdNw6in59tH4SIiIgcpkIn27du3cKsWbMKjbVr1w5ffPEFGjZsCAC4evUqjEYjGjdubPEZ+eOXL18uNtmuUaMGJBK3WOQvlq+vr6tDcCiDAdi1C0hPBwICgKeegl0HtxS0ahXwt78B168/HqtfH/jqK2D0aNueMXmyqfS56HMEfPklMHq07XXRkZEl3KDRAMnJwMKFwMaNMPcbrF4dmDgRmDoV0q5d4SkI8CzhUe42P8jxOEfIGs4Psqaqz48Km2yPHj0anTt3RnBwMDw9PXH58mUsWrQISUlJiI2NRXJyMry9vXH//n0AgHcxm7vyx3Nycop9r6ysLMd/gArE19cXmW5Uk2vvoTElPfNxf+zHK9KpqSLGjIFtJRyP9OsHHD1qeYXcEd8G6alTpp7Yy5dDUuCBuvBwaFUqaCMjAc9H6fW9eyU+z93mBzke5whZw/lB1rj7/LDlF4kKm2y/+uqrhb5u1aoVPvnkEwBAUlISli9fjilTprgiNHKhshwaU5yy9se2pLQ9r0si3LsHxYoVUKjVkB0/bh43BgZCM3GiabNjkyYOez8iIiJyjEpXOzF+/HgAwJFH3RV8fHwAFL9ynT9e3Mo3VR4lJcUA8M47njAYSvfcx/2xLbfkM/XHliAlpZx/NzUaIdu+HV7PP48arVrB8623IDt+HKJcDu2IEbi/bBmyjh9H3rvvMtEmIiKqoCrsynZx8pfrcx8dKd2gQQNIJBJcLrAprKD88eJquqnyKOuhMcUpa39sR5NcvQpFQgIUS5ZAeu2aeVzfujW0MTHQjh0LkQc1ERERVQqVLtk+ceIEgMcH23h4eCA0NBTHjh1DampqoY4koihi79698PT0RNu2bV0SLzmOs5Licjm5sSQPH0K+fj2U8fGQ79hhHjZWrw7t2LHQqlQwtG/Pkx2JiIgqmQpZRnLhwgU8fPjQ4vhnn30GAIgs0Kph3LhxAIAvvvgCYoFi3qVLl+LatWuIjIyEh4eHk6MmZ3NWUuyI/th2EUVIjx1DtTffRI3WreH9/PPmRFvXpw9yFixA1pkzePjppzB06MBEm4iIqBKqkCvb69evx6JFi9C1a1cEBgaiWrVquHz5Mnbu3AmdTocXXngBXbt2Nd8/atQorF+/HmvXrsX169fRtWtXXL16FZs2bUL9+vXx+uuvu+7DkMM46zhzh5/cWALh7l0oli+HIj4esj/+MI8b6teHNjratNnxUWtLIiIiqtwEUXyyr4PrHThwAAkJCThz5gxu376NvLw8+Pr6IjQ0FNHR0QgPDy/yGq1WiwULFiApKQnp6emoWbMm+vbti9dffx116tSx+n7u3JIGcK+2O/ndSABYTIrt6UZS8NlPthQMCjJi9mz7WwqaGQyQbdsGpVoN+W+/QdBqAQCiUgnd8OHQxMRA37s34IJ+7+40P8g5OEfIGs4Pssbd54ctrf8qZLJd3tx5EgDuN9GdmRSX5QRJSySXLkGRkADlkiWQpKWZx/Xt25t6Yj/zDEQXN/t3t/lBjsc5QtZwfpA17j4/KnWfbaLi2HOcua0c0h87NxeKNWugUKsh373bPGz09X282bFduzJGSkRERJUBk22qlBx9aEyZiSKkR45AGR8PxapVEB6dbCoKAvT9+kGjUkE3bBjAjbpERERVCpNtojIQbt2CYtkyKNVqSM+eNY8bGjWCVqWCZsIEiPXruzBCIiIiciUm20SlpddDtnWrqSf2hg0Q9KYVdtHDA9qoKGhVKuh79XLJZkciIiKqWJhsE9lIcv68abPj0qWQ3LhhHtd36gRNTAy0o0cD1au7MEIiIiKqaJhsE1mTkwNFcrJps2NKinnYWLs2tOPGQaNSwdi6tQsDJCIiooqMyTbRk0QR0gMHoFSroVi9GkJOjmlYIoFu4EBoVSrohgwBFAoXB0pEREQVHZNtokeEjAwoEhNNmx3PnTOPG5o2NW12HD8eYmCgCyMkIiKiyobJNlVtOh3kmzebykQ2bYJgMAAARE9PaEeMgDYmBvoePQCh6PHwRERERCVhsk1VkuTPP6FMSIAiMRGSmzfN4/quXaFRqaAdOZKbHYmIiKjMmGxT1ZGdDcXq1VCq1ZAdPGgeNvr5QTt+vGmzY0iICwMkIiIid8Nkm8rEYIBTjk13GFGEbN8+KOLjoUhKgpCbaxqWSqEbPNi02XHQIEAud3GgRERE5I6YbJPd1qyRY9YsT6SlPT68JTDQiDlzchEZqXNhZICQlgZlYiIUajWkFy+axw0tWpjKRMaPh+jv78IIiYiIqCpgsk12WbNGjthYL4hi4fH0dAGxsV6Ii3tQ/gm3Vgv5xo2mzY5btkAwGgEAorc3tCNHQqNSwdCtGzc7EhERUblhsk2lZjAAs2Z5Pkq0CyeuoihAEES8844nIiKyyqWkRHL6tKkn9rJlkNy5Yx7X9egBrUoF7YgRgLe38wMhIiIiegKTbSq1lBRZodKRJ4migNRUASkpMoSH650TRHY2FKtWQRkfD9mRI+ZhY7160EyYAG10NIzNmzvnvYmIiIhsxGSbSi0jw7YyDFvvs5nRCNmePVCo1VCsWQPh4UMAgCiTQTd0qGmz44ABgIzTmoiIiCoGZiVUav7+Ysk3leK+kgjXr0O5dCkUCQmQXr5sHjeEhDze7Ojn55D3IiIiInIkJttUamFhegQGGpGeLkAUi65eC4KIwEBTG0C7aTSQr19v6om9bRuERzsxRW9vaJ95xrTZsXNnbnYkIiKiCo3JNpWaVArMmZOL2FgvCIJYKOEWBFNSPHt2rl2bI6WnTpl6Yi9fDklmpnlcFx5u2uwYGQl4epb5MxARERGVBybbZJfISB3i4h486rP9ONkODBQxe3bp+mwL9+5BsWIFFGo1ZMePm8eNAQHQREebNjs2aeLQ+ImIiIjKA5NtsltkpA4REVn2nSBpNEK2cyeUajXka9dC0GgAAKJcDl1EBDQqFfT9+qFiHUdJREREVDpMtqlMpFKUqr2f5OpVKBISoFiyBNJr18zj+tatoY2JgXbsWIi1azsjVCIiIqJyx2TbBQwG2LcaXFk9fGja7BgfD/mOHeZhY/Xq0I4dC61KBUP79tzsSERERG6HyXY5W7NG/qjO+fGhMIGBRsyZU7o65wpPFCE9ftzUE3vFCkiyssyXdH36QBMTA11EBFCtmguDJCIiInIuJtvlaM0aOWJjvR4dc/5YerqA2FgvxMU9qPQJt3D3LhTLl0MRHw/ZH3+Yxw3160Obv9mxYUMXRkhERERUfphslxODAZg1y/NRol24XEIUBQiCiHfe8URERFblKykxGCDbts202fG33yBotQAAUamEbvhwaGJioO/dG5AUf8Q7ERERkTtisl1OUlJkhUpHniSKAlJTBaSkyEq14dCVJJcuQZGQAOWSJZCkpZnH9e3bm3piP/MMRF9fF0ZIRERE5FpMtstJRoZtm/9svc9lcnOhWLMGCrUa8t27zcPGmjWhHTfOtNmxXTsXBkhERERUcTDZLif+/mLJN5XivnIlipAeOQJlfDwUq1ZBuH/fNCwI0PfrB41KBd2wYYCHh4sDJSIiIqpYmGyXk7AwPQIDjUhPFwodb55PEEQEBpraAFYUwq1bUCxbBqVaDenZs+ZxQ6NG0KpU0EyYALF+fRdGSERERFSxMdkuJ1IpMGdOLmJjvSAIYqGEWxBMq9mzZ+e6fnOkXg/Z1q2mntgbNkDQm5J/0cMD2qgoaFUq6Hv14mZHIiIiIhsw2S5HkZE6xMU9eNRn+3GyHRgoYvZs1/bZlpw/b9rsuHQpJDdumMf1nTpBExMD7ejRQPXqLouPiIiIqDJisl3OIiN1iIjIqhgnSObkQJGcbNrsmJJiHjbWrg3tuHHQqFQwtm7tgsCIiIiI3AOTbReQSuG69n6iCOmBA1Cq1VCsXg0hJ8c0LJFAN3AgtCoVdEOGAAqFa+IjIiIiciNMtqsIISMDisRE02bHc+fM44amTU2bHcePhxgY6MIIiYiIiNwPk213ptNBvnkzsGwZaqxbB8FgAACInp7QjhgBbUwM9D16AEIF7+1NREREVEkx2XZDkj//NJWJJCZCcusWANMB8fquXaFRqaAdOZKbHYmIiIjKAZNtd5GdDcXq1VCq1ZAdPGgeNvr5QRIbi6zRo2EMCXFhgERERERVD5PtykwUIdu3D4r4eCiSkiDk5pqGpVLoBg82bXYcNAi+devCmJnp4mCJiIiIqh4m25WQkJYGZWIiFGo1pBcvmscNLVqYykTGj4fo7+/CCImIiIgIYLJdeWi1kG/cCGV8PGS//w7BaAQAiN7e0I4cCY1KBUO3btzsSERERFSBMNmu4CSnT5s2Oy5bBsmdO+ZxXY8e0MbEQBsVBXh7uzBCIiIiIioOk+2KKDsbilWrTKvYR46Yh4316kEzYQK00dEwNm/uwgCJiIiIyBZMtisKoxGyPXugUKuhSE6GkJcHABBlMuiGDoUmJgb6/v0BGb9lRERERJUFMzcXE65fh3LJEigSEiC9csU8bggJgSYmBtpx4yD6+bkwQiIiIiKyF5NtF5GeOoVqH30E2bZtEEQRACD6+ED7zDOmzY6dOnGzIxEREVElx2TbRap9/DHkW7cCAHTh4dCqVNBGRgKeni6OjIiIiIgchcm2izz84APo+vaFbuhQGJs0cXU4REREROQETLZdxNCmDQxt2rg6DCIiIiJyIomrAyAiIiIicldMtomIiIiInITJNhERERGRkzDZJiIiIiJyEibbREREREROwmSbiIiIiMhJmGwTERERETkJk20iIiIiIidhsk1ERERE5CRMtomIiIiInITJNhERERGRkzDZJiIiIiJyEibbREREREROwmSbiIiIiMhJmGwTERERETkJk20iIiIiIicRRFEUXR0EEREREZE74so2EREREZGTMNkmIiIiInISJttERERERE7CZJuIiIiIyEmYbBMREREROYnM1QFQ+dHpdNi6dSu2bt2KEydO4MaNGwCA5s2bY9SoURg/fjykUqmLoyRXOnPmDH777Tf88ccf+OOPP5CZmYlu3bph8eLFrg6NytmJEycwb948HD16FHq9HsHBwYiNjUVERISrQyMXS0pKwuHDh3Hq1Cn89ddf0Ol0mDNnDkaPHu3q0MjFMjIy8Ntvv2Hnzp24ePEibt++jRo1aqBTp0547rnn0L59e1eH6BJMtquQq1ev4rXXXoOnpyfCwsLQv39/3L9/H9u2bcM///lP7Ny5E9999x0EQXB1qOQiW7Zswf/+9z/I5XI0adIEmZmZrg6JXGDfvn147rnnoFAoMHz4cHh5eWHTpk34+9//jhs3bmDq1KmuDpFc6KuvvkJqaip8fX1Rt25dpKamujokqiAWL16MH374AQ0bNkSvXr1Qq1YtXLlyBVu2bMGWLVvw+eefV8lf2NlnuwrJyMjAli1bMGrUKHh6eprHc3NzMWnSJJw6dQpffvklhg0b5sIoyZXOnTsHrVaL4OBg3Lt3D+Hh4VzZrmL0ej2GDRuGGzduYNmyZWjVqhUA4P79+xgzZgxSU1OxceNGBAUFuThScpW9e/eiUaNGCAoKwoIFC/D5559zZZsAAJs2bULNmjXRrVu3QuOHDh1CbGwsPD09sXv3bigUChdF6Bqs2a5C/P39oVKpCiXaAODp6YkpU6YAAA4ePOiK0KiCaNGiBdq0aQO5XO7qUMhF9u3bh6tXr+Lpp582J9oA4OPjgxdffBE6nQ6//vqrCyMkV+vZsyd/2SKLBg8eXCTRBoAuXbqge/fuyMrKwp9//umCyFyLyTYBAGQyU0URa7aJqrYDBw4AAMLDw4tcyx/jL+VEVFr5eUb+f1clTLYJALBy5UoAlv8PloiqjsuXLwMAGjVqVOSan58fPD09ceXKlXKOiogqs7S0NOzduxd+fn4IDg52dTjljsk2ITExETt37kSPHj3Qp08fV4dDRC6Uk5MDwFQ2Yom3tzfu379fniERUSWm0+nw1ltvQavV4o033qiSf0Gvemv5bmDu3LnQarU23z958mQ0btzY4rVt27bh448/RlBQED799FMHRUiu5Mj5QUREZC+j0Yi3334bBw8exLhx4zBy5EhXh+QSTLYrocTEROTm5tp8/5AhQywmUzt27MBrr72G2rVr4+eff0bdunUdGCW5iqPmB1VN3t7eAFDs6nVOTg5q1KhRniERUSVkNBrxzjvvYO3atYiKisI///lPV4fkMky2K6GjR4+W+Rnbt2/HjBkz4Ovri19++QUNGjRwQGRUEThiflDVlf+L15UrV9C2bdtC127duoXc3FyEhoa6IDIiqiyMRiNmzZqF1atX4+mnn8bcuXMhkVTdyuWq+8mrsPxEu0aNGvjll18sboQioqqpa9euAIDdu3cXuZY/ln8PEdGTCibaERER+OSTT6pknXZBTLarmB07dhRKtFk+QEQFhYWFoUGDBli7di3OnDljHr9//z6+//57yOXyKlt3SUTW5ZeOrF69GkOHDsWnn35a5RNtgCdIVikXLlzAyJEjodVqMXz4cDRp0qTIPUFBQTwFrAq7cOECfvjhBwBAXl4efvvtN9SpUwdPPfWU+Z65c+e6KjwqJ8Ud156amoqZM2fyuPYqbvny5Th8+DAA4K+//sIff/yBTp06mf9K2rlzZ4wdO9aVIZKLzJs3D9988w08PT0xefJkiz21Bw4cWOjArKqANdtVyO3bt81dKtatW2fxnm7dujHZrsJu375d5HTAJ8eYbLu/Hj16ICEhAV9//TXWr18PvV6P4OBgvPHGG4iIiHB1eORihw8fLvJz4siRIzhy5Ij5aybbVVNqaioAIDc3F99//73Fe4KCgqpcss2VbSIiIiIiJ2HNNhERERGRkzDZJiIiIiJyEibbREREREROwmSbiIiIiMhJmGwTERERETkJk20iIiIiIidhsk1ERERE5CRMtomIiIiInITJNhERERGRkzDZJqJyExISUqr/9O/fHwCwf/9+hISE4O2333bxJ6gYXPXvcf36dYSEhGDSpEnl+r6VSXHfm1WrViEkJATz5s1zUWRE5CoyVwdARFXHqFGjiowdPnwYV69eRcuWLdGqVatC13x9fcsrtApl3rx5+OabbzBnzhyMHj3a1eFQAfzeEFFpMdkmonIzd+7cImNvv/02rl69ioEDB2LGjBkuiKryCQ0Nxfr16+Hj4+PqUOgJ/N4Q0ZOYbBMRVTLVqlVDs2bNXB0GWcDvDRE9iTXbRFSp3Lt3Dx9++CHCw8PRtm1bPP3001ixYkWx96enp+Nf//oXBg4ciHbt2qFbt2544YUXcOTIkWJfs2PHDkyZMgVdu3ZFu3btMGTIEHz22WfIzs4ucu+8efMQEhKCVatW4cSJE3jhhRfQvXt3hISE4MyZM+b7jh8/jtdee80cd+/evfHuu+8iLS2t0PP69++Pb775BgAwa9asQjXs+/fvB1ByzfbOnTvx4osvomfPnmjbti369OmDF154ARs3bix036FDh/Cvf/0LkZGR6Nq1K0JDQzF06NBiP6u90tPT8eabb6JHjx5o3749Ro8ejaSkpGJrwN9+++1Cn/dJBev582k0GixfvhwvvfQSBgwYgNDQUHTp0gUqlQrr1q2z+JyC73Pw4EFMnjwZHTt2RKdOnTB9+nScP3++0P2O+N5YIooi1q5di8mTJ5vn3LBhwzBv3jw8fPiwyP0PHjzA//73P0RFRaFz587o2LEjBg4ciNdeew27du2y+X2JqHxwZZuIKo3s7GyMHz8eubm56Ny5MzIzM3Ho0CG8++67EEURY8eOLXT/0aNH8cILLyArKwtNmjRB3759cffuXezevRu7du3CZ599hoiIiEKv+d///ocvvvgCMpkMXbt2ha+vL44cOYIffvgBmzdvhlqtRp06dYrEdvDgQXzwwQdo3LgxevXqhZs3b0IQBACAWq3G//t//w8A0K5dO3Tu3BmXLl3CihUrsHXrVsTHx5tXQ4cMGYK9e/fi7Nmz6NSpExo1amR+D0vv+6S5c+di0aJFkEgk6NChAwIDA3Hz5k0cOXIEN27cwJAhQ8z3fvLJJzh79ixCQkIQFhYGjUaDP/74Az/88AO2b9+OxMREeHl52fjdsezatWuYOHEibt26hQYNGqBnz57IyMjAzJkzoVKpyvTsgq5fv4733nsPdevWRZMmTRAaGorbt2/j6NGjOHToEC5evFhsmdK2bdvwyy+/mH8xOXPmDHbs2IHjx49j7dq18PPzA1D2740lRqMRb775JtauXQtPT0+0bdsWNWrUwKlTp/DNN99g586dWLx4MTw8PAAABoMBU6ZMwfHjx+Hr64tu3bpBqVTixo0b2LlzJzw9PfHUU0/ZFQsROYlIRORCM2fOFIODg8Wvv/662Hv27dsnBgcHi8HBweLf//53UaPRmK9t3rxZDA4OFvv27VvoNffv3xd79eoltmrVSkxKSip07cSJE2LXrl3FDh06iHfu3DGPHz9+XGzZsqXYoUMH8dixY+ZxjUYjvvbaa2JwcLA4Y8aMQs/6+uuvzbEtWLCgSOxHjx4VW7VqJT711FPiyZMnC11btmyZGBwcLI4dO9biM1euXGn132PmzJmFxlevXi0GBweL4eHh4unTpwtde/jwobh79+5CY9u3bxezs7MLjWk0GvH9998Xg4ODxXnz5hW6du3aNTE4OFiMiYmxGJcl06ZNE4ODg8VZs2aJOp3OPP7777+LrVq1svi8/Dmxb98+i88MDg4W+/XrV2js7t274p49e0Sj0Vho/OrVq2K/fv3Eli1biteuXbP4Pi1bthQ3b95sHtfr9eKMGTPE4OBg8csvvyz0Gnu/NytXrrQ4z3/44Qfzv8HNmzfN4xqNRnznnXfE4OBg8dNPPzWPp6SkiMHBweIzzzwj5uXlFXrW/fv3i8wxInI9lpEQUaXh7e2N999/HwqFwjw2cOBABAcHIy0tDdevXzePr1ixArdu3cKzzz6LqKioQs9p164dXn75ZeTm5iI5Odk8rlarYTQaMWnSJLRv3948rlAo8MEHH8DDwwObN29Genp6kdiCg4Px3HPPFRlfsGABDAYD/vnPf6Jt27aFro0dOxb9+/fH8ePHcfr06dL/gzzhf//7HwBTicOTnV08PDzQq1evQmN9+vQpspFPoVDgnXfegUwmw9atW8sUz7Vr17Br1y54e3tj1qxZkMke/zG1f//+hVbZy8rX1xc9e/Y0/zUhX4MGDfDSSy/BaDRi27ZtFl87fPhwDBw40Py1VCrF9OnTAZhKbZxFr9fjxx9/hKenJ/773/+aV9AB0/fh/fffh5+fH5YtWwaj0QgAuHv3LgCgU6dOUCqVhZ7n7e1dZI4RkeuxjISIKo02bdpYbAfYuHFj/PXXX7h16xbq168PANizZw8AYNCgQRaf1blzZwDAiRMnzGP5iVVkZGSR+2vXro1evXrh999/x5EjRzB8+PBC1/v161ck0TMajUhJSUG1atUQHh5uMY4uXbpg69atOHHiBFq3bm3xHltkZGTgwoULqF69OoYNG1aq123duhUXL15ETk4ORFEEAMjlcly+fNnueABTW0cAeOqppyx25xg+fDjWr19fpvd40qFDh3DgwAFkZGRAq9VCFEXcunULAHDlyhWLr7H0vWncuDEA4ObNmw6Nr6DTp08jMzMTvXr1sliG4uHhgTZt2mD79u24fPkymjZtilatWkEikWDVqlVo3rw5Bg0aVGVbZBJVFky2iajSqFevnsXx/LpirVZrHktNTQUATJw40eozMzMzzf87P7EKCgqyeG/+eEZGRpFrAQEBFp+dm5sLACWuOBaMwx43btwAYFrJfTLpL86iRYvw+eefQ6fTlem9i5P/7xkYGGjxev4vRo5w//59vPrqq9i3b1+x9zx48MDiuL+/f5Exb29vAHDavw0A819i9uzZg5CQEKv35s+PJk2a4M0338QXX3yB999/Hx9++CFatGiBsLAwjBo1Ci1btnRavERkHybbRFRpSCS2V77l/9l9yJAh8PT0LPa+pk2b2vxMa0nsk3/SLxiDp6dniSUTLVq0sDkORzh27Bjmzp0LHx8ffPzxx+jWrRv8/PzMJTrh4eHmFeGKJP/f9Emffvop9u3bh27dumHGjBlo0aIFqlevDqlUit27d2PatGnmVfsnlWZeOVJ+PI0aNUKnTp2s3luzZk3z/546dSqGDRuGLVu2YM+ePTh8+DDi4uLw888/Y9asWXj22WedGTYRlRKTbSJyS/Xq1cOlS5cwffp0m+tY69ati+vXryMtLQ3Nmzcvcj1/tdzSSqglvr6+UCqVkEgkmDNnjs0rzvbIX/W/du0aRFEs8b02b94MAPj73/9e5GTPvLw83L59u8wx5dcgP9neMF/+v+eT5HI5AJj/KlCQpXp5ANiyZQukUim+++4786p0vmvXrtkcc3nKn0dNmza1eOCTNQEBAZg0aRImTZoEvV6PdevW4Z133sGnn36KkSNHokaNGs4ImYjswA2SROSWevbsCeBxUmmLLl26AADWrl1b5Fp+y0BBEEpchcwnk8nQrVs35OTkICUlxeY48pNNg8Fg82v8/f3RrFkzZGdn47fffivx/vw+2pZ+cdiwYUOxq8ClkV8Xv2vXLuTk5BS5Xly9dn6SbqlmfO/evRZfk52dDW9v7yKJNgCb/j1sZc/3pjihoaHw8fHBgQMHcO/ePbufI5PJMGLECLRr1w46na7Y2nQicg0m20TkliZMmIDatWvjp59+QmJiYpHyA71ej127duGvv/4yj6lUKkgkEixevBgnT540j2u1Wnz88cfIy8vD4MGDLdZnF+fFF1+ERCLBrFmzLB7S8uDBA6xYsQJ5eXnmsbp16wIALl68aPP7ADB30Jg7dy7Onj1b6JpGozFvGgUebwBcsWJFobrk8+fP47PPPivV+xanYcOGCA8PR05ODubOnVsoQd2xYwc2bNhg8XVdu3YFACxZsqRQLfuZM2fw1VdfWXxN48aNkZWVVSSBj4uLK/ZwHHvY+72xRKFQ4LnnnsODBw8wY8YMiyvwGRkZWL16tfnrffv2Ye/evUXm87Vr13DhwgUIgmDzX16IqHywjISI3FL16tUxf/58vPjii/jggw/w3Xffmet4b9++jdOnTyM7OxvffvstgoODAZhWGv/2t7/hv//9LyZMmIBu3bqZD7VJT09H48aN8cEHH5Qqji5duuCDDz7Axx9/jMmTJyM4OBiNGzeGTCZDamoqzpw5A61Wi8GDB5sPLunVqxeUSiV+/vlnnDt3DnXr1oUgCJg2bZrVGvORI0fi1KlTWLx4MUaPHo0OHTogICAAN2/exNmzZxEYGIikpCQAwOjRo7Fo0SJs27YNQ4cORbt27ZCVlYWDBw9iwIABOHnyZLFlHqXx0UcfYcKECVi+fDn279+Pdu3a4ebNmzh06BCio6OhVquLvKZHjx7o1q0bDhw4gOHDh6NTp07IzMzE8ePHMWnSJCxcuLDIa6ZPn44333wTf//736FWq1GvXj2cPXsWFy9eRGxsLOLi4sr8WQD7vzfFmT59Oi5evIikpCQMGzYMrVu3Rv369aHT6XDp0iWcP38eISEhGDlyJADg7NmzmDNnDmrVqoU2bdqgZs2ayMzMxIEDB6DVajFp0iQm20QVDJNtInJbHTp0wJo1axAXF4cdO3bg4MGDAExlCl27dsWgQYMQFhZW6DUvvvgiWrZsibi4OJw8eRJ5eXkIDAzEc889h+nTp9tVCztx4kR06NABP//8Mw4cOIBt27ahWrVq8Pf3R2RkJAYPHlyoNZ6/vz/mz5+Pb7/9FocPHzbXLkdFRZWY0L333nsICwtDQkICTp06hRMnTqB27dro3LkznnnmGfN9vr6+WLFiBT799FMcPHgQW7duRf369fHaa69h2rRpxbZMLK0GDRpg2bJl+OKLL7B7925s2bIFTZs2xZw5c9C1a1eLybYgCJg/fz4+++wzbNmyBTt27ECjRo3w7rvvYuLEiRaT7aioKNSoUQPz58/HmTNn8Ndff6Ft27b48MMPIYqiw5LtsnxvLJFIJPjkk08wZMgQLFu2DCdPnsTp06dRvXp11KtXD9OmTSt0ymm/fv1w79497N+/H2fPnsW9e/dQq1YtdO7cGdHR0Q77vhGR4wiiIwrziIiISun69esYMGAAunXrhsWLF7s6HCIip2DNNhERERGRkzDZJiIiIiJyEibbREREREROwpptIiIiIiIn4co2EREREZGTMNkmIiIiInISJttERERERE7CZJuIiIiIyEmYbBMREREROQmTbSIiIiIiJ2GyTURERETkJEy2iYiIiIic5P8DRBYiWX//KUYAAAAASUVORK5CYII=", + "text/plain": [ + "<Figure size 720x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "az.style.use(\"arviz-darkgrid\")\n", + "st.probplot(df.iloc[:,0], plot=plt);" + ] + }, + { + "cell_type": "markdown", + "id": "498ec907-ad84-4b21-ab7f-af3c7c6e7662", + "metadata": {}, + "source": [ + "Die KDE-Darstellung (glatte Annäherung an ein Histogramm) dieses Datensatzes zeigt eine Gauss-ähnliche Verteilung, mit Ausnahme von zwei Datenpunkten, die weit vom Mittelwert entfernt sind." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "characteristic-delaware", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "([<matplotlib.axis.YTick at 0x7f668915ece0>], [Text(0, 0, '0')])" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 720x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_kde(df.values, rug=True, rug_kwargs={\"color\" : \"seagreen\"}, plot_kwargs={\"linewidth\" : 2, \"color\" : \"seagreen\"})\n", + "plt.yticks([0], alpha=0)" + ] + }, + { + "cell_type": "markdown", + "id": "9dd1ad3f-e8c7-437a-b1d9-72bf6eac1085", + "metadata": {}, + "source": [ + "Vergessen wir diese beiden Ausreisser für einen Moment und nehmen an, dass eine Gauss'sche Verteilung eine angemessene Beschreibung der Daten ist. Da wir weder den Mittelwert noch die Standardabweichung kennen, müssen wir eine Prior-Verteilungen für beide definieren. \n", + "\n", + "Ein vernünftiges Modell könnte daher lauten:\n", + "\\begin{align*}\n", + "\\mu &\\sim \\text{Uniform}(t_{\\mu},h_{\\mu})\\\\\n", + "\\sigma &\\sim \\text{Uniform}(t_{\\sigma},h_{\\sigma})\\\\\n", + "y&\\sim\\mathcal{N}(\\mu,\\sigma^{2})\n", + "\\end{align*}\n", + "Der Erwartungswert $ \\mu $ stammt somit aus einer Gleichverteilung, wie $ \\sigma $ auch. Im letzteren Fall müssen wir allerdings aufpassen, dass $ \\sigma $ nicht negativ wird. \n", + "\n", + "Wenn wir die möglichen Werte von $ \\mu $ und $ \\sigma $ nicht kennen, können wir deren Prior-Verteilungen so definieren, dass darin unser Vorwissen, respektive unsere Unkenntnis widerspiegelt wird. Eine Möglichkeit besteht darin, als Prior-Verteilung eine Gleichverteilung mit Intervallgrenzen $ t_{\\mu}=40 $ und $h_{\\mu}=70 $ zu wählen, so dass der Bereich der Daten grösser ist. Alternativ können wir auch einen Bereich wählen, der auf unserem Vorwissen beruht. Wissen wir zum Beispiel, dass es physikalisch nicht möglich ist, Werte unter 0 oder über 100 für diese Art von Messung zu erhalten, so können wir die Prior-Verteilung für den Mittelwert als uniforme Verteilung mit den Parametern $ t_{\\mu}=0 $ und $h_{\\mu}=100 $ wählen. Aus ähnlichen UeUberlegungen wählen wir die Prior-Verteilung für $ \\sigma $ im Bereich von $ t_{\\sigma}=0 $ bis $h_{\\sigma}=20 $.\n", + "\n", + "\\begin{align*}\n", + "\\mu &\\sim \\text{Uniform}(40,70)\\\\\n", + "\\sigma &\\sim \\text{Uniform}(0,20)\\\\\n", + "y&\\sim\\mathcal{N}(\\mu,\\sigma^{2})\n", + "\\end{align*}" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "electric-raise", + "metadata": { + "scrolled": true, + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [μ, σ]\n" + ] + }, + { + "data": { + "text/html": [ + "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n" + ], + "text/plain": [] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 4 seconds.\n" + ] + }, + { + "data": { + "text/plain": [ + "array([<Axes: title={'center': 'μ'}>, <Axes: title={'center': 'σ'}>],\n", + " dtype=object)" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 1656x552 with 2 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "az.style.use(\"arviz-darkgrid\")\n", + "with pm.Model() as model_g:\n", + " μ = pm.Uniform('μ', lower=40, upper=70)\n", + " σ = pm.Uniform('σ', lower=0, upper=20)\n", + " y = pm.Normal('y', mu=μ, sigma=σ, observed=df)\n", + " trace_g = pm.sample(1000)\n", + "az.plot_posterior(trace_g)" + ] + }, + { + "cell_type": "markdown", + "id": "760dae06-45cc-4229-a780-02b17b334999", + "metadata": {}, + "source": [ + "Der 94\\%-HDI ist $ [53,\\,54] $ für $ \\mu $ und $ [2.9,\\, 4.3] $ für $\\sigma$. Die Kenngrössen der Verteilungen sind in der folgenden Abbildung aufgeführt." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "stylish-computer", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "<div>\n", + "<style scoped>\n", + " .dataframe tbody tr th:only-of-type {\n", + " vertical-align: middle;\n", + " }\n", + "\n", + " .dataframe tbody tr th {\n", + " vertical-align: top;\n", + " }\n", + "\n", + " .dataframe thead th {\n", + " text-align: right;\n", + " }\n", + "</style>\n", + "<table border=\"1\" class=\"dataframe\">\n", + " <thead>\n", + " <tr style=\"text-align: right;\">\n", + " <th></th>\n", + " <th>mean</th>\n", + " <th>sd</th>\n", + " <th>hdi_3%</th>\n", + " <th>hdi_97%</th>\n", + " <th>mcse_mean</th>\n", + " <th>mcse_sd</th>\n", + " <th>ess_bulk</th>\n", + " <th>ess_tail</th>\n", + " <th>r_hat</th>\n", + " </tr>\n", + " </thead>\n", + " <tbody>\n", + " <tr>\n", + " <th>μ</th>\n", + " <td>53.495</td>\n", + " <td>0.521</td>\n", + " <td>52.571</td>\n", + " <td>54.504</td>\n", + " <td>0.009</td>\n", + " <td>0.006</td>\n", + " <td>3486.0</td>\n", + " <td>2680.0</td>\n", + " <td>1.0</td>\n", + " </tr>\n", + " <tr>\n", + " <th>σ</th>\n", + " <td>3.554</td>\n", + " <td>0.392</td>\n", + " <td>2.859</td>\n", + " <td>4.282</td>\n", + " <td>0.007</td>\n", + " <td>0.005</td>\n", + " <td>3774.0</td>\n", + " <td>2876.0</td>\n", + " <td>1.0</td>\n", + " </tr>\n", + " </tbody>\n", + "</table>\n", + "</div>" + ], + "text/plain": [ + " mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail \\\n", + "μ 53.495 0.521 52.571 54.504 0.009 0.006 3486.0 2680.0 \n", + "σ 3.554 0.392 2.859 4.282 0.007 0.005 3774.0 2876.0 \n", + "\n", + " r_hat \n", + "μ 1.0 \n", + "σ 1.0 " + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "az.summary(trace_g)" + ] + }, + { + "cell_type": "markdown", + "id": "5f043466-ecd2-46ec-b4fa-9c03f84edf85", + "metadata": {}, + "source": [ + "Die beiden Verteilungen können wir noch in einem sogenannten _Höhenliniendiagramm_ gemeinsam darstellen." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "musical-training", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[<Axes: >, None],\n", + " [<Axes: xlabel='μ', ylabel='σ'>, <Axes: >]], dtype=object)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 720x480 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "az.plot_pair(trace_g,kind=\"kde\",marginals=True)" + ] + }, + { + "cell_type": "markdown", + "id": "fa22eb37-e232-4873-bcf5-ae0295d8fdfc", + "metadata": {}, + "source": [ + "Höhenliniendiagramm der beiden Posterior-Verteilungen für $\\mu$ und $\\sigma$. Je heller die Farbe, desto wahrscheinlicher sind die Parameterwerte. In blau sind die Randdichten für $\\mu$ und $\\sigma$ abgebildet." + ] + }, + { + "cell_type": "markdown", + "id": "bef013bf-73f7-40ef-8c4d-57495471cd35", + "metadata": {}, + "source": [ + "Für die Prior-Verteilung von $ \\sigma $ hätten wir auch eine sogenannte _Halbnormalverteilung_ mit einer\n", + "Standardabweichung von $ \\sigma_{h} $ wählen können. Eine Halbnormalverteilung ist eine Normalverteilung, wobei der Wertebereich der Halbnormalverteilung nur auf positive Werte (ein\\-schliesslich Null) beschränkt ist. Wir wählen $ \\sigma_h=10 $." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "close-manner", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [μ, σ]\n" + ] + }, + { + "data": { + "text/html": [ + "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n" + ], + "text/plain": [] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 4 seconds.\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 1656x552 with 2 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with pm.Model() as model_h:\n", + " μ = pm.Uniform('μ', lower=40, upper=70)\n", + " σ = pm.HalfNormal('σ', sigma=10)\n", + " y = pm.Normal('y', mu=μ, sigma=σ, observed=df)\n", + " trace_h = pm.sample(1000)\n", + "az.plot_posterior(trace_h);" + ] + }, + { + "cell_type": "markdown", + "id": "12833697-ef78-47f3-9a6f-6ccbe0c90aab", + "metadata": {}, + "source": [ + "In der obigen Abbildung sind die Posterior-Verteilungen von $ \\mu $ und $ \\sigma $. Der 94\\%-HDI sind $ [53,\\,54] $ für $ \\mu $ und $ [2.9,\\, 4.2] $ für $\\sigma$. Wir sehen, dass es kaum einen Unterschied zur Abbildung gibt, welche aus der Normalverteilung resultierte. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "curious-objective", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "az.summary(trace_h)" + ] + }, + { + "cell_type": "markdown", + "id": "3c690fdf-690f-462f-b983-4d7ce1c82f94", + "metadata": {}, + "source": [ + "Wir müssen hier allerdings aufpassen, dass wir $ \\sigma $ und $ \\sigma_{h} $ nicht verwechseln. Ersteres bezieht sich auf die Likelihood-Funktion, die eine Normalverteilung ist. Letzters ist die Standardabweichung der Halbnormalverteilung für die Prior-Verteilung für $ \\sigma $.\n", + "\n", + "\n", + "Ein möglicher Einwand gegen die Modelle `model_g` und `model_h` ist, dass wir von einer Normalverteilung ausgehen, wobei zwei Datenpunkte allerdings weit rechts von der Mehrheit der Daten liegen. Die Normalverteilungsannahme scheint dann nicht erfüllt. Da die Normalverteilung schnell nach links oder rechts abfällt, ist die Normalverteilung \"überrascht\", wenn sie diese beiden Punkte sieht, und reagiert darauf, indem sie sich auf diese Punkte zubewegt und die Standardabweichung erhöht. \n", + "\n", + "Wir können uns vorstellen, dass diese Punkte bei der Schätzung der Parameterwerte der Normalverteilung ein übermässiges Gewicht haben. Was können wir also tun?\n", + "\n", + "Eine Möglichkeit besteht darin, diese Punkte als Ausreisser zu deklarieren und sie aus den Daten zu entfernen. Daten sollten allerdings nur entfernt werden, wenn wir einen triftigen Grund haben: z.B. eine Fehlfunktion des Geräts oder ein menschlicher Fehler bei der Messung dieser beiden Datenpunkte.\n", + "\n", + "Bevor wir voreilig Messungen aus dem Datensatz entfernen und damit die Daten manipulieren, können wir das Modell so ändern, wie im nächsten Abschnitt erläutert." + ] + }, + { + "cell_type": "markdown", + "id": "660eafc3-9d2c-4a33-a73f-6f5fb7af6e50", + "metadata": {}, + "source": [ + "In obiger Abbildung bezieht sich die schwarze Linie auf eine KDE der Daten und die vielen blauen Linien sind KDEs, die aus jeder der 100 Posterior-Predictive Stichproben berechnet wurden. Die blauen Linien spiegeln die Unsicherheit wider, die wir bezüglich der abgeleiteten Verteilung für die vorhergesagten Daten haben. Aus der Abbildung geht hervor, dass der Mittelwert der simulierten Daten leicht nach rechts verschoben ist und dass die Varianz der simulierten Daten größer zu sein scheint als die der tatsächlichen Daten. Dies ist eine direkte Folge der beiden Beobachtungen, die vom Grossteil der Daten getrennt sind.\n", + "\n", + "Können wir anhand dieser Darstellung mit Sicherheit sagen, dass das Modell fehlerhaft ist und geändert werden muss? Nun, wie immer ist die Interpretation des Modells und seine Bewertung kontextabhängig. Im Allgemeinen bildet dieses Modell die Daten ausreichend gut ab und dürfte für die meisten Analysen nützlich. Dennoch werden wir im nächsten Abschnitt sehen, wie wir `model_g` verfeinern können und damit Vorhersagen erhalten, die noch besser mit den Daten übereinstimmen." + ] + }, + { + "cell_type": "markdown", + "id": "138667e1-d4a6-4232-a51f-9d9d6bb0d2e9", + "metadata": {}, + "source": [ + "## $ t $-Verteilung\n", + "\n", + "\n", + "\n", + "In der Regel ziehen es Bayesianer vor, Annahmen über die Daten direkt im Modell zu kodieren, indem sie verschiedene Priors und Likelihoods verwenden, als mit Ad-hoc-Heuristiken wie Ausreisser-Entfernungsregeln zu arbeiten.\n", + "\n", + "Eine sehr nützliche Option beim Umgang mit Ausreissern und Normalverteilungen ist es, die Gauss'sche Likelihood-Funktion durch eine Student's $t$-Verteilung zu ersetzen. Diese Verteilung hat drei Parameter: den Mittelwert, die Skala (analog zur Standardabweichung) und die Freiheitsgrade, die üblicherweise mit dem griechischen Buchstaben $ \\nu $ (nü) bezeichnet werden. Werte von $\\nu$ können im Intervall $[0, \\infty]$ variieren, siehe folgende Abbildung." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "running-pastor", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(-5.0, 5.0)" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 500x300 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(5, 3))\n", + "x_values = np.linspace(-10, 10, 500)\n", + "for df in [1, 2, 30]:\n", + " distri = st.t(df)\n", + " x_pdf = distri.pdf(x_values)\n", + " plt.plot(x_values, x_pdf, label=fr'ν = {df}', lw=3)\n", + "x_pdf = st.norm.pdf(x_values)\n", + "plt.plot(x_values, x_pdf, 'k--', label=r'$ν = \\infty$')\n", + "plt.xlabel('$x$')\n", + "plt.yticks([])\n", + "plt.legend()\n", + "plt.xlim(-5, 5)" + ] + }, + { + "cell_type": "markdown", + "id": "82559197-5fd3-461d-86ee-158400f474fd", + "metadata": {}, + "source": [ + "Für einen Wert von $ \\nu=1 $ erhalten wir eine Verteilung mit sehr starken Ausläufern (Schwänzen), die auch als Cauchy- oder Lorentz-Verteilung bekannt ist. Letztere ist besonders unter Physikern beliebt. Mit starken Ausläufern ist es wahrscheinlicher, Werte zu finden, die weit vom Mittelwert entfernt sind. Die Werte sind nicht so stark um den Mittelwert