From 58ebc69a802bbf240f02d94cdd9fefb34fb5724b Mon Sep 17 00:00:00 2001
From: Hartmut Stadie <hartmut.stadie@cern.ch>
Date: Mon, 7 Oct 2024 11:02:17 +0200
Subject: [PATCH] lecture 2 done
---
lecture_2.ipynb | 762 ++++++++++++++++++++++--------------------------
1 file changed, 355 insertions(+), 407 deletions(-)
diff --git a/lecture_2.ipynb b/lecture_2.ipynb
index 5d76581..49f9dc5 100644
--- a/lecture_2.ipynb
+++ b/lecture_2.ipynb
@@ -4,6 +4,7 @@
"cell_type": "markdown",
"id": "74976eec-e9a9-46b1-824d-01dad15478bc",
"metadata": {
+ "cell_style": "center",
"slideshow": {
"slide_type": "slide"
},
@@ -98,33 +99,12 @@
},
{
"cell_type": "code",
- "execution_count": 1,
+ "execution_count": null,
"id": "662bb993",
"metadata": {
"cell_style": "split"
},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "Text(0, 0.5, '$P(k)$')"
- ]
- },
- "execution_count": 1,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- "<Figure size 640x480 with 1 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"import numpy as np\n",
"import scipy\n",
@@ -587,7 +567,7 @@
},
{
"cell_type": "code",
- "execution_count": 6,
+ "execution_count": null,
"id": "641ec6cc-6f1a-4399-b652-7e3da333782a",
"metadata": {
"slideshow": {
@@ -595,25 +575,7 @@
},
"tags": []
},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "(array([24., 45., 66., 67., 58., 25., 18., 1., 2., 0.]), array([-0.5, 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5]), <BarContainer object of 10 artists>)\n"
- ]
- },
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- "<Figure size 640x480 with 1 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
@@ -701,7 +663,7 @@
},
{
"cell_type": "code",
- "execution_count": 7,
+ "execution_count": null,
"id": "5052bdb2-6e4b-4ea6-b08e-ba22f2a4a3d2",
"metadata": {
"cell_style": "split",
@@ -710,28 +672,7 @@
},
"tags": []
},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "(1.000000000000001, 4.6105475479254554e-11)"
- ]
- },
- "execution_count": 7,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- "<Figure size 640x480 with 1 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"import scipy\n",
"\n",
@@ -769,26 +710,23 @@
},
{
"cell_type": "code",
- "execution_count": 8,
+ "execution_count": null,
+ "id": "c595233d",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
"id": "7c461ddf-0cb8-49b0-adc6-a7ae6f11212b",
"metadata": {
"slideshow": {
- "slide_type": ""
+ "slide_type": "skip"
},
"tags": []
},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "(0.6781977937903096, 7.529508059159858e-15)"
- ]
- },
- "execution_count": 8,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"scipy.integrate.quad(lambda x: scipy.stats.poisson.pmf(18,x), 18-np.sqrt(18), 18+np.sqrt(18))"
]
@@ -796,7 +734,11 @@
{
"cell_type": "markdown",
"id": "e34f6d9d",
- "metadata": {},
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
"source": [
"...Ok-ish..."
]
@@ -836,31 +778,30 @@
"\n",
"Naive confidence interval: $1\\pm 1$\n",
"\n",
- "Test:"
+ "Test it:\n",
+ " - draw the Poisson probability $P(1,\\mu$ vs. \\mu\n",
+ " - compute the confidence for the interval $[0, 2]$ numerically with [scipy.integrate.quad](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html)"
]
},
{
"cell_type": "code",
- "execution_count": 27,
+ "execution_count": null,
+ "id": "06885d9b",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
"id": "e6102fec-1275-439a-b6b4-8cb1ee4960fc",
"metadata": {
"slideshow": {
- "slide_type": ""
+ "slide_type": "skip"
},
"tags": []
},
- "outputs": [
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- "<Figure size 640x480 with 1 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"mus = np.linspace(0,10,1000)\n",
"plt.plot(mus, scipy.stats.poisson.pmf(1,mus))\n",
@@ -869,21 +810,14 @@
},
{
"cell_type": "code",
- "execution_count": 10,
+ "execution_count": null,
"id": "a0595e97",
- "metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "(0.593994150290162, 6.594659821447934e-15)"
- ]
- },
- "execution_count": 10,
- "metadata": {},
- "output_type": "execute_result"
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
}
- ],
+ },
+ "outputs": [],
"source": [
"scipy.integrate.quad(lambda x: scipy.stats.poisson.pmf(1,x), 1-np.sqrt(1), 1+np.sqrt(1))"
]
@@ -896,7 +830,7 @@
"source_hidden": true
},
"slideshow": {
- "slide_type": ""
+ "slide_type": "skip"
},
"tags": []
},
@@ -920,36 +854,33 @@
"### Let's find a better interval: $[\\mu_-, \\mu_+]$\n",
"\n",
"here:\n",
- "$\\mu_- = 0$"
+ "$\\mu_- = 0$\n",
+ "\n",
+ "\n",
+ "find $\\mu_+$, so that the integral from $[0,\\mu_+]$ is $0.6827$:\n",
+ " - define a function that returns the integral for a given $mu_+$\n",
+ " - plot the function \n",
+ " - use root finding with [scipy.optimize.brentq](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.brentq.html) to find the value of $\\mu_+$ where the integral minus 0.6827 is 0."
]
},
{
"cell_type": "code",
- "execution_count": 11,
- "id": "630c83e0-2be4-41dd-a124-2ac672a2c507",
+ "execution_count": null,
+ "id": "2d187a99",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "2.359784379558492"
- ]
- },
- "execution_count": 11,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- "<Figure size 640x480 with 1 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "630c83e0-2be4-41dd-a124-2ac672a2c507",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
}
- ],
+ },
+ "outputs": [],
"source": [
"def intervall(mu_plus):\n",
" return scipy.integrate.quad(lambda x: scipy.stats.poisson.pmf(1,x), 0, mu_plus)[0]\n",
@@ -967,7 +898,7 @@
"id": "f20e18c3",
"metadata": {
"slideshow": {
- "slide_type": "-"
+ "slide_type": "skip"
},
"tags": []
},
@@ -996,7 +927,7 @@
},
{
"cell_type": "code",
- "execution_count": 12,
+ "execution_count": null,
"id": "5fffd76e-14da-4854-8af0-5262e0c3c9a3",
