{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "*This notebook contains material from [cbe67701-uncertainty-quantification](https://ndcbe.github.io/cbe67701-uncertainty-quantification);\n", "content is available [on Github](https://github.com/ndcbe/cbe67701-uncertainty-quantification.git).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [12.1 Predictions under epistemic uncertainty with p-boxes](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.01-Epistemic-uncertainty-with-p-boxes.html) | [Contents](toc.html) |

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\"Download\"" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 1, "link": "[12.2 Epistemic Uncertainty Quantification](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2-Epistemic-Uncertainty-Quantification)", "section": "12.2 Epistemic Uncertainty Quantification" } }, "source": [ "# 12.2 Epistemic Uncertainty Quantification" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 1, "link": "[12.2 Epistemic Uncertainty Quantification](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2-Epistemic-Uncertainty-Quantification)", "section": "12.2 Epistemic Uncertainty Quantification" } }, "source": [ "Created by Jian-Ren Lim (jlim6@nd.edu)\n", "\n", "These examples and codes were adapted from:\n", "\n", "Nadim Kawwa, Statistic datasets and experiments. https://github.com/NadimKawwa/Statistics\n", "\n", "Scipy.org, scipy.stats.ks_2samp. https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.ks_2samp.html\n", "\n", "McClarren, Ryan G (2018). Uncertainty Quantification and Predictive Computational Science: A Foundation for Physical Scientists and Engineers, Chapter 12, Epistemic Uncertainties: Dealing with a Lack of Knowledge, Springer, https://link.springer.com/chapter/10.1007/978-3-319-99525-0_12" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[12.2.1 $\\delta_n$ in Probability Box (P-box)](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2.1-$\\delta_n$-in-Probability-Box-(P-box))", "section": "12.2.1 $\\delta_n$ in Probability Box (P-box)" } }, "source": [ "## 12.2.1 $\\delta_n$ in Probability Box (P-box)\n", "\n", "A p-box is used to express simultaneously incertitude (epistemic uncertainty), which is represented by the breadth between the left and right edges of the p-box, and variability (aleatory uncertainty), which is represented by the overall slant of the p-box.