konzentriert wie bei einer Gauss-Verteilung. Zum Beispiel sind 95\\% der Werte einer Cauchy-Verteilung zwischen $-12.7$ und $12.7$ zu finden. Bei einer Gauss-Verteilung (mit einer Standard\n", + "Abweichung von eins) befinden sich 95\\% der Werte zwischen $-1.96$ und $1.96$. " + ] + }, + { + "cell_type": "markdown", + "id": "dc21b5e6-0f3c-4de5-b86f-4e6959c1e01a", + "metadata": {}, + "source": [ + "Wir werden das vorherige Modell umschreiben, indem wir die Gauss-Verteilung durch die \n", + "Student's t-Verteilung ersetzen:\n", + "\n", + "\\begin{align*}\n", + "\\mu &\\sim \\text{Uniform}(t_{\\mu},h_{\\mu})\\\\\n", + "\\sigma &\\sim |\\mathcal{N}(0,\\sigma_{h}^{2})|\\\\\n", + "\\nu&\\sim \\text{Exp}(\\lambda)\\\\\n", + "y&\\sim\\mathcal{T}(\\mu,\\sigma,\\nu)\n", + "\\end{align*}\n", + "\n", + "Da die Student's $t$-Verteilung einen Parameter ($ \\nu $) mehr hat als die Gauss-Verteilung, müssen wir einen weiteren Prior angeben. Wir wählen eine Exponentialverteilung mit einem Mittelwert von $30$. Aus der Abbildung mit den t-Verteilungen ist ersichtlich, dass eine Student's $t$-Verteilung mit $ \\nu=30 $ ziemlich\n", + "ähnlich wie eine Gauss-Verteilung aussieht (auch wenn sie es nicht ist). \n", + "\n", + "Der Exponential-Prior mit einem Mittelwert von 30 ist ein schwach informativer Prior, der dem Modell sagt, dass wir\n", + "mehr oder weniger denken, dass der Wert von $\\nu$ um 30 herum sein sollte, sich aber mit Leichtigkeit zu kleineren und grösseren Werten bewegen kann. \n", + "\n", + "Wie üblich erlaubt uns `PyMC`, Modelle (neu) zu schreiben, indem wir die entsprechenden Prior-Verteilungen hinzufügen. Wir sollten allerdings aufpassen, dass die Exponential-Verteilung in `PyMC` mit dem Kehrwert des Mittelwertes parametrisiert ist." + ] + }, + { + "cell_type": "markdown", + "id": "10b72c1b-d682-495e-b009-e817945272d0", + "metadata": {}, + "source": [ + "Wie üblich erlaubt uns `PyMC`, Modelle (neu) zu schreiben, indem wir die entsprechenden Prior-Verteilungen hinzufügen. Wir sollten allerdings aufpassen, dass die Exponential-Verteilung in `PyMC` mit dem Kehrwert des Mittelwertes parametrisiert ist." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "spare-bleeding", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [ν, σ, μ]\n" + ] + }, + { + "data": { + "text/html": [ + "\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:not([value]), progress:not([value])::-webkit-progress-bar {\n", + " background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n", + 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\n", + "text/plain": [ + "<Figure size 2484x552 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with pm.Model() as model_t:\n", + " μ = pm.Uniform('μ', lower=40, upper=75)\n", + " σ = pm.HalfNormal('σ', sigma=10)\n", + " ν = pm.Exponential('ν', 1/30)\n", + " y = pm.StudentT('y', mu=μ, sigma=σ, nu=ν, observed=df)\n", + " trace_t = pm.sample(1000)\n", + "az.plot_posterior(trace_t);" + ] + }, + { + "cell_type": "markdown", + "id": "17d14a27-12f2-4088-aeee-8160c6a1ab82", + "metadata": {}, + "source": [ + "Posterior-Verteilungen sind für die drei Parameter $\\mu$, $\\sigma $ und $\\nu$ dargestellt. Im Folgenden ist die Zusammenfassung der Kenngrössen der Verteilungen aufgeführt." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "subjective-feature", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Got error No model on context stack. trying to find log_likelihood in translation.\n" + ] + }, + { + "data": { + "text/html": [ + "<div>\n", + "<style scoped>\n", + " .dataframe tbody tr th:only-of-type {\n", + " vertical-align: middle;\n", + " }\n", + "\n", + " .dataframe tbody tr th {\n", + " vertical-align: top;\n", + " }\n", + "\n", + " .dataframe thead th {\n", + " text-align: right;\n", + " }\n", + "</style>\n", + "<table border=\"1\" class=\"dataframe\">\n", + " <thead>\n", + " <tr style=\"text-align: right;\">\n", + " <th></th>\n", + " <th>mean</th>\n", + " <th>sd</th>\n", + " <th>hdi_3%</th>\n", + " <th>hdi_97%</th>\n", + " <th>mcse_mean</th>\n", + " <th>mcse_sd</th>\n", + " <th>ess_bulk</th>\n", + " <th>ess_tail</th>\n", + " <th>r_hat</th>\n", + " </tr>\n", + " </thead>\n", + " <tbody>\n", + " <tr>\n", + " <th>μ</th>\n", + " <td>48.343</td>\n", + " <td>7.697</td>\n", + " <td>40.000</td>\n", + " <td>63.643</td>\n", + " <td>0.162</td>\n", + " <td>0.115</td>\n", + " <td>2228.0</td>\n", + " <td>2330.0</td>\n", + " <td>1.0</td>\n", + " </tr>\n", + " <tr>\n", + " <th>σ</th>\n", + " <td>13.195</td>\n", + " <td>5.702</td>\n", + " <td>3.994</td>\n", + " <td>24.437</td>\n", + " <td>0.121</td>\n", + " <td>0.086</td>\n", + " <td>2039.0</td>\n", + " <td>1805.0</td>\n", + " <td>1.0</td>\n", + " </tr>\n", + " <tr>\n", + " <th>ν</th>\n", + " <td>29.245</td>\n", + " <td>31.085</td>\n", + " <td>0.012</td>\n", + " <td>85.603</td>\n", + " <td>0.614</td>\n", + " <td>0.434</td>\n", + " <td>1907.0</td>\n", + " <td>1975.0</td>\n", + " <td>1.0</td>\n", + " </tr>\n", + " </tbody>\n", + "</table>\n", + "</div>" + ], + "text/plain": [ + " mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail \\\n", + "μ 48.343 7.697 40.000 63.643 0.162 0.115 2228.0 2330.0 \n", + "σ 13.195 5.702 3.994 24.437 0.121 0.086 2039.0 1805.0 \n", + "ν 29.245 31.085 0.012 85.603 0.614 0.434 1907.0 1975.0 \n", + "\n", + " r_hat \n", + "μ 1.0 \n", + "σ 1.0 \n", + "ν 1.0 " + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "az.summary(trace_t)" + ] + }, + { + "cell_type": "markdown", + "id": "7e0b3c5c-cdd0-4558-b83a-4b82771da650", + "metadata": {}, + "source": [ + "Vergleichen wir die Posterior-Verteilungen von `model_g` mit den Posterior-Verteilungen von `model_t` und ebenso die Zusammenfassung der Kenngrössen von `model_t` mit der von `model_g`, so stellen wir Folgendes fest: Die Schätzungen der beiden Modelle für $ \\mu $ sind ähnlich, mit einem Unterschied von $ \\approx 0.5$. Die Schätzung von $ \\sigma $ ändert sich von $\\approx 3.5$ auf $ \\approx 2.2 $. Dies ist eine Folge der Wahl der Student's $t$-Verteilung als Likelihood-Funktion, welche den Werten, die vom Mittelwert abweichen, weniger Gewicht verleiht. Wir beobachten ebenfalls, dass wir nun eine _nicht sehr Gauss-ähnliche Verteilung_ mit ausgeprägteren Schwänzen erhalten haben.