"metadata": {
"slideshow": {
@@ -1004,16 +935,7 @@
},
"tags": []
},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "naive: 13.757359312880716 22.242640687119284\n",
- "symmetric in P: 13.599062608025005 22.185865296670393\n"
- ]
- }
- ],
+ "outputs": [],
"source": [
"def intervall_minus(mu):\n",
" return scipy.integrate.quad(lambda x: scipy.stats.poisson.pmf(18,x), mu, 18)[0]\n",
@@ -1029,21 +951,10 @@
},
{
"cell_type": "code",
- "execution_count": 13,
+ "execution_count": null,
"id": "52f8f412-cb94-4c32-95b6-03f178cbcdb6",
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "(0.6827000000000286, 7.579492589116262e-15)"
- ]
- },
- "execution_count": 13,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"scipy.integrate.quad(lambda x: scipy.stats.poisson.pmf(18,x), mu_minus, mu_plus)"
]
@@ -1063,7 +974,7 @@
},
{
"cell_type": "code",
- "execution_count": 14,
+ "execution_count": null,
"id": "e0a6084d-dd5d-4ffc-8849-a61a8327fb4e",
"metadata": {
"cell_style": "split",
@@ -1072,18 +983,7 @@
},
"tags": []
},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "(0.8565084673723236, 4.724262071904028)"
- ]
- },
- "execution_count": 14,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"def intervall_minus(k, mu):\n",
" return scipy.integrate.quad(lambda x: scipy.stats.poisson.pmf(k,x), mu, k)[0]\n",
@@ -1109,30 +1009,12 @@
},
{
"cell_type": "code",
- "execution_count": 15,
+ "execution_count": null,
"id": "382e5a13-5f5f-44e5-90dd-7272fbdb171a",
"metadata": {
"cell_style": "split"
},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[0. 3.51925775]\n"
- ]
- },
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- "<Figure size 640x480 with 1 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"ks = np.arange(0, 20)\n",
"\n",
@@ -1166,23 +1048,12 @@
},
{
"cell_type": "code",
- "execution_count": 16,
+ "execution_count": null,
"id": "cb5826ae-29df-41c3-ad8f-dde61b5d90ba",
"metadata": {
"cell_style": "split"
},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "(1.9999782866774654, 4.000021713322534)"
- ]
- },
- "execution_count": 16,
- "metadata": {},
- "output_type": "execute_result"
- }
- ],
+ "outputs": [],
"source": [
"def intervall_minus(x, mu, sigma):\n",
" return scipy.integrate.quad(lambda y: scipy.stats.norm.pdf(x,y, sigma), mu, x)[0]\n",
@@ -1203,7 +1074,7 @@
},
{
"cell_type": "code",
- "execution_count": 17,
+ "execution_count": null,
"id": "e87da118-0c11-4345-a656-096de6f980e9",
"metadata": {
"cell_style": "split",
@@ -1212,25 +1083,7 @@
},
"tags": []
},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "[-0.59598131 1.40406212]\n"
- ]
- },
- {
- "data": {
- "image/png": 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++/pRXrITMzQAgJbhutLWrdJzz/nPzOTnS+PH6/DmzfrfXbs0eNSoxMdYR6QqVloq/e530cctrYpBJDQAgJbQiGcwmexsHbKgr7kpHUywByUnAEB8+bUDSVbXalzXv4Np6lSrw0YNzNAAAJovUqs5/njp2mv9V9FaVquJhJydLd1wg38HU79+dDAFBQkNAKB5AliraWjIdDAFByUnAEDTxepgmjTJ2lpNrJALCqwNGQ3ADA0AoHEitZqePaW//MV/mmPYMGnyZKtqNZGwX3/dP+Rf/EK69VarQkYjkNAAABquZq3GcfzXylhYq2lE05UtIaORkl5yev311/XTn/5Uubm5chxHL7zwQq3jV1xxhRzHqfWrb9++yQkWAFqzurWaSDIzYIDVtZpYJabQkZ+AFoaMJkj6DM2BAwfUu3dvXXnllRoxYoTvOT/60Y80Z86c6q+POeaYRIUHAIjUasrK/Kc47rrLm96wqFYTCTkvT7r9dv+w58+3qukKzZT0hGbo0KEaOnRovedkZmaqU6dOCYoIAFAtgLWaADZdIQ6SntA0xLJly9SxY0d985vf1MCBA3XvvfeqY8eOMc+vqKhQRUVF9dfl5eWSpMrKSlVWVsY1tsj14n1dWzC+4Ev1MTK+FuS6Sr/mGjk1MgMjSaGQnHBYJi1NVUVFMtnZUjPii+cYvfJSusJhp8arRr/+dVjz54dUVeUoLc2oqKhK2dmmOWE3GN+jzb92QzjGxHqGaOI5jqOFCxfq0ksvrX7tueee0ze+8Q3l5eVpx44duu2223T48GGtXbtWmZmZvtcpLCzUnXfeGfX6vHnz1LZt25YKHwBSyrf/53/Ue+bMqNffuuEGfdWhgw7k5OhQVlYSIou2d28bffzxN/Thh+319NNnRB2/++43lJNzQB9/fJxycg4oK+tQEqJEYx08eFAjR47Uvn371L59+3rPtT6hqevjjz9WXl6e5s+fr+HDh/ue4zdD06VLF+3du/eofyGNVVlZqZKSEg0ZMkQZGRlxvbYNGF/wpfoYGV+cua6cDz6Q8/LLCj3xRK3ZGUkyaWk6XFoa11pNc8c4Z46jgoK0I7MyRpJT63hamlFp6eGklZf4Hm268vJyZWVlNSihCUTJqaacnBzl5eWptLQ05jmZmZm+szcZGRkt9s3Ukte2AeMLvlQfI+OLA7/FJ+eeK61dK1VVSWlpcmbOVEa3bi3yxzdljK7rbYj3dcheMhMKea95HUyOunVL/vcG36NNu2ZDBS6h+fTTT1VWVqacnJxkhwIAqWPnTu/pjDUn7UMh6fnnvd9b2MHUvbv00EN0MMGT9ITmiy++0LZt26q/3rFjh9avX68TTjhBJ5xwggoLCzVixAjl5ORo586duvXWW5WVlaWf/exnSYwaAFKE60qvvirdc0/0JnnhsJfIDBpkTVZABxNiSXpC8/bbb+uiiy6q/vr666+XJI0ePVqPP/64Nm7cqD//+c/6/PPPlZOTo4suukjPPfec2rVrl6yQASA1PPmkNHas/26/0tct2ZaItUHesGHSSy9VV8XYJK+VSnpCM2jQINW3Lnnx4sUJjAYAWok33vCyg5ocxyszWZYZREpMW7b4z8xMmiTNmGFVVQxJkPSEBgCQIK7rZQWrV0t33x193Bjp2WetWnwSwH39kCQkNADQGgRw8Ul9z2D6uoPJmnCRZEl/OCUAoIWVlXkdTDUzA8eR7r/f6odKFhfH7mBautRrzBozJuFhwVLM0ABAqnJdadUqaerU6IW/xnh7zOzcadXiE9f1tr15+mnphReij1s2iQSLkNAAQCqaPdur1xytg8mixSdz5jgaN+7rkB1H+o//kBYtsm6dMixEQgMAqWb9eq/EVJOlHUwRZWXf0G9/m1Yr/3Ic6YknvN9bNIkES5HQAEAqiPQ2b9sm/e530cct7GCSvLDnzQvpnnsukDG1n8Fk4b5+sBgJDQAEXQA7mCSpqEiaOFEyJk1Smuo+WNKyff1gObqcACDIXNe/g2nqVKs7mBYskCZMUFSJyeKQYTlmaAAgiFzXWyvz0EP+HUz9+lnZwfTee9LChdKsWdHHjXFsrIohIEhoACBoArh9rl/IjlM7F0tLM+rXz7ElZAQMJScACJKtW/1LTBbXarZvjw45FJKmT/867FAorKKiKpvCRsAwQwMAlmuzd6+cZcukL76IrKKtfYLFHUyLFkl33RUdcjgsnX22VxXbvPmwdu36X40aNTgpcSI1kNAAgMWcOXOUP26cnFgb5ElWdjDNmqVam+TVVbMqlp1t9MorhxIbIFIOJScAsJXrKq2goHYy4zjelIfFJaalS6WxY+lgQmIxQwMANolskJeXJ91+u5y6C3+NkQYMsLKDafNmafly75mXdVlaFUMKIaEBAFs0dIO8AHQw1WVhVQwphpITANjAdX2zgqqRIxUOHflftYW1mt27j97BZGHYSEHM0ABAMkVKTOvW+U5xmCuv1KuDB+sHeXlK79XLiqwgEvKxx0rjx/t3MJ1zjnVVMaQ4EhoASJYGbJBnunfXoQMHZAYOlDIyEhufj4BWxdAKUHICgGSIUWKSxeWlWCHfeCPlJSQfMzQAkCiRWk337tKDD/pPc8yfX7sVqLIy8XHW4breBsULF/qHPHSodO21lJeQXCQ0AJAIAW0FCuBjo9BKUXICgJYWq1ZzySVW12pcN7qDSbI6ZLRizNAAQEuJlJi2bPGf4rjuOumxx6yq1URCzsrywvN7dAEb5MFGJDQA0BICWKsJaFUMkETJCQDiL4U6mCZOpMSEYGCGBgDirbi4YR1MFoiUmF57zT/kESOkm26yqioG+CKhAYB4cF1p7Vrp6aelF16IPm5hrSaAVTEgJhIaAGiu4mKvHSiygtZxvM1ZFi+WqqqsrNXUVxULh60MGagXCQ0ANMcHH9ROZiQvoZk50/u9RbWaSHmpc2dpypTAVMWABiGhAYCmcF3pueek++7zfzrjtm3SoEHWZAV0MCHV0eUEAI1VVCR17SrdcIP06afRxyOLTywRq7x05ZV0MCF1MEMDAI2xcKE0YULt1xzHW3xi2XqZSIlpzRr/mZlRo6S77rKqKgY0GQkNAByN60qbNkkLFkizZkUfN8a67XPpYEJrQ0IDAPXxywwcp/a6GcsWn9DBhNaIhAYAYtm+PbqDKRSS7r9fuvlmq0pMkfLSySdL06bRwYTWh4QGAOpyXWnRIunuu/07mM4+W9q505rFJ3QwASQ0AFDbrFnSuHH+j5mWrFt8Equ8NGKEt2GxRZNIQIsioQGAiKVLpbFja79maQdTxIoV/jMzEydKDz9szSQS0OJIaAC0bq4rbd4sLV/urY2py8IOJkkqK5P+9Cfpsceij1k2iQQkBAkNgNYroItPHnzQ29MvomNHae9eOpjQurFTMIDWafdur4OpZjITCknTp1u7fa4x3qxMzWRG8jYrXr3aq5jt3CmNGZOU8ICkYoYGQOsR6W1u21YqKPDvYDrnHKs6mCRp7942WrjQ0Zw5XvNVXVVV0oED3qOjgNaKhAZA69DQ8pJli0/mzHE0bly+jHEkeWuUpeh9/Sx6dBSQFJScAKS+WL3NN95obXlJkjZulMaOTatOZiQvobG4KgYkDTM0AFKX60pbt3oPlPSbmRk6VLr2WqvKS5Gq2O7d0vXXS5JT67iF+/oBViChAZCaAvh0Rv+QjWomNRaGDViBkhOA1OO60R1MktV1Gr+qmONId99dpVDIe9HCsAFrMEMDIDW4rleHycqSrrvO/9EFFm6Q57rShg3SI49E51/GSH37SrNmlSgv7wfq1SvdlrAB65DQAAi8riUlSh8+PHAb5DWkKta9u9GBA4c0cKBRRkZi4wOChJITgGBzXZ1ZVCSnblYwcaLVJabS0uiqmONYHTJgNWZoAATTkXagUEmJHL/y0ogR0k03WdUKFOlg+uILacKE6KqY32OjKiuTEysQNCQ0AIKnRq0mze+4ha1AAX1sFBAYlJwABItPO5CRZEJH/ndmYa0mVgdTYSElJiBemKEBYL9IraZzZ2nKlKhpDkfS4b/+Vek5OdaUlyQv7A8+kJ580r+DaeBA70GSFlXFgMAioQFgtwbUasKhkEzfvlK3bgkMrH4B3NcPCDRKTgDsFesZTFdcUV2rMWlperegwKqsYNcuOpiARGOGBoB9IiWmNWv8pzhGj5buvlvatk2H8/K0e8MGnZ74KGuJhJyeLhUUNKyDCUD8kNAAsEtjazWVld5Wu0lEBxOQfJScANgjVokpYB1MknTLLZSYgERihgZAckVqNSefLE2b5j/NMX++dbUa15W2bpWee84/5Px8afx4OpiARCGhAZA8Aa3V0MEE2IeSE4DkiFWrGTHC6lpNWVl0B5NkdchAq8AMDYDkeOMN/ymOiROlhx+2qlYTqYodf7x07bXRHUwSHUxAsiV9hub111/XT3/6U+Xm5spxHL3wwgu1jhtjVFhYqNzcXB177LEaNGiQNm3alJxgATRfWZl0443Sb34TfaxmrWbQICsyg+JiKS9PGjxYOussLw+rK1IVsyRkoFVqVEJTVlYW9wAOHDig3r17a8aMGb7Hp0+froceekgzZszQmjVr1KlTJw0ZMkT79++PeywAWtiDD0pdu0oPPCB9+aWUlRXIDqZJkygxAbZpVMkpLy9Pxx9/vHr37q3evXvrzDPPVO/evVVRUaHHHntMf/7znxsdwNChQzV06FDfY8YYPfzww5oyZYqGDx8uSZo7d66ys7M1b948jR07ttF/HoAkMEZ69FHphhtqv/7ZZ9Lq1dKBA1bVaiIlpiVL/Ktiw4ZJkydbVRUDWr1GJTTbt2/X+vXrtX79eq1bt07/+Mc/9NFHH0mS2rdvH/fgduzYoT179ig/P7/6tczMTA0cOFArV66MmdBUVFSooqKi+uvy8nJJUmVlpSorK+MaY+R68b6uLRhf8CV1jK4rZ80ahZ56SqHFi6OPV1Xp8L59MgMHel83IcZ4j2/OHEcFBWkKhx3f42lpRnl5h5WdLWVnR2KIyx/ti+/R4GN8zb92QzjG+C1va7hVq1Zp9OjRuv/++/Wzn/2sOZeS4zhauHChLr30UknSypUr1b9/f/3rX/9Sbm5u9XnXXHONdu3apcV+/4OUVFhYqDvvvDPq9Xnz5qlt27bNihFAw3QtKdGZRUVyjvwvJizvqdg104RwKKSSWbN0KCsrGSFG2bu3ja6+Ol/G1IzSKBSSwmFHoVBYBQXvasiQ3UmLEWhNDh48qJEjR2rfvn1HnThpdpdTv3799Mgjj+j3v/99sxOaWByn9r+UjDFRr9V0yy236Prrr6/+ury8XF26dFF+fn7cZ5IqKytVUlKiIUOGKCMjI67XtgHjC76kjPG995T+2GO1khcnFFLVvfcq7fe/l1NVJZOWpnBRkQaPGtWsP6q543Ndads2Rzk5RsXFoTrJjCQ5+utfD+vEE6Xu3Y06dz5dSuCTo/geDT7G13SRCktDNCqhqays9A22Z8+eLdJ51KlTJ0nSnj17lJOTU/36J598ouzIXK+PzMxMZWZmRr2ekZHRYt9MLXltGzC+4GvxMUYWnpSVSdddF3XYCYeV3revtHOntG2bnB49lB7HxSdNGV9D9/UbMCA96etk+B4NPsbXtGs2VKMSmuOOO06nnXaazjrrLJ155pk666yzlJubq0cffbTWOpd46datmzp16qSSkhKdddZZkqSvvvpKy5cv1/333x/3Pw9AEzU0M7Bo+9xYHUxXXy099ZRUVUUHExAkjUpoXnvtNb377rt699139cwzz+jWW2/Vl19+KUnKz8/XlClT9L3vfU/f+973dOqppzboml988YW2bdtW/fWOHTu0fv16nXDCCeratasmTZqkqVOnqmfPnurZs6emTp2qtm3bauTIkY0JHUBL8csMHEe65x7p9tutygwik0g9e0ovvuiff40c6YVNBxMQLI1KaC644AJdcMEF1V+Hw2Ft2bKluvNp7dq1euqpp/TJJ5+oqqqqQdd8++23ddFFF1V/HVn7Mnr0aD399NO68cYb9eWXX2r8+PH67LPPdN5552nJkiVq165dY0IHEG+uK23YID3ySHRmYIx0/vnV5SUbMoOak0iO47/br2WTSAAaoVmLgkOhkE499VSdeuqp+tWvflX9+r///e8GX2PQoEGqr9HKcRwVFhaqsLCwOaECiKeAPZ2x7iRS5H85vXtL771n1SQSgCZqkWc51bdgF0DAbdvmLTSp+Q8Rx/F2/LU0M9i82T/3evhhL++yZBIJQDPwcEoARxdZfHLggDRhQnS9xhgrn87outKrr0rTp0cfs2wSCUAzkdAAqF9DO5j69bMqM3jySWns2K9zr4wMbwIpHLZyEglAMyX9adsALBarg6mw0OqnM65Y4YVdcyIpHPYeG7V0qbdWecyYpIUHoAUwQwMgmut6C09mz/bvYBo40MsILFp84rrS9u3SqlVex3hdVVVexWzQoISHBiABSGgA1BawDiZJKinpquHD0xu0rx+A1ETJCcDXdu3yOpjqlpgsLi+VlUlFRWfWejp2KCTdf7/VYQOIM2ZogNYu0sGUkSEVFASqg2nVKunee9OiHigZDkvnnmvVvn4AWhgJDdCaBbSDafbsmot+Q5KMVOPZ3hZWxQC0MEpOQGsV6+mMt9xida1m/froff0kKS3NHPmvdSEDSABmaIDWxnWlrVulv/3Nf2YmP18aP96qWk2kKlZaKv3ud35nOPrLXw4rJyfdlpABJBgJDdCaBLCDqSFVsVAorL59jbp1S1xcAOxCyQloLcrKojuYJKvLS67r33Q1dWrNsI0KCt61KWwAScAMDZDKXFfOBx+o/Y4dSvvDH6IXnkjWdjCtXy89+KB/01W/fl93MOXlHdaGDbslnZ6ESAHYgoQGSFVHajXp4bAGqWYPUA0WdjA1tipWWSlt2JDYGAHYh5ITkIrqdDA58hqbNWmS1SWmrVsDt68fAEswQwOkkkg70JIlUVMcjiQNGyZNnmxlB9Nnn0nXXhuYff0AWIaEBkgVR6nVmLQ0OQHsYLKwKgbAQpScgFQQa5O8kPcRD4dCqioqsior8AvZcaS77qLEBKDxmKEBgipSqznpJOnGG/2nOebP1+Hjj9f/7tqlwaNGJT5GH64rvf++9MQT0SEbIw0YwDOYADQeCQ0QRI2o1ZjsbB165ZXExVaPAO7rByAgKDkBQROrvHT11VbXanbupIMJQMthhgYIgkh5qWdP6b//23+KY+RI6fbbrarVRMI2RioooIMJQMshoQFsV7NO4zj+u/1aWKuhgwlAIlFyAmxWt7wUSWbOPNPqWk2sqtiUKVaHDSDAmKEBbLZ5s/8Uxx//6M3IWFhe6t7dewaTX9g//KE0bpxVYQNIESQ0gI1cV3r1VWn69OhjAS4vWRY2gBRCyQmwzZNPSl27SldeKX3wgZSRUb1Bno11mljlpWHDKC8BSBxmaACbrFjhZQc1hcPS6tXSgQNW1WkiJaYtW/xnZiZNkmbMoLwEIDFIaIBkc10vK1i1SrrnnujjVVVeMjNoUMJDi4UN8gDYhoQGSKbGLD6xRH2PjQqHKS8BSA4SGiBZysq8rXNr7ivjONK0adKtt3ozM5ZkBzX39SsujvnYKDbIA5A0JDRAormuV16aOtV/69xzz7Xq6YxskAcgCEhogESaPdvLDvx2+5WsW3wSq7w0eLC0fLlVk0gAWjkSGiBR1q/3Skw1OY63+MTSzGD9ev+Zmdtuk+bOtWYSCQBIaIAWFVl8sm2b9LvfRR+39OmMris995z0wAPRxyybRAIASSQ0QMsJ6OKToiJp4sSvq2Lf+IZ08CAdTADsxk7BQEtwXa+8VDOZcRxvIbDF2+c+/7w0YULtJT5ffunt67d0qbdWecyYpIUHADExQwPEk+t6C08efNC/g6lfP6s6mCQv5PfekxYs8J66UJeF+/oBQBQSGiBeArh9rl/IjlM7F7NsXz8A8EXJCYiHrVv9S0wWl5e2b48OORTyHvBtcdgA4IsZGqCpIh1Mn30mXXutf4nJ0g6mRYuku+6KDjkcls4+27qqGAAcFQkN0BQB7WCaNUsaNy4w+/oBQINRcgIay2/7XMfxpjwsrtUsXSqNHRv96CiLQwaABmOGBmgo15Xef1964onomRljpAEDrKvVuK60aZOjZ545RS+8EP1xt7QqBgCNRkIDNESgO5jSJfXyPcfCqhgANAklJ+Bodu4MXAfT7t1+HUyGDiYAKYsZGsBPpINJkgoKAtXBtGKFdO+9fh1Mjs45x7qqGADEBQkNUFdAO5hmz/bCjt3BZNSjh2NTVQwA4oaSE1CTXweTJE2ZYnWt5u23vRJTrA6mUCisoqIqm0IGgLhihgatXpu9e+UsWyadcor3DCa/mZkf/tDbwMWiWo3rehsUb9ok3Xpr9PFIVez44w9r167/1ahRgxMfJAAkCAkNWjVnzhzljxsnJ1adRrK8gyn2OZGqWHa20SuvHEpccACQBJSc0Hq5rtIKCqKTmWHDrC4vua5/09V991kdNgC0KGZo0PpEOpi2bJHjN8UxaZI0Y4Z15aXSUikrS7ruOv+mq7596WAC0HqR0KB1CfQGebHPsTBsAEgoSk5oPXw6mIwk4zjeFxbWaWI1XU2cSHkJAGpihgapLVKr6dnTm+qokxk4kt6aPFnfv/hipffqZU1WEAn7tdf8Z2ZGjJBuuonyEgBEkNAgdTWgVmPS0vRZr14yAwdKGRkJDC62AFbFACDpKDkhNcWq1QweXKtWU1VUpENZWYmPL4ZYYYeOfFIpLwGAP2ZokFoitZpdu/ynOG67TZo7t7pWY7KzpVdeSXycNURC7tLF