\n", "\n", "The KS test statistic δN is the maximum vertical distance between the true (but\n", "unknown) CDF, F(x), and the empirical CDF derived from N samples, FN(x):\n", "\n", "$$\\delta_n = sup |F_N(x) - F(x)|$$\n", "\n", "If our maximum difference is less than $\\delta_{critical}$ we fail to reject the null hypothesis. The critical value at 95% is approximated by:\n", "\n", "$$\\delta_{critical} = \\frac{1.3581}{\\sqrt{N}}$$" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[12.2.1 $\\delta_n$ in Probability Box (P-box)](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2.1-$\\delta_n$-in-Probability-Box-(P-box))", "section": "12.2.1 $\\delta_n$ in Probability Box (P-box)" } }, "source": [ "Suppose we have n observations x1, x2, ...xn that we think come from a distribution P. The KS test is used to evaluate:\n", "- Null Hypothesis: The samples do indeed come from P\n", "- Alternative Hypothesis: The amples do not come from P\n", "\n", "To build intution for the KS test, we take a step back and consider descriptive statistics. Distributions sucha s the normal distribution are known to have a mean of 0 and a standard deviation of 1. Therefore we expect no more than 15% of the data to lie below the mean.\n", "\n", "In this task we will use the Cumulative Distribution Function (CDF). More specifically, we will use the Empirical Distribution Function (EDF): an estimate of the cumulative distribution function that generated the points in the sample." ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[12.2.2 Example 1: KS Test on Distributions of the Same Mean](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2.2-Example-1:-KS-Test-on-Distributions-of-the-Same-Mean)", "section": "12.2.2 Example 1: KS Test on Distributions of the Same Mean" } }, "source": [ "## 12.2.2 Example 1: KS Test on Distributions of the Same Mean\n", "\n", "The cumulative distribution function uniquely characterizes a probability distribution.\n", "We want to compare the empirical distribution function of the data, **F_obs**, with the cumulative distribution function , **F_exp** (expected CDF).\n", "\n", "In the first example we want to compare the empirical distribution function of the observed data, with the cumulative distribution function associated with the null hypothesis (normal distribution).\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "nbpages": { "level": 2, "link": "[12.2.2 Example 1: KS Test on Distributions of the Same Mean](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2.2-Example-1:-KS-Test-on-Distributions-of-the-Same-Mean)", "section": "12.2.2 Example 1: KS Test on Distributions of the Same Mean" } }, "outputs": [], "source": [ "## import all needed Python libraries here\n", "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import ttest_ind\n", "import scipy.stats as st\n", "\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "nbpages": { "level": 2, "link": "[12.2.2 Example 1: KS Test on Distributions of the Same Mean](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2.2-Example-1:-KS-Test-on-Distributions-of-the-Same-Mean)", "section": "12.2.2 Example 1: KS Test on Distributions of the Same Mean" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "

" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Avg_d = 0.05762471726299765 \tMax_d = 0.10519625892159334\n", "d_critical = 0.19206434390589006\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Avg_d = 0.020095815616920566 \tMax_d = 0.04252122301737027\n", "d_critical = 0.04294689290274677\n" ] } ], "source": [ "#generate random aray\n", "for size in [50,1000]:\n", " arr_1 = np.random.normal(0, 1, size)\n", " arr_1_edf = np.arange(1/len(arr_1), 1+1/len(arr_1), 1/len(arr_1))\n", " delta = []\n", "\n", " #sort\n", " arr_1_sorted = np.sort(arr_1)\n", " cdf_null_hyp = [st.norm.cdf(x) for x in arr_1_sorted]\n", " #calculate absolute difference\n", " plt.figure(figsize=(9, 6))\n", " plt.plot(arr_1_sorted, arr_1_edf,'C0', label='F_obs')\n", " plt.plot(arr_1_sorted, cdf_null_hyp,'C1', label='F_exp')\n", " max=[0,0,0,0]\n", " for x, y1, y2 in zip(arr_1_sorted, arr_1_edf, cdf_null_hyp):\n", " plt.plot([x, x], [y1, y2], color='green', alpha=0.4)\n", " delta.append(y2-y1)\n", " if np.abs(y2-y1) > max[3]:\n", " max=[x,y1,y2,np.abs(y2-y1)]\n", "\n", " plt.plot([max[0],max[0]], [max[1], max[2]],'r', lw=4)\n", " plt.text(max[0]-1,(max[1]+max[2])/2,'$\\delta^{.95}_{N,max}$(x)', fontsize=16)\n", " plt.legend()\n", " plt.ylabel(\"F(x)\")\n", " plt.xlabel('x')\n", " plt.title(f\"KS Goodness of Fit, N = {size}\")\n", " plt.show()\n", "\n", " print('Avg_d = ',np.average(np.abs(delta)),'\\tMax_d = ', np.max(np.abs(delta)))\n", " d_critical = 1.3581/np.sqrt(size)\n", " print('d_critical = ',d_critical)\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[12.2.2 Example 1: KS Test on Distributions of the Same Mean](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2.2-Example-1:-KS-Test-on-Distributions-of-the-Same-Mean)", "section": "12.2.2 Example 1: KS Test on Distributions of the Same Mean" } }, "source": [ "Observation: Larger number of measurements (N=1000) show that $\\delta_{max}$ < $\\delta_{critical}$, therefore we fail to reject the null hypothesis (i.e. the samples do indeed come from P).\n", "\n", "## Example 2: Distributions of Different Means\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "nbpages": { "level": 2, "link": "[12.2.2 Example 1: KS Test on Distributions of the Same Mean](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2.2-Example-1:-KS-Test-on-Distributions-of-the-Same-Mean)", "section": "12.2.2 Example 1: KS Test on Distributions of the Same Mean" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Avg_d = 0.3053476779126938 \tMax_d = 0.4574502969227086\n", "d_critical = 0.19206434390589006\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Avg_d = 0.257883193972548 \tMax_d = 0.39037146570090075\n", "d_critical = 0.04294689290274677\n" ] } ], "source": [ "#generate random