\n", + "\n", + "\n", + "\n", + "Die Student's $t$-Verteilung ermöglicht uns eine _robustere_ Schätzung, da die Ausreisser den Effekt haben, $ \\nu $ zu verringern, was dann dazu führt, dass sich die Standardabweichung erhöht. Der Mittelwert und die Skala (\"Standardabweichung\" der t-Verteilung) werden also geschätzt, indem die Grossmehrheit der Daten stärker gewichtet wird als diejenigen Werte, welche sich außerhalb der Masse befinden. \n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/Multi-Parameter Distributions/MPD_6_2.ipynb b/notebooks/Multi-Parameter Distributions/MPD_6_2.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..cdeb5285182822c6273ab8bfd565c404311f917f --- /dev/null +++ b/notebooks/Multi-Parameter Distributions/MPD_6_2.ipynb @@ -0,0 +1,332 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "9875fd00-2c4a-4f01-9f23-955f55f4de8c", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + } + ], + "source": [ + "%matplotlib inline\n", + "import pymc as pm\n", + "import matplotlib.pyplot as plt\n", + "import scipy.stats as st\n", + "import arviz as az\n", + "import metropolis_commands as mc\n", + "import numpy as np\n", + "import pandas as pd\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")\n", + "plt.rcParams['figure.figsize'] = [5, 3]" + ] + }, + { + "cell_type": "markdown", + "id": "bb7b0492-99b1-4352-b152-94a7f1020bcb", + "metadata": {}, + "source": [ + "## $ t $-Verteilung\n", + "\n", + "\n", + "\n", + "In der Regel ziehen es Bayesianer vor, Annahmen über die Daten direkt im Modell zu kodieren, indem sie verschiedene Priors und Likelihoods verwenden, als mit Ad-hoc-Heuristiken wie Ausreisser-Entfernungsregeln zu arbeiten.\n", + "\n", + "Eine sehr nützliche Option beim Umgang mit Ausreissern und Normalverteilungen ist es, die Gauss'sche Likelihood-Funktion durch eine Student's $t$-Verteilung zu ersetzen. Diese Verteilung hat drei Parameter: den Mittelwert, die Skala (analog zur Standardabweichung) und die Freiheitsgrade, die üblicherweise mit dem griechischen Buchstaben $ \\nu $ (nü) bezeichnet werden. Werte von $\\nu$ können im Intervall $[0, \\infty]$ variieren, siehe folgende Abbildung." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "de750492-8907-40cc-a97f-2289e9557f86", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(-5.0, 5.0)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 500x300 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(5, 3))\n", + "x_values = np.linspace(-10, 10, 500)\n", + "for df in [1, 2, 30]:\n", + " distri = st.t(df)\n", + " x_pdf = distri.pdf(x_values)\n", + " plt.plot(x_values, x_pdf, label=fr'ν = {df}', lw=3)\n", + "x_pdf = st.norm.pdf(x_values)\n", + "plt.plot(x_values, x_pdf, 'k--', label=r'$ν = \\infty$')\n", + "plt.xlabel('$x$')\n", + "plt.yticks([])\n", + "plt.legend()\n", + "plt.xlim(-5, 5)" + ] + }, + { + "cell_type": "markdown", + "id": "2522619c-43d8-4eeb-80f1-49842cebd4d5", + "metadata": {}, + "source": [ + "Für einen Wert von $ \\nu=1 $ erhalten wir eine Verteilung mit sehr starken Ausläufern (Schwänzen), die auch als Cauchy- oder Lorentz-Verteilung bekannt ist. Letztere ist besonders unter Physikern beliebt. Mit starken Ausläufern ist es wahrscheinlicher, Werte zu finden, die weit vom Mittelwert entfernt sind. Die Werte sind nicht so stark um den Mittelwert konzentriert wie bei einer Gauss-Verteilung. Zum Beispiel sind 95\\% der Werte einer Cauchy-Verteilung zwischen $-12.7$ und $12.7$ zu finden. Bei einer Gauss-Verteilung (mit einer Standard\n", + "Abweichung von eins) befinden sich 95\\% der Werte zwischen $-1.96$ und $1.96$. " + ] + }, + { + "cell_type": "markdown", + "id": "4c90089c-697c-4a12-b086-43f089f0bc8b", + "metadata": {}, + "source": [ + "Wir werden das vorherige Modell umschreiben, indem wir die Gauss-Verteilung durch die \n", + "Student's t-Verteilung ersetzen:\n", + "\n", + "\\begin{align*}\n", + "\\mu &\\sim \\text{Uniform}(t_{\\mu},h_{\\mu})\\\\\n", + "\\sigma &\\sim |\\mathcal{N}(0,\\sigma_{h}^{2})|\\\\\n", + "\\nu&\\sim \\text{Exp}(\\lambda)\\\\\n", + "y&\\sim\\mathcal{T}(\\mu,\\sigma,\\nu)\n", + "\\end{align*}\n", + "\n", + "Da die Student's $t$-Verteilung einen Parameter ($ \\nu $) mehr hat als die Gauss-Verteilung, müssen wir einen weiteren Prior angeben. Wir wählen eine Exponentialverteilung mit einem Mittelwert von $30$. Aus der Abbildung mit den t-Verteilungen ist ersichtlich, dass eine Student's $t$-Verteilung mit $ \\nu=30 $ ziemlich\n", + "ähnlich wie eine Gauss-Verteilung aussieht (auch wenn sie es nicht ist). \n", + "\n", + "Der Exponential-Prior mit einem Mittelwert von 30 ist ein schwach informativer Prior, der dem Modell sagt, dass wir\n", + "mehr oder weniger denken, dass der Wert von $\\nu$ um 30 herum sein sollte, sich aber mit Leichtigkeit zu kleineren und grösseren Werten bewegen kann. \n", + "\n", + "Wie üblich erlaubt uns `PyMC`, Modelle (neu) zu schreiben, indem wir die entsprechenden Prior-Verteilungen hinzufügen. Wir sollten allerdings aufpassen, dass die Exponential-Verteilung in `PyMC` mit dem Kehrwert des Mittelwertes parametrisiert ist." + ] + }, + { + "cell_type": "markdown", + "id": "f9bc5dbe-ff0b-44be-814c-9e3a5d09ac34", + "metadata": {}, + "source": [ + "Wie üblich erlaubt uns `PyMC`, Modelle (neu) zu schreiben, indem wir die entsprechenden Prior-Verteilungen hinzufügen. Wir sollten allerdings aufpassen, dass die Exponential-Verteilung in `PyMC` mit dem Kehrwert des Mittelwertes parametrisiert ist." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "d59ce97d-13b5-4bf5-a723-1dcce961c073", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [μ, σ, ν]\n" + ] + }, + { + "data": { + "text/html": [ + "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n" + ], + "text/plain": [] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 4 seconds.\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "<Figure size 1725x345 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with pm.Model() as model_t:\n", + " μ = pm.Uniform('μ', lower=40, upper=75)\n", + " σ = pm.HalfNormal('σ', sigma=10)\n", + " ν = pm.Exponential('ν', 1/30)\n", + " y = pm.StudentT('y', mu=μ, sigma=σ, nu=ν, observed=df)\n", + " trace_t = pm.sample(1000)\n", + "az.plot_posterior(trace_t);" + ] + }, + { + "cell_type": "markdown", + "id": "fdbf0060-bf38-46e6-9607-3f17b96b5908", + "metadata": {}, + "source": [ + "Posterior-Verteilungen sind für die drei Parameter $\\mu$, $\\sigma $ und $\\nu$ dargestellt. Im Folgenden ist die Zusammenfassung der Kenngrössen der Verteilungen aufgeführt." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "c864c1bc-5d3a-4a96-9973-f4a7a16d0582", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "<div>\n", + "<style scoped>\n", + " .dataframe tbody tr th:only-of-type {\n", + " vertical-align: middle;\n", + " }\n", + "\n", + " .dataframe tbody tr th {\n", + " vertical-align: top;\n", + " }\n", + "\n", + " .dataframe thead th {\n", + " text-align: right;\n", + " }\n", + "</style>\n", + "<table border=\"1\" class=\"dataframe\">\n", + " <thead>\n", + " <tr style=\"text-align: right;\">\n", + " <th></th>\n", + " <th>mean</th>\n", + " <th>sd</th>\n", + " <th>hdi_3%</th>\n", + " <th>hdi_97%</th>\n", + " <th>mcse_mean</th>\n", + " <th>mcse_sd</th>\n", + " <th>ess_bulk</th>\n", + " <th>ess_tail</th>\n", + " <th>r_hat</th>\n", + " </tr>\n", + " </thead>\n", + " <tbody>\n", + " <tr>\n", + " <th>μ</th>\n", + " <td>48.248</td>\n", + " <td>7.665</td>\n", + " <td>40.003</td>\n", + " <td>64.059</td>\n", + " <td>0.156</td>\n", + " <td>0.112</td>\n", + " <td>2267.0</td>\n", + " <td>2009.0</td>\n", + " <td>1.0</td>\n", + " </tr>\n", + " <tr>\n", + " <th>ν</th>\n", + " <td>29.062</td>\n", + " <td>30.260</td>\n", + " <td>0.014</td>\n", + " <td>82.156</td>\n", + " <td>0.568</td>\n", + " <td>0.402</td>\n", + " <td>1967.0</td>\n", + " <td>1804.0</td>\n", + " <td>1.0</td>\n", + " </tr>\n", + " <tr>\n", + " <th>σ</th>\n", + " <td>13.258</td>\n", + " <td>5.676</td>\n", + " <td>4.033</td>\n", + " <td>24.190</td>\n", + " <td>0.112</td>\n", + " <td>0.079</td>\n", + " <td>2326.0</td>\n", + " <td>1899.0</td>\n", + " <td>1.0</td>\n", + " </tr>\n", + " </tbody>\n", + "</table>\n", + "</div>" + ], + "text/plain": [ + " mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail \\\n", + "μ 48.248 7.665 40.003 64.059 0.156 0.112 2267.0 2009.0 \n", + "ν 29.062 30.260 0.014 82.156 0.568 0.402 1967.0 1804.0 \n", + "σ 13.258 5.676 4.033 24.190 0.112 0.079 2326.0 1899.0 \n", + "\n", + " r_hat \n", + "μ 1.0 \n", + "ν 1.0 \n", + "σ 1.0 " + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "az.summary(trace_t)" + ] + }, + { + "cell_type": "markdown", + "id": "7f635d64-8252-4e7e-8897-bc7e5d020262", + "metadata": {}, + "source": [ + "Vergleichen wir die Posterior-Verteilungen von `model_g` mit den Posterior-Verteilungen von `model_t` und ebenso die Zusammenfassung der Kenngrössen von `model_t` mit der von `model_g`, so stellen wir Folgendes fest: Die Schätzungen der beiden Modelle für $ \\mu $ sind ähnlich, mit einem Unterschied von $ \\approx 0.5$. Die Schätzung von $ \\sigma $ ändert sich von $\\approx 3.5$ auf $ \\approx 2.2 $. Dies ist eine Folge der Wahl der Student's $t$-Verteilung als Likelihood-Funktion, welche den Werten, die vom Mittelwert abweichen, weniger Gewicht verleiht. Wir beobachten ebenfalls, dass wir nun eine _nicht sehr Gauss-ähnliche Verteilung_ mit ausgeprägteren Schwänzen erhalten haben.\n", + "\n", + "\n", + "\n", + "Die Student's $t$-Verteilung ermöglicht uns eine _robustere_ Schätzung, da die Ausreisser den Effekt haben, $ \\nu $ zu verringern, was dann dazu führt, dass sich die Standardabweichung erhöht. Der Mittelwert und die Skala (\"Standardabweichung\" der t-Verteilung) werden also geschätzt, indem die Grossmehrheit der Daten stärker gewichtet wird als diejenigen Werte, welche sich außerhalb der Masse befinden. \n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/notebooks/Multi-Parameter Distributions/Untitled.ipynb b/notebooks/Multi-Parameter Distributions/Untitled.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..cdeb5285182822c6273ab8bfd565c404311f917f --- /dev/null +++ b/notebooks/Multi-Parameter Distributions/Untitled.ipynb @@ -0,0 +1,332 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "9875fd00-2c4a-4f01-9f23-955f55f4de8c", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING (pytensor.tensor.blas): Using NumPy C-API based implementation for BLAS functions.\n" + ] + } + ], + "source": [ + "%matplotlib inline\n", + "import pymc as pm\n", + "import matplotlib.pyplot as plt\n", + "import scipy.stats as st\n", + "import arviz as az\n", + "import metropolis_commands as mc\n", + "import numpy as np\n", + "import pandas as pd\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")\n", + "plt.rcParams['figure.figsize'] = [5, 3]" + ] + }, + { + "cell_type": "markdown", + "id": "bb7b0492-99b1-4352-b152-94a7f1020bcb", + "metadata": {}, + "source": [ + "## $ t $-Verteilung\n", + "\n", + "\n", + "\n", + "In der Regel ziehen es Bayesianer vor, Annahmen über die Daten direkt im Modell zu kodieren, indem sie verschiedene Priors und Likelihoods verwenden, als mit Ad-hoc-Heuristiken wie Ausreisser-Entfernungsregeln zu arbeiten.\n", + "\n", + "Eine sehr nützliche Option beim Umgang mit Ausreissern und Normalverteilungen ist es, die Gauss'sche Likelihood-Funktion durch eine Student's $t$-Verteilung zu ersetzen. Diese Verteilung hat drei Parameter: den Mittelwert, die Skala (analog zur Standardabweichung) und die Freiheitsgrade, die üblicherweise mit dem griechischen Buchstaben $ \\nu $ (nü) bezeichnet werden. Werte von $\\nu$ können im Intervall $[0, \\infty]$ variieren, siehe folgende Abbildung." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "de750492-8907-40cc-a97f-2289e9557f86", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(-5.0, 5.0)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 500x300 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(5, 3))\n", + "x_values = np.linspace(-10, 10, 500)\n", + "for df in [1, 2, 30]:\n", + " distri = st.t(df)\n", + " x_pdf = distri.pdf(x_values)\n", + " plt.plot(x_values, x_pdf, label=fr'ν = {df}', lw=3)\n", + "x_pdf = st.norm.pdf(x_values)\n", + "plt.plot(x_values, x_pdf, 'k--', label=r'$ν = \\infty$')\n", + "plt.xlabel('$x$')\n", + "plt.yticks([])\n", + "plt.legend()\n", + "plt.xlim(-5, 5)" + ] + }, + { + "cell_type": "markdown", + "id": "2522619c-43d8-4eeb-80f1-49842cebd4d5", + "metadata": {}, + "source": [ + "Für einen Wert von $ \\nu=1 $ erhalten wir eine Verteilung mit sehr starken Ausläufern (Schwänzen), die auch als Cauchy- oder Lorentz-Verteilung bekannt ist. Letztere ist besonders unter Physikern beliebt. Mit starken Ausläufern ist es wahrscheinlicher, Werte zu finden, die weit vom Mittelwert entfernt sind. Die Werte sind nicht so stark um den Mittelwert konzentriert wie bei einer Gauss-Verteilung. Zum Beispiel sind 95\\% der Werte einer Cauchy-Verteilung zwischen $-12.7$ und $12.7$ zu finden. Bei einer Gauss-Verteilung (mit einer