2yDPL+z58617bBQAWIWEBqmjKbWaysrExecjoI+NAgDrUHJCaghgrSZWyFdeSQcTADQWMzRIDQsXBqZWEykxrVnjH/KoUdJdd9HBBACNQUKD4HJd78mMCxZIs2ZFH7ewVkMHEwC0DBIaBJNfZtC/v7R6tVRVZWWtpr6qWDhsZcgAEBgkNAie7du9pzPWfKBRKOSVlySrajWR8tLJJ0vTpgWmKgYAgWP9ouDCwkI5jlPrV6dOnZIdFpLBdaXZs6WLLop+OmM47CUynTtLgwZZkRkUF0t5ed7WN9/+tvTEE9HnRKpiloQMAIEViBma7373u3r11Verv06LtICg9Zg1Sxo3LjqRiYgsPrFErPLSz3/urV+2tCoGAIEViIQmPT29UbMyFRUVqqioqP66vLxcklRZWanKOO87ErlevK9rCyvGt2yZ0seOlVPjJeM4Uigkp6pK5siOvyY7u9H7ysR7fK4rbdvm6P33pXA4+uM1duxhTZ9u9OGHjrp3N+rcueW3wrHiHrYgxhd8qT5Gxtf8azeEY0ysf/LaobCwUA888IA6dOigzMxMnXfeeZo6dapOPvnket9z5513Rr0+b948tW3btiXDRZy02btX33BdfWvTJvVcsEBpVVVR57x1ww36qkMHHcjJseLxBSUlXVVUdKaMceQ9x9updTwUCmvWrBJlZR1KSnwAEDQHDx7UyJEjtW/fPrVv377ec61PaP7nf/5HBw8e1He+8x39+9//1j333KPNmzdr06ZN+ta3vuX7Hr8Zmi5dumjv3r1H/QtprMrKSpWUlGjIkCHKsOThhvGUjPE5c+YoraBATo16Td30wKSl6XBpabPrNfEan+tKPXqkKxyuFeWRDiZHaWlGRUVVuvLKxH/c+B4NtlQfn5T6Y2R8TVdeXq6srKwGJTTWl5yGDh1a/fszzjhD/fr1U/fu3TV37lxdf/31vu/JzMxUZmZm1OsZGRkt9s3Ukte2QcLGt3t39FqZUEjOtGnSLbdULz5xZs5URrducftjmzM+Y7y1ytEdTE6NDiZHnTsn9+PG92iwpfr4pNQfI+Nr2jUbyvqEpq7jjjtOZ5xxhkpLS5MdCuLJdaU33pDuuce/g+mcc6SdO61ryX7rLenJJ6VFi6KPW7ivHwCkrMAlNBUVFfrggw80YMCAZIeCeJk922sJOloHk0Xb5xYX194KJxSSLrlE+u//poMJAJLB+n1obrjhBi1fvlw7duzQm2++qZ///OcqLy/X6NGjkx0a4uHtt6M3yXMcq5/OuHGjdNVV0fnXo496k0hLl3r/HTMmGdEBQOtk/QyN67r61a9+pb179+rEE09U3759tXr1auXl5SU7NDSV60pbt3rPYbr11ujjxkjPPmvd9rmuK/3lL9L06dHHIvv6sUEeACSH9QnN/Mh29kgNR3s6o2Tl4pMZM6Tf/jYw+/oBQKtjfckJKcR1vfJSzWTGcaT77rO6xDR/vnTttYGqigFAq2P9DA0CLvJ0xhNPlCZNip7iMEbq29fKDqYNG6S//U2aOzf6uKVVMQBotUho0HIaWl6ysIOpbtiOUzsXs7AqBgCtGiUntIxYT2ecONHqWk1paXRVLBTyFgJbHDYAtHrM0CC+IiWm117zn5kZMUK66Sarykt797bRsmWODh2SJkzw39fv7LOtq4oBAGogoUH8HK3EZGF5ac4cR+PG5R95oKQ/C8MGANRByQnxEavEFDryLWZhncZ1pYKCtFrJjONIhYWUlwAgaJihQdNFyktdungb5PnNzHz9dEZrsgLXlTZv9p7BVPvp2F65aeBAb5dfyksAEBwkNGiagG6QF8CqGACgASg5ofFilZeuvNLqWs2uXX77+hmFQt4qYAtDBgA0EDM0aLhIiWnNGv8pjlGjpLvusqpWEwk5PV0qKPDb18/R5Mlv6eKLv69evdJtCBkA0AQkNGgQZ84cLyMIUK2mYVUxo169PtPAgUYZGYmLDQAQX5SccFRt9u5Vml8yY3kHk18yc8sttatiRUVVyso6lPgAAQBxxQwN/NXoYPrO3/8uJ0AdTFu3Ss895z8zk58vjR//dVUsO9volVcSHycAIL5IaBCtRq0mXVI3v3NSpIOpsjJx8QEAWg4lJ9RWp1bjSDKSqoYPt7qDqawsuoNJsjpkAEAcMUMDT6TE9P77UVmBI8kUFEiPPGJlB9Pxx0vXXhvdwSRJzz5rXVUMANACSGhw1FpNOBSS6d49gB1M1lXFAAAthJJTa3eUZzCZtDS9W1BgVVYQK+RJkygxAUBrxQxNa2aM9Pjj9T6D6XBennZv2KDTEx9dlEiJafFi/5CHDZMmT7aqKgYASBASmtbIdaW33vKezrhoUfTxmrWaykppw4bEx1gHz2ACANSHhKa1KS722oEiK2hDIemnP5VeekmqqrKyVlNfVSwctjJkAECCkdC0Jhs3SlddFf36jBneL4tqNZHy0kknSTfeWG9VzJaQAQBJRELTGriu9Je/SNOnRx8Lh71EZtAga7ICOpgAAI1Fl1OqmzFD6tpVuvVW6fPPo49HFp9YIlZ56eqr6WACAMTGDE0qmz/f23GuJsfxFp9Ytl4mUmJaudJ/ZmbkSOn2262qigEALEJCk2pc1+tK+tvfpLlzo48bY932uXQwAQCai4QmlfhlBo5T+5kAli0+oYMJABAPJDSpYtu22u3YkpcV3H+/dPPNVpWYIuWlbt2ku++mgwkA0HwkNEEWyQwOHJAmTIh+OmM4LJ19trRzpzWLT+hgAgC0BBKaoGpoZmDR4pNY5aVf/lL6+9+tmkQCAAQMbdtB5JcZOI5UWGh1b/OyZf7519ix3iTS0qXef8eMSXBgAIDAY4YmSFxX2rxZmj07OjMwRho40MsGLCkvSV7IW7Z47dhTp0Yft2wSCQAQUCQ0QRHA3ma/kE85xcu3KC8BAOKJhCYIdu2K7mCydIO8iLIy/5CXLPHCtmgSCQCQAkhobBXpYEpPlwoKojuYLNwgT/LCXrXKKy/5hbx9u1WPjQIApAgSGhsFtLd59mwv7LqJTIRlj40CAKQQupxsE6u3+ZZbrO5gWr/ev8RkccgAgBTCDI0tXFfautV7BpPfzEx+vjR+vFWLTyJVsdJS6Xe/iz5uaVUMAJCCSGhskCIdTHVZWBUDAKQoSk7JFmkHqpsZWFyrcd3okB3HWwhscdgAgBTGDE0yRGo1xx8v/fa3/qtoLazVuK63VubBB/07mPr1s+qxUQCAVoSEJtECWquZM8dRQUGgqmIAgFaEklMixepgmjTJ6lrNv/51nMaNS4sqMVkcMgCglWGGJhEiJaYlS/ynOIYNkyZPtqpWEwl5715Hv/99fxnj1DpOBxMAwCYkNC0t8B1MafK+TYykr5MaC6tiAIBWjJJTS4pVYgod+Wu3sFYTHbIjyeiOO6ooMQEArMUMTbxFajUnnSTdeKP/zMz8+dbValxX2rRJeuIJv5AdXXABHUwAAHuR0MRTQDuYjhZ2KBRW9+7GpqoYAAC1UHKKl1jlpauvtrodaOdO/03yvg7ZqKDgXZtCBgAgCjM0zeW6ytq4UaGNG/2nOEaOlG6/3apaTaQqZoxUUOC/SV6kgykv77A2bNgt6fSkxAoAQEOQ0DRHcbHSr7lG/cNh+ez1G4AOJn81q2KVldKGDYmLDwCApqDk1FRHSkzOkcyguqE5UB1MnilTrK6KAQBwVMzQNFVpaaA6mLZskZ55xj/kH/5QGjfOqqoYAACNQkLTVD17erMxNTOEAHYwWVgVAwCg0Sg5NVXnztKsWTJHajXGwlpNWVl0B5NEeQkAkHqYoWmOMWN0ePBgvfnMMzrv179WRrduyY6ouoOpXTtp4sToDiaJZzABAFIPCU1zde6sT884w4rMIKD7+gEA0GyUnFJErA6myZMpMQEAUh8zNAEWKS/17OnNzvjNzPzkJ9KkSXQwAQBSGwlNQDW0vEQHEwCgNaDkFECxykuDB1NeAgC0TszQBEikxLRzp//MzG23SXPnUl4CALQ+JDQBwQZ5AADERskpAGKVmCx+bBQAAAkVmISmqKhI3bp1U5s2bdSnTx+tWLEi2SG1KNeVli71/rtgQezHRi1d6pWgxoxJeIgAAFgjECWn5557TpMmTVJRUZH69++vmTNnaujQoXr//ffVtWvXZIcXdzXLS47jv9svG+QBAPC1QMzQPPTQQxozZoyuuuoqnXrqqXr44YfVpUsXPf7448kOLe7qlpciyczZZ9PBBABALNbP0Hz11Vdau3atbr755lqv5+fna+XKlb7vqaioUEVFRfXX5eXlkqTKykpVVlbGNb7I9eJ13Q0bHIXD0bflvvsOq3t3ow8/dNS9u1HnzlKch+Ir3uOzTaqPT0r9MTK+4Ev1MTK+5l+7IRxj/Aoa9vjoo4900kkn6Z///KfOP//86tenTp2quXPnasuWLVHvKSws1J133hn1+rx589S2bdsWjbep9u5to3fe6agFC3poz552tY6FQmHNmlWirKxDSYoOAIDEO3jwoEaOHKl9+/apffv29Z5r/QxNhOM4tb42xkS9FnHLLbfo+uuvr/66vLxcXbp0UX5+/lH/QhqrsrJSJSUlGjJkiDIyMpp0jdmzHU2YkCZjvPFkZhpVVkrhsKO0NKOiorBGjRocz7AbLB7js1mqj09K/TEyvuBL9TEyvqaLVFgawvqEJisrS2lpadqzZ0+t1z/55BNlZ2f7viczM1OZmZlRr2dkZLTYN1NTr/3aa9L48bVfO3zY0erV0oEDUo8ejjp3Tv5tasm/Oxuk+vik1B8j4wu+VB8j42vaNRvK+kXBxxxzjPr06aOSkpJar5eUlNQqQQWJ60qvvurt7PujH0Ufr6rykplBg1j4CwBAQyT/n/4NcP311+vyyy/X2WefrX79+mnWrFnavXu3xo0bl+zQGq0xD5UEAAANE4iE5rLLLtOnn36qu+66Sx9//LFOP/10vfLKK8rLy0t2aI2ye7d09dW195UJhaRp06RbbvFmZmjJBgCg8QKR0EjS+PHjNb7uYpOAcF3pjTeke+6J3iQvHJbOOcfb7ZeHSgIA0DSBSWiCavZsr8QUqzmeh0oCANB81i8KDrK3344uMTkOO/4CABBvzNDEmetKW7dK770nTZkSfdwY6dlnpRNPpLwEAEC8kNDEUUM7mHioJAAA8UXJKU5c1ysv1UxmHEe67z5KTAAAtDRmaJrJdaU338zW9OlpUQt/jZH69qWDCQCAlkZC0wzFxdLVV6fLmL6+x+lgAgAgMSg5NVGkxBR5oKREBxMAAMnCDE0TlZZG7y1DBxMAAMlBQtNEPXt6jy2ouQiYDiYAAJKDklMTde4szZolpaV50zRpaYYSEwAASUJC0wxjxkilpYd1991vqLT0sMaMSXZEAAC0TiQ0zdS5s3TGGZ8yMwMAQBKR0AAAgMAjoQEAAIFHQgMAAAKPhAYAAAQeCQ0AAAg8EhoAABB4JDQAACDwSGgAAEDgkdAAAIDAI6EBAACBR0IDAAACLz3ZASSCMd4TscvLy+N+7crKSh08eFDl5eXKyMiI+/WTjfEFX6qPkfEFX6qPkfE1XeTnduTneH1aRUKzf/9+SVKXLl2SHAkAAGis/fv3q0OHDvWe45iGpD0BFw6H9dFHH6ldu3ZyHCeu1y4vL1eXLl1UVlam9u3bx/XaNmB8wZfqY2R8wZfqY2R8TWeM0f79+5Wbm6tQqP5VMq1ihiYUCqlz584t+me0b98+Jb9RIxhf8KX6GBlf8KX6GBlf0xxtZiaCRcEAACDwSGgAAEDgkdA0U2Zmpu644w5lZmYmO5QWwfiCL9XHyPiCL9XHyPgSo1UsCgYAAKmNGRoAABB4JDQAACDwSGgAAEDgkdAAAIDAI6E5iqKiInXr1k1t2rRRnz59tGLFinrPX758ufr06aM2bdro5JNP1hNPPJGgSBvvvvvu0znnnKN27dqpY8eOuvTSS7Vly5Z637Ns2TI5jhP1a/PmzQmKuuEKCwuj4uzUqVO97wnS/ZOkb3/72773Y8KECb7n237/Xn/9df30pz9Vbm6uHMfRCy+8UOu4MUaFhYXKzc3Vscceq0GDBmnTpk1Hve7zzz+v0047TZmZmTrttNO0cOHCFhpB/eobX2VlpW666SadccYZOu6445Sbm6tRo0bpo48+qveaTz/9tO89PXToUAuPxt/R7uEVV1wRFWvfvn2Pet0g3ENJvvfCcRw98MADMa9p0z1syM8FWz+HJDT1eO655zRp0iRNmTJF69at04ABAzR06FDt3r3b9/wdO3boP/7jPzRgwACtW7dOt956q37729/q+eefT3DkDbN8+XJNmDBBq1evVklJiQ4fPqz8/HwdOHDgqO/dsmWLPv744+pfPXv2TEDEjffd7363VpwbN26MeW7Q7p8krVmzptb4SkpKJEn/+Z//We/7bL1/Bw4cUO/evTVjxgzf49OnT9dDDz2kGTNmaM2aNerUqZOGDBlS/bw2P6tWrdJll12myy+/XO+++64uv/xy/eIXv9Cbb77ZUsOIqb7xHTx4UO+8845uu+02vfPOO1qwYIG2bt2qSy655KjXbd++fa37+fHHH6tNmzYtMYSjOto9lKQf/ehHtWJ95ZVX6r1mUO6hpKj78NRTT8lxHI0YMaLe69pyDxvyc8Haz6FBTOeee64ZN25crdd69eplbr75Zt/zb7zxRtOrV69ar40dO9b07du3xWKMp08++cRIMsuXL495ztKlS40k89lnnyUusCa64447TO/evRt8ftDvnzHG/Nd//Zfp3r27CYfDvseDdP8kmYULF1Z/HQ6HTadOncy0adOqXzt06JDp0KGDeeKJJ2Je5xe/+IX50Y9+VOu1iy++2Pzyl7+Me8yNUXd8ft566y0jyezatSvmOXPmzDEdOnSIb3Bx4jfG0aNHm2HDhjXqOkG+h8OGDTODBw+u9xyb72Hdnws2fw6ZoYnhq6++0tq1a5Wfn1/r9fz8fK1cudL3PatWrYo6/+KLL9bbb7+tysrKFos1Xvbt2ydJOuGEE4567llnnaWcnBz94Ac/0NKlS1s6tCYrLS1Vbm6uunXrpl/+8pfavn17zHODfv+++uor/fWvf9VvfvOboz6ENSj3r6YdO3Zoz549te5RZmamBg4cGPMzKcW+r/W9xxb79u2T4zj65je/We95X3zxhfLy8tS5c2f95Cc/0bp16xITYBMtW7ZMHTt21He+8x1dffXV+uSTT+o9P6j38N///rdefvlljRkz5qjn2noP6/5csPlzSEITw969e1VVVaXs7Oxar2dnZ2vPnj2+79mzZ4/v+YcPH9bevXtbLNZ4MMbo+uuv1wUXXKDTTz895nk5OTmaNWuWnn/+eS1YsECnnHKKfvCDH+j1119PYLQNc9555+nPf/6zFi9erCeffFJ79uzR+eefr08//dT3/CDfP0l64YUX9Pnnn+uKK66IeU6Q7l9dkc9dYz6Tkfc19j02OHTokG6++WaNHDmy3gf+9erVS08//bRefPFFPfvss2rTpo369++v0tLSBEbbcEOHDtUzzzyj1157TQ8++KDWrFmjwYMHq6KiIuZ7gnoP586dq3bt2mn48OH1nmfrPfT7uWDz57BVPG27Oer+S9cYU++/fv3O93vdNhMnTtSGDRv0xhtv1HveKaecolNOOaX66379+qmsrEx/+MMfdOGFF7Z0mI0ydOjQ6t+fccYZ6tevn7p37665c+fq+uuv931PUO+fJBUXF2vo0KHKzc2NeU6Q7l8sjf1MNvU9yVRZWalf/vKXCofDKioqqvfcvn371lpU279/f33/+9/Xo48+qj/96U8tHWqjXXbZZdW/P/3003X22WcrLy9PL7/8cr0/+IN2DyXpqaee0q9//eujroWx9R7W93PBxs8hMzQxZGVlKS0tLSp7/OSTT6KyzIhOnTr5np+enq5vfetbLRZrc1177bV68cUXtXTpUnXu3LnR7+/bt2/S/yXREMcdd5zOOOOMmLEG9f5J0q5du/Tqq6/qqquuavR7g3L/Ih1qjflMRt7X2PckU2VlpX7xi19ox44dKikpqXd2xk8oFNI555wTiHsqebOGeXl59cYbtHsoSStWrNCWLVua9Jm04R7G+rlg8+eQhCaGY445Rn369KnuGokoKSnR+eef7/uefv36RZ2/ZMkSnX322crIyGixWJvKGKOJEydqwYIFeu2119StW7cmXWfdunXKycmJc3TxV1FRoQ8++CBmrEG7fzXNmTNHHTt21I9//ONGvzco969bt27q1KlTrXv01Vdfafny5TE/k1Ls+1rfe5IlksyUlpbq1VdfbVIibYzR+vXrA3FPJenTTz9VWVlZvfEG6R5GFBcXq0+fPurdu3ej35vMe3i0nwtWfw7jtrw4Bc2fP99kZGSY4uJi8/7775tJkyaZ4447zuzcudMYY8zNN99sLr/88urzt2/fbtq2bWuuu+468/7775vi4mKTkZFh/vGPfyRrCPUqKCgwHTp0MMuWLTMff/xx9a+DBw9Wn1N3jH/84x/NwoULzdatW817771nbr75ZiPJPP/888kYQr0mT55sli1bZrZv325Wr15tfvKTn5h27dqlzP2LqKqqMl27djU33XRT1LGg3b/9+/ebdevWmXXr1hlJ5qGHHjLr1q2r7vKZNm2a6dChg1mwYIHZuHGj+dWvfmVycnJMeXl59TUuv/zyWp2I//znP01aWpqZNm2a+eCDD8y0adNMenq6Wb16tVXjq6ysNJdcconp3LmzWb9+fa3PZEVFRczxFRYWmkWLFpkPP/zQrFu3zlx55ZUmPT3dvPnmmwkfnzH1j3H//v1m8uTJZuXKlWbHjh1m6dKlpl+/fuakk05KiXsYsW/fPtO2bVvz+OOP+17D5nvYkJ8Ltn4OSWiO4rHHHjN5eXnmmGOOMd///vdrtTSPHj3aDBw4sNb5y5YtM2eddZY55phjzLe//e2Y39A2kOT7a86cOdXn1B3j/fffb7p3727atGljjj/+eHPBBReYl19+OfHBN8Bll11mcnJyTEZGhsnNzTXDhw83mzZtqj4e9PsXsXjxYiPJbNmyJepY0O5fpK287q/Ro0cbY7yW0TvuuMN06tTJZGZmmgsvvNBs3Lix1jUGDhxYfX7E3//+d3PKKaeYjIwM06tXr6QlcPWNb8eOHTE/k0uXLq2+Rt3xTZo0yXTt2tUcc8wx5sQTTzT5+flm5cqViR/cEfWN8eDBgyY/P9+ceOKJJiMjw3Tt2tWMHj3a7N69u9Y1gnoPI2bOnGmOPfZY8/nnn/tew+Z72JCfC7Z+Dp0jAwAAAAgs1tAAAIDAI6EBAACBR0IDAAACj4QGAAAEHgkNAAAIPBIaAAAQeCQ0AAAg8EhoAABA4JHQAACAwCOhAQAAgUdCAwAAAo+EBkAgPfvss2rTpo3+9a9/Vb921VVX6Xvf+5727duXxMgAJAMPpwQQSMYYnXnmmRowYIBmzJihO++8U7Nnz9bq1at10kknJTs8AAmWnuwAAKApHMfRvffeq5///OfKzc3VI488ohUrVpDMAK0UMzQAAu373/++Nm3apCVLlmjgwIHJDgdAkrCGBkBgLV68WJs3b1ZVVZWys7OTHQ6AJGKGBkAgvfPOOxo0aJAee+wxzZ8/X23bttXf//73ZIcFIElYQwMgcHbu3Kkf//jHuvnmm3X55ZfrtNNO0znnnKO1a9eqT58+yQ4PQBIwQwMgUP7v//5P/fv314UXXqiZM2dWvz5s2DBVVFRo0aJFSYwOQLKQ0AAAgMBjUTAAAAg8EhoAABB4JDQAACDwSGgAAEDgkdAAAIDAI6EBAACBR0IDAAACj4QGAAAEHgkNAAAIPBIaAAAQeCQ0AAAg8P4/fEM1eb9LNw8AAAAASUVORK5CYII=",
- "text/plain": [
- "<Figure size 640x480 with 1 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"xs = np.linspace(0,20,100)\n",
"sigma = 1\n",
@@ -1251,18 +1104,10 @@
},
{
"cell_type": "code",
- "execution_count": 18,
+ "execution_count": null,
"id": "202144ae-1057-41fc-8757-7f6f40c75868",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "0.341344746068543 0.341344746068543\n"
- ]
- }
- ],
+ "outputs": [],
"source": [
"print(scipy.integrate.quad(lambda y: scipy.stats.norm.pdf(3, y, 1), 2, 3)[0], scipy.integrate.quad(lambda x: scipy.stats.norm.pdf(x, 3, 1), 2,3)[0])"
]
@@ -1292,22 +1137,10 @@
},
{
"cell_type": "code",
- "execution_count": 19,
+ "execution_count": null,
"id": "580b83dc-3cb0-40df-bc77-8ad48d90fce5",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "1 0.6826894921370859\n",
- "2 0.9544997361036416\n",
- "3 0.9973002039367398\n",
- "4 0.9999366575163338\n",
- "5 0.9999994266968562\n"
- ]
- }
- ],
+ "outputs": [],
"source": [
"def conv_gaus(z):\n",
" return scipy.stats.norm.cdf(z) - scipy.stats.norm.cdf(-z)\n",
@@ -1326,21 +1159,10 @@
},
{
"cell_type": "code",
- "execution_count": 20,
+ "execution_count": null,
"id": "5a71ee06-db32-4349-a3da-ae0e394fbd74",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "0.68 0.9944578832101837\n",
- "0.9 1.6448536269514868\n",
- "0.95 1.9599639845401604\n",
- "0.99 2.5758293035489013\n"
- ]
- }
- ],
+ "outputs": [],
"source": [
"for c in [0.68, 0.90, 0.95, 0.99]:\n",
" print(c, scipy.optimize.brentq(lambda z: conv_gaus(z)-c,0, 10))"
@@ -1365,22 +1187,10 @@
},
{
"cell_type": "code",
- "execution_count": 21,
+ "execution_count": null,