aray\n", "for size in [50,1000]:\n", " arr_1 = np.random.normal(-1, 1, size)\n", " arr_1_edf = np.arange(1/len(arr_1), 1+1/len(arr_1), 1/len(arr_1))\n", " delta = []\n", "\n", " #sort\n", " arr_1_sorted = np.sort(arr_1)\n", " cdf_null_hyp = [st.norm.cdf(x) for x in arr_1_sorted]\n", " #calculate absolute difference\n", " plt.figure(figsize=(9, 6))\n", " plt.plot(arr_1_sorted, arr_1_edf,'C0', label='F_obs')\n", " plt.plot(arr_1_sorted, cdf_null_hyp,'C1', label='F_exp')\n", " max=[0,0,0,0]\n", " for x, y1, y2 in zip(arr_1_sorted, arr_1_edf, cdf_null_hyp):\n", " plt.plot([x, x], [y1, y2], color='green', alpha=0.4)\n", " delta.append(y2-y1)\n", " if np.abs(y2-y1) > max[3]:\n", " max=[x,y1,y2,np.abs(y2-y1)]\n", "\n", " plt.plot([max[0],max[0]], [max[1], max[2]],'r', lw=4)\n", " plt.text(max[0]-1,(max[1]+max[2])/2,'$\\delta^{.95}_{N,max}$(x)', fontsize=16)\n", " plt.legend()\n", " plt.ylabel(\"F(x)\")\n", " plt.xlabel('x')\n", " plt.title(f\"KS Goodness of Fit, N = {size}\")\n", " plt.show()\n", "\n", " print('Avg_d = ',np.average(np.abs(delta)),'\\tMax_d = ', np.max(np.abs(delta)))\n", " d_critical = 1.3581/np.sqrt(size)\n", " print('d_critical = ',d_critical)\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 2, "link": "[12.2.2 Example 1: KS Test on Distributions of the Same Mean](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2.2-Example-1:-KS-Test-on-Distributions-of-the-Same-Mean)", "section": "12.2.2 Example 1: KS Test on Distributions of the Same Mean" } }, "source": [ "Observation: Both measurements show that $\\delta_{max}$ > $\\delta_{critical}$, therefore we can reject the null hypothesis (i.e. the samples do not come from P).\n", "\n", "## Example 3: Distributions of Different Mean and Standard Deviation" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "nbpages": { "level": 2, "link": "[12.2.2 Example 1: KS Test on Distributions of the Same Mean](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2.2-Example-1:-KS-Test-on-Distributions-of-the-Same-Mean)", "section": "12.2.2 Example 1: KS Test on Distributions of the Same Mean" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import random\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from scipy.stats import norm\n", "r = np.arange(-3,3,.01)\n", "min=[1 for _ in range(len(r))]; max=[0 for _ in range(len(r))]\n", "plt.figure(figsize=(9, 6))\n", "\n", "for _ in range(20):\n", " a = random.uniform(-0.25,0.25);\n", " b = random.uniform(0.55,1.45);\n", " plt.plot(r, norm.cdf(r, a, b),'k--',lw=1,alpha=0.4)\n", " for i in range(len(r)):\n", " if norm.cdf(r, a, b)[i] < min[i]: \n", " min[i] = norm.cdf(r, a, b)[i]\n", " elif norm.cdf(r, a, b)[i] > max[i]: \n", " max[i] = norm.cdf(r, a, b)[i]\n", "plt.title('Figure 12.3: Horsetail Plot of 20 Potential