Standard\n", + "Abweichung von eins) befinden sich 95\\% der Werte zwischen $-1.96$ und $1.96$. " + ] + }, + { + "cell_type": "markdown", + "id": "4c90089c-697c-4a12-b086-43f089f0bc8b", + "metadata": {}, + "source": [ + "Wir werden das vorherige Modell umschreiben, indem wir die Gauss-Verteilung durch die \n", + "Student's t-Verteilung ersetzen:\n", + "\n", + "\\begin{align*}\n", + "\\mu &\\sim \\text{Uniform}(t_{\\mu},h_{\\mu})\\\\\n", + "\\sigma &\\sim |\\mathcal{N}(0,\\sigma_{h}^{2})|\\\\\n", + "\\nu&\\sim \\text{Exp}(\\lambda)\\\\\n", + "y&\\sim\\mathcal{T}(\\mu,\\sigma,\\nu)\n", + "\\end{align*}\n", + "\n", + "Da die Student's $t$-Verteilung einen Parameter ($ \\nu $) mehr hat als die Gauss-Verteilung, müssen wir einen weiteren Prior angeben. Wir wählen eine Exponentialverteilung mit einem Mittelwert von $30$. Aus der Abbildung mit den t-Verteilungen ist ersichtlich, dass eine Student's $t$-Verteilung mit $ \\nu=30 $ ziemlich\n", + "ähnlich wie eine Gauss-Verteilung aussieht (auch wenn sie es nicht ist). \n", + "\n", + "Der Exponential-Prior mit einem Mittelwert von 30 ist ein schwach informativer Prior, der dem Modell sagt, dass wir\n", + "mehr oder weniger denken, dass der Wert von $\\nu$ um 30 herum sein sollte, sich aber mit Leichtigkeit zu kleineren und grösseren Werten bewegen kann. \n", + "\n", + "Wie üblich erlaubt uns `PyMC`, Modelle (neu) zu schreiben, indem wir die entsprechenden Prior-Verteilungen hinzufügen. Wir sollten allerdings aufpassen, dass die Exponential-Verteilung in `PyMC` mit dem Kehrwert des Mittelwertes parametrisiert ist." + ] + }, + { + "cell_type": "markdown", + "id": "f9bc5dbe-ff0b-44be-814c-9e3a5d09ac34", + "metadata": {}, + "source": [ + "Wie üblich erlaubt uns `PyMC`, Modelle (neu) zu schreiben, indem wir die entsprechenden Prior-Verteilungen hinzufügen. Wir sollten allerdings aufpassen, dass die Exponential-Verteilung in `PyMC` mit dem Kehrwert des Mittelwertes parametrisiert ist." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "d59ce97d-13b5-4bf5-a723-1dcce961c073", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [μ, σ, ν]\n" + ] + }, + { + "data": { + "text/html": [ + "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n" + ], + "text/plain": [] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 4 seconds.\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "<Figure size 1725x345 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "with pm.Model() as model_t:\n", + " μ = pm.Uniform('μ', lower=40, upper=75)\n", + " σ = pm.HalfNormal('σ', sigma=10)\n", + " ν = pm.Exponential('ν', 1/30)\n", + " y = pm.StudentT('y', mu=μ, sigma=σ, nu=ν, observed=df)\n", + " trace_t = pm.sample(1000)\n", + "az.plot_posterior(trace_t);" + ] + }, + { + "cell_type": "markdown", + "id": "fdbf0060-bf38-46e6-9607-3f17b96b5908", + "metadata": {}, + "source": [ + "Posterior-Verteilungen sind für die drei Parameter $\\mu$, $\\sigma $ und $\\nu$ dargestellt. Im Folgenden ist die Zusammenfassung der Kenngrössen der Verteilungen aufgeführt." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "c864c1bc-5d3a-4a96-9973-f4a7a16d0582", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "text/html": [ + "<div>\n", + "<style scoped>\n", + " .dataframe tbody tr th:only-of-type {\n", + " vertical-align: middle;\n", + " }\n", + "\n", + " .dataframe tbody tr th {\n", + " vertical-align: top;\n", + " }\n", + "\n", + " .dataframe thead th {\n", + " text-align: right;\n", + " }\n", + "</style>\n", + "<table border=\"1\" class=\"dataframe\">\n", + " <thead>\n", + " <tr style=\"text-align: right;\">\n", + " <th></th>\n", + " <th>mean</th>\n", + " <th>sd</th>\n", + " <th>hdi_3%</th>\n", + " <th>hdi_97%</th>\n", + " <th>mcse_mean</th>\n", + " <th>mcse_sd</th>\n", + " <th>ess_bulk</th>\n", + " <th>ess_tail</th>\n", + " <th>r_hat</th>\n", + " </tr>\n", + " </thead>\n", + " <tbody>\n", + " <tr>\n", + " <th>μ</th>\n", + " <td>48.248</td>\n", + " <td>7.665</td>\n", + " <td>40.003</td>\n", + " <td>64.059</td>\n", + " <td>0.156</td>\n", + " <td>0.112</td>\n", + " <td>2267.0</td>\n", + " <td>2009.0</td>\n", + " <td>1.0</td>\n", + " </tr>\n", + " <tr>\n", + " <th>ν</th>\n", + " <td>29.062</td>\n", + " <td>30.260</td>\n", + " <td>0.014</td>\n", + " <td>82.156</td>\n", + " <td>0.568</td>\n", + " <td>0.402</td>\n", + " <td>1967.0</td>\n", + " <td>1804.0</td>\n", + " <td>1.0</td>\n", + " </tr>\n", + " <tr>\n", + " <th>σ</th>\n", + " <td>13.258</td>\n", + " <td>5.676</td>\n", + " <td>4.033</td>\n", + " <td>24.190</td>\n", + " <td>0.112</td>\n", + " <td>0.079</td>\n", + " <td>2326.0</td>\n", + " <td>1899.0</td>\n", + " <td>1.0</td>\n", + " </tr>\n", + " </tbody>\n", + "</table>\n", + "</div>" + ], + "text/plain": [ + " mean sd hdi_3% hdi_97% mcse_mean mcse_sd ess_bulk ess_tail \\\n", + "μ 48.248 7.665 40.003 64.059 0.156 0.112 2267.0 2009.0 \n", + "ν 29.062 30.260 0.014 82.156 0.568 0.402 1967.0 1804.0 \n", + "σ 13.258 5.676 4.033 24.190 0.112 0.079 2326.0 1899.0 \n", + "\n", + " r_hat \n", + "μ 1.0 \n", + "ν 1.0 \n", + "σ 1.0 " + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "az.summary(trace_t)" + ] + }, + { + "cell_type": "markdown", + "id": "7f635d64-8252-4e7e-8897-bc7e5d020262", + "metadata": {}, + "source": [ + "Vergleichen wir die Posterior-Verteilungen von `model_g` mit den Posterior-Verteilungen von `model_t` und ebenso die Zusammenfassung der Kenngrössen von `model_t` mit der von `model_g`, so stellen wir Folgendes fest: Die Schätzungen der beiden Modelle für $ \\mu $ sind ähnlich, mit einem Unterschied von $ \\approx 0.5$. Die Schätzung von $ \\sigma $ ändert sich von $\\approx 3.5$ auf $ \\approx 2.2 $. Dies ist eine Folge der Wahl der Student's $t$-Verteilung als Likelihood-Funktion, welche den Werten, die vom Mittelwert abweichen, weniger Gewicht verleiht. Wir beobachten ebenfalls, dass wir nun eine _nicht sehr Gauss-ähnliche Verteilung_ mit ausgeprägteren Schwänzen erhalten haben.\n", + "\n", + "\n", + "\n", + "Die Student's $t$-Verteilung ermöglicht uns eine _robustere_ Schätzung, da die Ausreisser den Effekt haben, $ \\nu $ zu verringern, was dann dazu führt, dass sich die Standardabweichung erhöht. Der Mittelwert und die Skala (\"Standardabweichung\" der t-Verteilung) werden also geschätzt, indem die Grossmehrheit der Daten stärker gewichtet wird als diejenigen Werte, welche sich außerhalb der Masse befinden. \n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}