"id": "73c11f8d-c8e4-4dc7-ad37-4ca4a33c55ea",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "1 0.6826894921370859 0.4660649426743922 0.31817763901728086\n",
- "2 0.9544997361036416 0.9110697462219214 0.8696158323408357\n",
- "3 0.9973002039367398 0.9946076967722628 0.9919224588280288\n",
- "4 0.9999366575163338 0.9998733190449377 0.9998099845855578\n",
- "5 0.9999994266968562 0.9999988533940409 0.9999982800915544\n"
- ]
- }
- ],
+ "outputs": [],
"source": [
"def conv_gaus_nd(z, n):\n",
" return np.power(scipy.stats.norm.cdf(z) - scipy.stats.norm.cdf(-z),n)\n",
@@ -1405,21 +1215,10 @@
},
{
"cell_type": "code",
- "execution_count": 24,
+ "execution_count": null,
"id": "7f14d38e-1e41-460e-9876-2afb62bed08b",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "0.68 0.9944578832101837 1.355121421071763 1.5521176915949972\n",
- "0.9 1.6448536269514868 1.948821862507059 2.11405446879861\n",
- "0.95 1.9599639845401604 2.236476644557793 2.387737887070821\n",
- "0.99 2.5758293035489013 2.806225314687492 2.934161015263926\n"
- ]
- }
- ],
+ "outputs": [],
"source": [
"for c in [0.68, 0.90, 0.95, 0.99]:\n",
" print(c, scipy.optimize.brentq(lambda z: conv_gaus_nd(z, 1)-c,0, 10), scipy.optimize.brentq(lambda z: conv_gaus_nd(z, 2)-c,0, 10), scipy.optimize.brentq(lambda z: conv_gaus_nd(z,3)-c,0, 10))"
@@ -1435,20 +1234,10 @@
},
{
"cell_type": "code",
- "execution_count": 25,
+ "execution_count": null,
"id": "702daac8-81e8-406c-b70f-c3146c58a493",
"metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "0.6826894921370859 1.3602534296492095 1.5569757057024747\n",
- "0.9544997361036416 2.273185951560801 2.422767471908681\n",
- "0.9973002039367398 3.204960455845192 3.3198237010363014\n"
- ]
- }
- ],
+ "outputs": [],
"source": [
"for k in [1, 2, 3]:\n",
" c = conv_gaus_nd(k, 1)\n",
@@ -1467,7 +1256,7 @@
"source": [
"# Hypothesis tests\n",
"\n",
- "\n",
+ "**Bundesliga**:\n",
"Hypothesis: \"The $k_i$ goals in each Bundesliga match $i$ are Poisson distributed with a common parameter $\\mu = <k>$.\"\n",
"\n",
"We need an alternative Hypothesis for the test: \"The goals in each Bundesliga match $k_i$ are Poisson distributed with parameter $\\mu_i = ki$ for each match.\"\n",
@@ -1519,7 +1308,7 @@
},
{
"cell_type": "code",
- "execution_count": 28,
+ "execution_count": null,
"id": "85e25147-c902-4434-b3dc-908486408c5b",
"metadata": {
"cell_style": "split",
@@ -1528,18 +1317,7 @@
},
"tags": []
},
- "outputs": [
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- "<Figure size 640x480 with 1 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "outputs": [],
"source": [
"x = np.linspace(-5,5,100)\n",
"xout1 = np.linspace(-5, -1.9599639845401602)\n",
@@ -1568,7 +1346,9 @@
{
"cell_type": "markdown",
"id": "cb79afd6-ba74-448b-9096-05cedeb842a6",
- "metadata": {},
+ "metadata": {
+ "cell_style": "split"
+ },
"source": [
"Needs an alternative hypothesis!\n",
"\n",
@@ -1577,28 +1357,12 @@
},
{
"cell_type": "code",
- "execution_count": 30,
+ "execution_count": null,
"id": "603a31e1-1425-4eb6-9b12-c44ba31d06a6",
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "error of second kind: beta: 0.14916123167296857\n"
- ]
- },
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- "<Figure size 640x480 with 1 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
+ "metadata": {
+ "cell_style": "split"
+ },
+ "outputs": [],
"source": [
"x = np.linspace(-5,8,200)\n",
"xin = np.linspace(-1.9599639845401602, 1.9599639845401602)\n",
@@ -1624,29 +1388,25 @@
"tags": []
},
"source": [
- "# Neyman-Pearson Test\n",
+ "## Neyman-Pearson Lemma\n",
"\n",
- "Hypothese: $H$\n",
+ "Hypothesis: $H$\n",
"\n",
- "Alternative Hypothese: $A$\n",
+ "Alternative hypothesis: $A$\n",
"\n",
- "Suche Kriterium, das $\\alpha$ und $\\beta$ minimiert. $H$ wird für $x$ im Bereich $V$ verworfen:\n",
+ "Goal: a criterion for an acceptance region giving the highest power (signal purity).\n",
"\n",
- "$\\int_{V} P_{H}(x) dx = \\alpha$ (klein)\n",
+ "Assume $H$ is accepted for $x$ in range $V$:\n",
"\n",
- "$\\int_{V} P_{A}(x) dx = 1 - \\beta$ (groß)\n",
+ "$\\int_{V} P_{H}(x) dx = 1 - \\alpha$ (large)\n",
"\n",
- "In $V$ sind die $x$-Werte, für die $\\frac{P_{A}(x)}{P_{H}(x)}$ groß ist.\n",
+ "$\\int_{V} P_{A}(x) dx = \\beta$ (small)\n",
"\n",
- "Neyman-Pearson-Kriterium: $\\frac{P_{A}(x)}{P_{H}(x)} > c$"
+ "In $V$ are the values of $x$, for which $\\frac{P_{H}(x)}{P_{A}(x)}$ is large.\n",
+ "\n",
+ "Neyman-Pearson lemma: best range selected with $\\frac{P_{H}(x)}{P_{A}(x)} > c$ (likelihood ratio)"
]
},
- {
- "cell_type": "markdown",
- "id": "39da5505-d3e1-4be6-a1b5-ecef10c58bce",
- "metadata": {},
- "source": []
- },
{
"cell_type": "markdown",
"id": "b636ff7e-5ba1-4fc5-bb40-fb29b63ca88c",
@@ -1657,17 +1417,19 @@
"tags": []
},
"source": [
- "# Endlich: Passt das Modell?\n",
+ "### Finally: Does are model for the Bundesliga work?\n",
+ "\n",
+ "**Bundesliga**:\n",
+ "Hypothesis: \"The $k_i$ goals in each Bundesliga match $i$ are Poisson distributed with a common parameter $\\mu = <k>$.\"\n",
"\n",
- "Hypothese: \"Die $k_i$ Tore pro Bundesligaspiel $i$ sind Poisson-verteilt mit einem gemeinsamen $\\mu = <k>$.\"\n",
+ "Alternative hypothesis: \"The goals in each Bundesliga match $k_i$ are Poisson distributed with parameter $\\mu_i = ki$ for each match.\"\n",
"\n",
- "Benötigt für den Test eine alternative Hypothese: \"Die Tore pro Bundesligaspiel $k_i$ sind Poisson verteilt mit $\\mu_i = ki$.\"\n",
+ "Neyman-Pearson: likelihood ratio: $\\frac{P_{A}(x)}{P_{H}(x)} = \\frac{\\hat L(\\vec k; \\vec k)}{L(\\mu; \\vec k)} > c$\n",
"\n",
- "Wie gut unser Modell einer Poissonverteilung für alle Spiele zu den Daten passt, lässt sich durch den Vergleich der log-Likelihood unseres Modells $-lnL(\\mu; \\vec k)$ zur log-Likelihood eines saturierten Modells (je Spiel ein eigener $\\mu$-Parameter mit $\\mu_i = k_i$), also $-ln\\hat L(\\vec k; \\vec k)$, abschätzen.\n",
+ "We look at the $log$ of the likelihood ratio for our model $-lnL(\\mu; \\vec k)$ and the alternative (saturated model) $-ln\\hat L(\\vec k; \\vec k)$.\n",
"\n",
"$P_{H} (\\vec k) = \\prod_{i} P(k_i,\\mu)$; $P_{A} (\\vec k) = \\prod_{i} P(k_i, k_i)$\n",
"\n",
- "Neyman-Pearson: Likelihoodquotient: $\\frac{P_{A}(x)}{P_{H}(x)} = \\frac{\\hat L(\\vec k; \\vec k)}{L(\\mu; \\vec k)} > c$\n",
"\n",
"$d = \\ln \\frac{P_{A}(\\vec k)}{P_{H}(\\vec k)} = -\\ln \\frac{P_{H}(\\vec k)}{P_{A}(\\vec k)} = -\\ln L(\\mu; \\vec k)-(-\\ln\\hat L(\\vec k; \\vec k))$\n",
"\n"
@@ -1681,9 +1443,7 @@
"outputs": [],
"source": [
"mu = np.mean(summe)\n",
- "\n",
"print(\"mu:\", mu)\n",
- "\n",
"print(\"P(H):\", np.prod(scipy.stats.poisson.pmf(summe,mu)))\n",
"print(\"P(A):\", np.prod(scipy.stats.poisson.pmf(summe,summe)))\n",
"print(\"-ln P(H):\", -np.sum(scipy.stats.poisson.logpmf(summe,mu)))\n",
@@ -1701,19 +1461,21 @@
"tags": []
},
"source": [
- "Ist das gut?\n",
+ "### What does this mean?\n",
"\n",
- "Wie sieht die Verteilung von d aus, wenn das Modell stimmt und $\\mu=<k>$?"
+ "Which distribution of our test statistic $d$ do we expect for pseudo-data from our model and $\\mu=<k>$?"
]
},
{
"cell_type": "code",
"execution_count": null,
- "id": "90e27f87-36fd-4b11-add1-c82a4eeb79dd",
+ "id": "c2d1227f",
"metadata": {
+ "cell_style": "split",
"jupyter": {
"source_hidden": true
},
+ "scrolled": true,
"slideshow": {
"slide_type": ""
},
@@ -1723,9 +1485,7 @@
"source": [
"#simuliere 1000 Spielzeiten\n",
"muobs = np.mean(summe)\n",
- "\n",
"tore = scipy.stats.poisson.rvs(muobs,size=(1000,306))\n",
- "\n",
"d = np.zeros(len(tore))\n",
"mu = np.zeros(len(tore))\n",
"for i in range(len(tore)):\n",
@@ -1736,26 +1496,80 @@
"muobs = np.mean(summe)\n",
"plt.plot([muobs, muobs], [0, 100], linestyle = 'dotted')\n",
"plt.grid()\n",
- "plt.xlabel(\"$\\hat \\mu$\")\n",
- "plt.show()\n",
+ "plt.xlabel(\"$\\hat \\mu$\");"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "90e27f87-36fd-4b11-add1-c82a4eeb79dd",
+ "metadata": {
+ "cell_style": "split",
+ "jupyter": {
+ "source_hidden": true
+ },
+ "slideshow": {
+ "slide_type": ""
+ },
+ "tags": []
+ },
+ "outputs": [],
+ "source": [
"dobs = -np.sum(scipy.stats.poisson.logpmf(summe,muobs)) + np.sum(scipy.stats.poisson.logpmf(summe,summe))\n",
"plt.hist(d, bins=50)\n",
"plt.plot([dobs, dobs], [0, 100], linestyle = 'dotted')\n",
"\n",
"plt.grid()\n",
"plt.xlabel(\"$-\\ln(P(H)/P(A))$\")\n",
- "plt.show()\n",
- "\n"
+ "plt.show()"
]
},
{
"cell_type": "markdown",
"id": "f6db4bd4-de67-48e1-add9-4fdc05dbbcf7",
- "metadata": {},
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
"source": [
- "$p$-Wert \n",
+ "### The $p$-value \n",
"\n",
- "Anteil der erwarteter Werte, die höher als der Daten-Wert sind."
+ "Fraction of expected outcomes that have a higher value than we get for data:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "18f65b9d",
+ "metadata": {
+ "cell_style": "split"
+ },
+ "outputs": [],
+ "source": [
+ "plt.hist(mu, bins=50)\n",
+ "plt.plot([muobs, muobs], [0, 100], linestyle = 'dotted')\n",
+ "plt.grid()\n",
+ "plt.xlabel(\"$\\hat \\mu$\")\n",
+ "plt.show()\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "b82090eb",
+ "metadata": {
+ "cell_style": "split"
+ },
+ "outputs": [],
+ "source": [
+ "dobs = -np.sum(scipy.stats.poisson.logpmf(summe,muobs)) + np.sum(scipy.stats.poisson.logpmf(summe,summe))\n",
+ "plt.hist(d, bins=50)\n",
+ "plt.plot([dobs, dobs], [0, 100], linestyle = 'dotted')\n",
+ "\n",
+ "plt.grid()\n",
+ "plt.xlabel(\"$-\\ln(P(H)/P(A))$\")\n",
+ "plt.show()"
]
},
{
@@ -1778,75 +1592,197 @@
"tags": []
},
"source": [
- "## Geht es auch ohne MC?\n",
+ "### Can we do this analytically, without Monte Carlo?\n",
"\n",
- "Einfacherer Fall: Gauß-Verteilungen:\n",
+ "Simple case: Gaussian distributions:\n",
"\n",
- "$d = -\\ln L(\\mu; \\vec x)-(-\\ln\\hat L(\\vec x; \\vec x) = -\\ln \\prod_{i} \\frac{G(x_i,\\mu, \\sigma)}{G(x_i, x_i, \\sigma)}=-\\ln \\prod_{i} \\frac{\\exp(-\\frac{1}{2}(\\frac{x_i-\\mu}{\\sigma})^2)}{\\exp(-\\frac{1}{2}(\\frac{x_i-x_i}{\\sigma})^2)} = -\\ln \\exp(-\\frac{1}{2}(\\frac{x_i-\\mu}{\\sigma})^2) = \\frac{1}{2} \\sum_i\\left(\\frac{x_i - \\mu}{\\sigma}\\right)^2$\n",
+ "$$d = -\\ln L(\\mu; \\vec x)-(-\\ln\\hat L(\\vec x; \\vec x) = -\\ln \\prod_{i} \\frac{G(x_i,\\mu, \\sigma)}{G(x_i, x_i, \\sigma)}=-\\ln \\prod_{i} \\frac{\\exp(-\\frac{1}{2}(\\frac{x_i-\\mu}{\\sigma})^2)}{\\exp(-\\frac{1}{2}(\\frac{x_i-x_i}{\\sigma})^2)} = -\\ln \\exp(-\\frac{1}{2}(\\frac{x_i-\\mu}{\\sigma})^2) = \\frac{1}{2} \\sum_i\\left(\\frac{x_i - \\mu}{\\sigma}\\right)^2 = \\frac{1}{2}\\chi^2$$\n",
"\n",
- "$\\chi^2 = -2 \\ln\\frac{P(H}{P(A)}$ (Wilks Theorem)\n",
+ "For Gaussian: $-2 \\ln\\frac{P(H}{P(A)}$ follows $\\chi^2$ \n",
"\n",
- "$-2 \\ln\\frac{P(H}{P(A)}$ sollte gemäß $\\chi^2$-Verteilung verteilt sein, mit n Freiheitsgraden n = Zahl der Messpunkte - Zahl der Modellparameter"
+ "\n",
+ "Wilk's Theorem:\n",
+ "$-2 \\ln\\frac{P(H}{P(A)}$ approaches a $\\chi^2$ distribution (asymptotic limit) with $n$ degrees of freedom $n = \\text{number of data points} - \\text{number of model parameters}$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f09138b6",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### Let's try it\n",
+ "\n",
+ " - use $\\chi^2$ p.d.f. and c.d.f. from [scipy](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chi2.html)\n",
+ " - what is the value of `df`\n",
+ " \n",
+ " - draw the $\\chi^2$ distribution in the interval $[200, 425]$\n",
+ " \n",
+ " - compute the $p$-value for our data\n",
+ " \n",
+ " - does it work? Add the histgram for the simulated $\\chi^2=2d$ values."
]
},
{
"cell_type": "code",
"execution_count": null,
- "id": "9d667a3b-6a89-419a-8be4-79cb7de96151",
+ "id": "e609ea07",
"metadata": {},
"outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9d667a3b-6a89-419a-8be4-79cb7de96151",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "skip"
+ }
+ },
+ "outputs": [],
"source": [
"plt.hist(2*d, bins=50, density=True)\n",
"plt.plot([2*dobs, 2*dobs], [0, 0.02], linestyle = 'dotted')\n",
"ds = np.linspace(200, 425, 100)\n",
"plt.plot(ds,scipy.stats.chi2.pdf(ds, 305))\n",
"\n",
- "plt.grid()\n",
- "plt.xlabel(\"$-2\\ln(P(H)/P(A))$\")\n",
- "plt.show()\n",
"\n",
"\n",
- "print(\"p-Wert über Chi2:\", scipy.stats.chi2.sf(2*dobs, 305))"
+ "print(\"p-Wert via Chi2:\", scipy.stats.chi2.sf(2*dobs, 305))\n",
+ "\n",
+ "plt.grid()\n",
+ "plt.xlabel(\"$-2\\ln(P(H)/P(A))$\")\n",
+ "plt.show()"
]
},
{
"cell_type": "markdown",
- "id": "eb7b32c7-a9a7-44de-aa70-ce9744218a35",
- "metadata": {},
+ "id": "9f258f33",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
"source": [
- "Stimmt die Gaußsche Näherung in unserem Fall?"
+ "### How are the $p$-values using Wilk's theorem from the simulation distributed?"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "cda0957a-414f-4bea-ab33-e61218a4a4f5",
- "metadata": {},
+ "metadata": {
+ "cell_style": "center"
+ },
"outputs": [],
"source": [
- "plt.hist( scipy.stats.chi2.sf(2*d, 305), bins=50)\n",
- "plt.plot([ scipy.stats.chi2.sf(2*dobs, 305), scipy.stats.chi2.sf(2*dobs, 305)], [0, 200], linestyle = 'dotted')\n",
+ "plt.hist( scipy.stats.chi2.sf(2*d, 305), bins=50, density=True)\n",
+ "plt.plot([ scipy.stats.chi2.sf(2*dobs, 305), scipy.stats.chi2.sf(2*dobs, 305)], [0, 12], linestyle = 'dotted')\n",
"\n",
"plt.grid()\n",
"plt.xlabel(\"p\")\n",
"plt.show()"
]
},
+ {
+ "cell_type": "markdown",
+ "id": "9378e3ba",
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
+ "source": [
+ "### What distribution should we get if it works?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "59be1788",
+ "metadata": {
+ "cell_style": "split"
+ },
+ "source": [
+ "For the simulation:"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5d172ac9",
+ "metadata": {
+ "cell_style": "split"
+ },
+ "source": [
+ "For the $chi^2$ distribution:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "a096afa1",
+ "metadata": {
+ "cell_style": "split"
+ },
+ "outputs": [],
+ "source": [
+ "pvalues = [np.sum(d > dsim)/len(d) for dsim in d]\n",
+ "\n",
+ "plt.hist(pvalues, bins=50, density=True)\n",
+ "plt.grid()\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "648b37eb",
+ "metadata": {
+ "cell_style": "split"
+ },
+ "outputs": [],
+ "source": [
+ "d2 = scipy.stats.chi2.rvs(305, size=10000)\n",
+ "pvalues = [np.sum(d2 > d2sim)/len(d2) for d2sim in d2]\n",
+ "\n",
+ "plt.hist(pvalues, bins=50, density=True)\n",
+ "plt.grid()\n",
+ "plt.show()"
+ ]
+ },
{
"cell_type": "markdown",
"id": "557559e1-8e4a-412a-9486-a2fb9b97de90",
- "metadata": {},
+ "metadata": {
+ "slideshow": {
+ "slide_type": "slide"
+ }
+ },
"source": [
- "Für große $\\mu$? Handball??"
+ "### Does is work better for large $\\mu$ (hand ball?\n",
+ "\n",
+ "- simulate 1000 season for $\\mu_\\text{obs} = 35$\n",
+ "- and rerun the tests"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "770f4472",
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
{
"cell_type": "code",
"execution_count": null,
"id": "472aac93-e2dd-424a-ba0e-51c10d409f8e",
"metadata": {
"slideshow": {
- "slide_type": ""
+ "slide_type": "skip"
},
"tags": []
},
@@ -1891,12 +1827,12 @@
"tags": []
},
"source": [
- "# $\\chi^2$-Test\n",
- "\n",
+ "### Pearson's $\\chi^2$-Test\n",
"\n",
- "Haben wir schon die ganze Zeit gemacht...\n",
+ "What are the confidence regions for $n$ degrees of freedom/dimensions:\n",
"\n",
- "Wie sind die Konfidenzintervalle $n$ Freiheitsgrade/Dimensionen?\n",
+ "data: $\\vec y = y_1,\\dots, y_n$\n",
+ "predicted values from model: $\\vec{f} = f_1,\\dots,f_n$\n",
"\n",
"$$\\chi^2 = (\\overrightarrow{y\\ } - \\vec{f})^{T} V(\\vec{y}- \\vec{f})$$\n",
"\n"
@@ -1905,7 +1841,7 @@
{
"cell_type": "code",
"execution_count": null,
- "id": "2fd5c302-732b-4c6b-b224-5b9f79df57cc",
+ "id": "f703d4ed",
"metadata": {
"slideshow": {
"slide_type": ""
@@ -1919,10 +1855,22 @@
"\n",
"\n",
"for z in [1,2,3,4,5]:\n",
- " print(z, conv_chi2_nd(z, 1), conv_chi2_nd(z, 2), conv_chi2_nd(z, 3))\n",
- "\n",
- "\n",
- "print(\"Kritische chi2-Werte\")\n",
+ " print(z, conv_chi2_nd(z, 1), conv_chi2_nd(z, 2), conv_chi2_nd(z, 3))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "2fd5c302-732b-4c6b-b224-5b9f79df57cc",
+ "metadata": {
+ "slideshow": {
+ "slide_type": ""
+ },
+ "tags": []
+ },
+ "outputs": [],
+ "source": [
+ "print(\"critical chi2 values\")\n",
"for k in [1, 2, 3]:\n",
" c = conv_gaus_nd(k, 1)\n",
" print(c, scipy.optimize.brentq(lambda z: conv_chi2_nd(z, 1)-c,0, 30), scipy.optimize.brentq(lambda z: conv_chi2_nd(z, 2)-c,0, 30), scipy.optimize.brentq(lambda z: conv_chi2_nd(z,3)-c,0, 30))"
@@ -2128,7 +2076,7 @@
"id": "a038c48f-7143-480d-b0ba-817f0e5211c1",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "skip"
},
"tags": []
},
@@ -2157,7 +2105,7 @@
"id": "d32672c8-da0b-468b-bf73-df40aef7245a",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "skip"
},
"tags": []
},
@@ -2181,7 +2129,7 @@
"id": "4021d6cd-150e-4a6d-bdc4-ed049fd983d3",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "skip"
},
"tags": []
},
@@ -2204,7 +2152,7 @@
"id": "4dfd3266-a5a2-4db7-a96b-ef21118bc85e",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "skip"
},
"tags": []
},
@@ -2230,7 +2178,7 @@
"id": "1621af0b-8216-4959-9cc9-8c41cdb8cc79",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "skip"
},
"tags": []
},
@@ -2248,7 +2196,7 @@
"id": "8fdd0fc7-af9c-492c-9c7f-5a195ee58c50",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "skip"
},
"tags": []
},
@@ -2272,7 +2220,7 @@
"id": "0c34b270-4e04-40be-82b1-f305eadf82a9",
"metadata": {
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "skip"
},
"tags": []
},
@@ -2298,7 +2246,7 @@
"metadata": {
"jp-MarkdownHeadingCollapsed": true,
"slideshow": {
- "slide_type": "slide"
+ "slide_type": "skip"
},
"tags": []
},
@@ -2361,7 +2309,7 @@
"scroll": true
},
"toc": {
- "base_numbering": 1
+ "base_numbering": 43
}
},
"nbformat": 4,
--
GitLab