CDFs')\n", "plt.ylabel('F(x)')\n", "plt.xlabel('x')\n", "plt.legend(['randomized CDFs'])\n", "plt.show()\n", "\n", "plt.figure(figsize=(9, 6))\n", "plt.plot(r, norm.cdf(r, -0.168, 1.25),lw=3)\n", "plt.plot(r, max,'C1--',label='max',lw=3)\n", "plt.plot(r, min,'C2--',label='min',lw=3)\n", "plt.title('Figure 12.3: Horsetail Plot of 20 Potential CDFs')\n", "plt.text(-0.3,0.8,'$P_{upper}$(x)', fontsize=12)\n", "plt.text(0,0.3,'$P_{lower}$(x)', fontsize=12)\n", "plt.ylabel('F(x)')\n", "plt.xlabel('x')\n", "plt.legend()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "nbpages": { "level": 2, "link": "[12.2.2 Example 1: KS Test on Distributions of the Same Mean](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2.2-Example-1:-KS-Test-on-Distributions-of-the-Same-Mean)", "section": "12.2.2 Example 1: KS Test on Distributions of the Same Mean" } }, "outputs": [ { "data": { "image/png": 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p4cYbb+Thhx/mkUce4cYbb0wLlXpTawHxPWCbv78NuCtQfq2/mulCoD+liqoXySKd5IJk2SEsaJ9hzHkqEe77Jz/5CVu3bqWzs5OOjg62bt16gtCpF1XzpBaR24A3AYtEpAv4DPB54A4R+TDwKvA7fvW7gcuBPcAI8KFq9atY3Gk4yaXrLVjARLcn15J9fbB69RRXGIZRCW586Maqtf2ZLZ+ZVv3phvsuVD4TqJqAUNWrC5y6NE9dBf6wWn0phWJDfQfJDto3M6aIhmHMDAqF+57JYcBnipF6xjFdGwRYXgjDMKYf7nsmhwG3YH0FyFrmWtIMwpa6GkatmK4aqJpMN9z32972Nj796U+nDdM//elP+dznPlfPR0hjAiIPqjptRznIjcdkKibDmOtUItx3Z2cnf/mXf8l5550HwF/91V+dYPiuFyYg8qDj42giCYBEIjjRaFHXZYfb8HwhZoou0TCMylOpcN/XX389119/fUX7VgnMBpGH7DwQxamXAJzGRpzGGACaSGTNQgzDMGYbJiDykO1FXZx6KV3fgvYZhjFHMAGRh2QJK5hSmKHaMIy5ggmIPAR9IIp1kksRtrwQhmHMEUxA5KGUFUwpLLOcYRhzBRMQeZhuqO8gljjIMIy5ggmIPJQ1gzAVk2HMG6od7vuxxx7jrLPO4pRTTuETn/hEzdMImIDIg1tCJNcUuSomywthGHOXaof7/tjHPsZNN92Uvq7WUV5NQOQhWUIk1xQSiyENDQDoxAQ6MlLRvhmGMXOoZrjvgwcPMjAwwJYtWxARrr322nRbtcI8qfOQFcl1miomESG0oJ3EYS/Eb7Kvb9ptGIYxPQ7+VfViMS3/6+mFEq9UuO8DBw6watWqE8pric0gctCJCXR83DsIOYifJW46BNVMlp/aMAyYfrjvmRAG3AREDkEnuVBzc0l/EHOWM4z5S6XCfa9atYqurq4TymuJqZhycIczNoNSVUPZeSFMQBhGtZmuGqiaVCrcd2dnJ62trfz617/mggsu4NZbb+XjH/94TZ/FBEQO5fhApLAZhGHMD6od7vtLX/oS1113HaOjo1x22WVcdtllNX0+ExA5ZAfqK1FAtAcExIBlljOMuUq1w31v3ryZZ555prxOloHZIHIoJdVoLqG21kx7A4Nl98kwDKMemIDIoRwnucx1LeAbt92RETSRqEjfDMMwaokJiBzKcZJLIY5DqDVzbXLQZhGGYcw+TEDkkOUkV6KAAHBa2zJtmoAwDGMWYgIih0rYICDbDpHsHyirT4ZhGPXABEQOlVjFBLkzCBMQhmHMPuoiIETkv4vIsyLyjIjcJiIxEVkvIg+LyG4R+YaIRGvdL3Vd3NHRVCdxmppKbitrBjE4NElNwzBmK/UK913oHpWm5gJCRFYCnwA2q+qZQAi4Cvg74AuqugHoBT5c6765w8Pg/wGcxkbEKf3rcVoDAsJ8IQxjTlKvcN+F7lFp6qViCgONIhIGmoCDwFuAb/nntwPvrnWnKqVeAgi1BVRM5gthGHOSeoX7LnSPSlNzT2pVPSAi/wC8CowCPwUeA/pUNeUw0AWszHe9iHwE+AjAmjVrKtq3SvhApK8PziDMBmEYVeXnX3uham2/+ZrTplW/FuG+C92j0tRDxdQBXAmsB1YAzUC+ACN5U7Gp6k2qullVNy9evLiifavUCibIzk3tDgxaZjnDmOdYuO/ieCuwV1WPquoE8B3g9cACX+UEsArornXHkkPlO8mlkGgUiXp2dk0k0LGxstozDGN2UItw34XuUWnqEazvVeBCEWnCUzFdCuwEfg68F7gd2AbcVeuOZdkgypxBiAihtlYSx44DkBwYxCkh+ZBhGFMzXTVQNalFuO9C96g09bBBPCwi3wIeBxLAE8BNwA+B20Xkb/yym2vdt2wbRPYMIplwcUIyrSme09oGvoBwB/phaXWkvGEY9aFe4b4L3aPSyGzWjW/evFl37txZsfZ6bv0PxvfsAaDjmg8Q27jRKz84zDO/OEBDY5jNl60jFClOM9f37W8z+punAGh/97tpOvecivXVMOY7zz//PJs2bap3N2Y8+b4nEXlMVTdPda15UgcolCzo0Ev9JBMuI4NxjncX7/QWXMlk3tSGYcw2TEAEcEeC6UYzXtQT8WR6PxF3i24v6AuRHDABYRjG7MIERACNx9P7TkNDej854ebdn4psb2oTEIZRaWazirwWlPv9mIDwUVXc8fH0cWqJKngG6hSJRGkzCNfiMRlGRYnFYhw/ftyERAFUlePHjxOLxUpuw3JSp0gkwPV+aBIOIeHMV1PqDCJkMwjDqBopP4GjR4/WuyszllgsluWNPV1MQPi44xn1kkSyA8kGZxDJacwgnNZWL/WoKu7wMJpMIqFQ+Z01DINIJML69evr3Y05jamYfHQiICAC9geAZCIzhZ3ODEJCoYzDnWqWn4VhGMZMxwSEjxawP6irJJOlzSAgJy+EqZkMw5hFmIDwCa5gkoaAgTqZLRAS05hBQK4vhIX9Ngxj9mACwic4g3CCK5hyBMJ0VEyQ6wthAsIwjNmDCQgfN57fBhG0P3jHpc8gLLOcYRizCRMQPlpgFVNiIplVb7oqpmxfCJtBGIYxezAB4aMFZhBumTOILF8IExCGYcwiTED4aDy4iimS3s+dMSQT7rQ8N52s3NS2iskwjNlDUQJCRL4tIu8QkTkrUArGYcozY5jOLCLbm9pmEIZhzB6KHfC/BHwA2C0inxeRmZO+qUJkxWEqEKhvsrJCSGNjOmyHxuNZ9zEMw5jJFCUgVPUeVb0GOBd4BdghIg+KyIdEJDL51bODLCN1gUB9mbLiVUwighNwljM1k2EYs4WiVUYishC4Dvg9vJSg/4QnMHZUpWc1JstIHZ1cxZS7smkqQq0BXwgzVBuGMUsoKlifiHwHOA34D+BdqnrQP/UNEalczs86EjRSOw2FHeUKlU2GzSAMw5iNFBvN9cuqenewQEQaVHW8mLyms4FickFkyqYXfz5rBmECwjCMWUKxKqa/yVP2UCU7Um8K+UHkc4ybfrgN84UwDGP2MekMQkSWASuBRhE5BxD/VBvQVPDCWUghI7WbdwYxPRuE02re1IZhzD6mUjG9Dc8wvQr4x0D5IPDpKvWpLhQ2Up+oTpp+uI3ADKLfVEyGYcwOJhUQqrod2C4i71HVb9eoT3WhkJE634ql6dogsrypB01AGIYxO5hKxfRBVf1PYJ2I/I/c86r6j3kum3VoMomm1EYiEMxHnUcYTNsGEfSmHhpCXRdx5qxTumEYc4SpRik/XyYtQGueT0mIyAIR+ZaIvCAiz4vIFhHpFJEdIrLb33aU2v50yU0WJCLp47yrmKbpByHhME6Tb7JxvfzUhmEYM52pVEz/7m9vrPB9/wn4saq+V0SieAbvTwP3qurnReQG4AbgkxW+b16ykgXl5qPOt4ppmiom8Hwh3JERwPOFCM4qDMMwZiLFBuv7exFpE5GIiNwrIsdE5IOl3FBE2oBLgJsBVDWuqn3AlcB2v9p24N2ltF8KboFcEFDIk3p6KiYwb2rDMGYfxSrCf0tVB4B3Al3AqcD/LPGeJwFHga+KyBMi8mURaQaWpjy0/e2SfBeLyEdEZKeI7Dx69GiJXchGJwrkgki6uG75NgjIWclkznKGYcwCihUQqYB8lwO3qWpPGfcM48Vw+pKqngMM46mTikJVb1LVzaq6efHixWV0I9BmQS/q/Kqk6fpBgPlCGIYx+yhWQHxfRF4ANgP3ishiYKzEe3YBXar6sH/8LTyBcVhElgP42yMltj9tco3UKQrlfSjFBpE9gzABYRjGzKfYcN83AFuAzao6gffWf2UpN1TVQ8B+EdnoF10KPAd8D9jml20D7iql/ZL6VMBIHVQlhcOZr6oUG0TWDGKgf9rXG4Zh1Jpig/UBbMLzhwhec2uJ9/048DV/BdPLwIfwhNUdIvJh4FXgd0pse9q4ReSCiDaFSQzETygvlux4TEOldNMwDKOmFBvu+z+Ak4EngZQCXilRQKjqk3jqqlwuLaW9cikmF0Q0FmYkICBUNctfYiqybRBmpDYMY+ZT7AxiM3C6qk5f+T4LCIbZkGgmQV5QlRSOOITCTlpoJBMu4Uio6Hs4zU0QciDp4o6OofF41mzFMAxjplGskfoZYFk1O1JPgjOILBtEYAYR8gVE+tw07RAiYr4QhmHMKoqdQSwCnhORR4D067aqXlGVXtWYQsmCgqG+Q2GHcMQh7q/dSky4ZPtcT02orZVkXx/g+UKEFy4suc+GYRjVplgB8dlqdqLeFJMsKBR2CIUDMZrKXclkMwjDMGY4RQkIVb1fRNYCG1T1HhFpAopXwM9wCiULCvo7eDaIUOBcud7UJiAMw5jZFBuL6b/iObT9u1+0ErizWp2qNdmrmAICIncGEQnYIEoQELaSyTCM2USxRuo/BC4CBgBUdTcFYiXNRrKSBRXwgwhFhHCkPGc5yyxnGMZsolgBMa6q6dds31luzix5dQvYILJnEKGsGUS+XNVT4QRCfLtDpmIyDGNmU6yAuF9EPg00ishW4JvA96vXrdqSZYMouMxVspa5ljaDCCxzNRuEYRgznGIFxA14IbqfBn4fuBv4i2p1qtYUiuZ6wiqmSOl+EJCTenRwAHWn34ZhGEatKHYVkysidwJ3qmplkjDMENR10YmJ9HGhWEwnLHMtIaKrRKM4LS24Q0OQdEn29xPuqFlmVcMwjGkx6QxCPD4rIseAF4BdInJURP6qNt2rPrnCISsf9US2J3U4awYx/ZwQAOHOjEBI9vaW1IZhGEYtmErF9Md4q5fOU9WFqtoJXABcJCL/veq9qwGF1EuQbwaR8YMoxQYBEOrMeE8njx8vqQ3DMIxaMJWAuBa4WlX3pgpU9WXgg/65WU+hZEFw4gyiXD8IgPDCzvR+osdmEIZhzFymEhARVT2WW+jbISJ56s86spIFBWYQqpolBMLhXBVTaat8Q50ZAZHssRmEYRgzl6kERLzEc7MGt0AuCNfVtKNHyBHEEZwsI3VpNohQR3AGUU5qb8MwjOoy1Sqm14hIPpdfAWJV6E/NKRSoL6hecvyZQzD/QymrmCBbxZQ83jPtxEOGYRi1YlIBoapzJiBfIbKN1BmtWa6B2ttmBvJSjdROYyNOYyPu6CiaSOAODmY50BmGYcwUinWUm7MUTBaUk00OKNtRLkW2HcLUTIZhzEzmvYAolCwo/wwiICCSLuqWaqjO+ELYSibDMGYq815AFJssCPy0oeFKLHUN+ELYSibDMGYoJiDGC6xiChihg6qlcgP2AYQ7bSWTYRgzHxMQ8fxG6uwZRMY4Ha6As5zZIAzDmA2YgChkpE5ke1Gn98PlG6pDOTMI1TmTWsMwjDlE3QSEiIRE5AkR+YF/vF5EHhaR3SLyDRGJTtVGJcgyUhdMFhQQEBWYQTjNzWmDuI6NoyMjJbVjGIZRTeo5g/gj4PnA8d8BX1DVDUAv8OFadCLbBjH5KiaojIpJRHJiMpmayTCMmUddBISIrALeAXzZPxbgLcC3/CrbgXfXoi9aINRGMSqmUo3UkB1yw+wQhmHMROo1g/h/gT8DUiPsQqBPVRP+cRewMt+FIvIREdkpIjuPHi0/d1EhI3WWo1whFVNZznJBXwgTEIZhzDxqLiBE5J3AEVV9LFicp2pey62q3qSqm1V18+LFi8vuT1lG6hJVTJDrC1G8gFBVJpITDMYHOTpylP7xfjNyG4ZRFYpKOVphLgKuEJHL8QL+teHNKBaISNifRawCumvRGXeaNohqhNsoNINIuAle6HmBJ448Qd94H2OJMcaT4yQ1O5LsgoYFnNR+EictOIn1betpijSV3C/DMIwUNRcQqvop4FMAIvIm4E9V9RoR+SbwXuB2YBtwVw36Mi1PashWN5Vjgwg6yyWPZwuI4YlhHjv8GDsP7WRwYnDKtvrG+3j8yOM8fuRxBGF583JOWnASm5dupr2hveQ+GoYxv6nHDKIQnwRuF5G/AZ4Abq76HScmwFfPSDiMOJnB3y2kYqrAKiYAp60NCYfQRBJ3ZAR3bIwjyT4ePvgwTx97+oRZQpCQhGgMN9IQamAwPkjczQg5Reke7qZ7uJuHuh/iguUXcPHKi2kMN5bcV8M83pv3AAAgAElEQVQw5id1FRCqeh9wn7//MnB+Le/vFpg9QOEZRKVUTCJCqKOTxNGjuOrykyfu4BH2nlCvJdLCecvOY1PnJk8ohBuIOAFjupuka6iLl/te5uX+lzkwdIBUqqOkJnmw+0EeP/w4b1j5Bs5bfl7WtYZhGJMxk2YQNUcLRHKF7IRA1TBSA4QWdjJ2uJuX+l9m994BWJ9RO61sWckFyy5g08JNhJ3Cf6aQE2Jt21rWtq3lzbyZ0cQoe/v38mD3gxwYOgDAWHKMHa/u4JFDj/DmNW/mrEVn4ci8d6I3DGMK5reAyJpB5AqI/Mtcg45y5dggAIaaHF7oeYF4Mk7DoGcr2NixkYtXXsyq1lUltdkYbuT0haezqXMTz/U8x89e/Rk9Y56Noz/ez5177uSxw4/xng3vMfuEYRiTMq9fI4MzCCcwg1DVLAERzEUd3HfLmEE8f/x5ftz3IPGkJ6Rig3HeuuatvH/j+0sWDkFEhDMWnsHHXvMxLlt3Gc3h5vS5/YP7+fen/p0Xe18s+z6GYcxd5rWAcIvxog47WTmjg3mpS5lBqCr377+fO168g+EWbwIXckJcEDuNi1ZeVPH81GEnzPnLz+fj536cN6x8A47/Jx9NjHLbC7dxz757SLqFDeKGYcxf5rWAKByHKWB/CGd/ReUYqVWVO/fcyX1d9wEw1hajIdTAaR0b6RyrbvrvhlADb1nzFq474zpao63p8l91/4rtz22nf7y/qvc3DGP2Mb8FxET+VUz58lGnj8sI9/2Lrl/w1LGn0scrl2/ktEWbiIUbSQ4MZtlEqsXqttV89OyPcsqCU9JlKZXTnt49Vb+/YRizh/ktIMYLxGHKUjFlq3ycsKTjgiRdLTov9XPHn0vPHABeu/i1XHPGB2lYmAkXkujtm0bvS6cp0sQHTvsAl665NEvl9PUXvs6jhx6tSR8Mw5j5zG8BUSgOU5YPRLbqR0Rwgt7URRiqDw0f4ru7v5s+Pqn9JN518rsIOSHCWVFda5efWkS4eOXFXHvGtWmVk6Lcvfdu7n31XovvZBjG/BYQbgE/iOxAfScajaejZhqKD3HbC7eR8APVdsY6ec+G96T9EELBvBDHax/VdW3bWn7/7N9nZUsmeO4DBx7grpfuMuO1Ycxz5rWA0PhEen+yVUy5FBtuY8Kd4Bu7vsFAfACAWCjG1addnRVMLysmU299wn43R5q59vRr2bBgQ7rsN0d/w+27bk8vwzUMY/4xvwVEgRlEVpiNyBQCosAMQlX5wUs/oGuoy2sf4T0b3sOixkXZbXWWFva70kRDUa467SrOWXJOumxP3x62P7udofhQ3fplGEb9mN8CIpgsqGHqUN/5ygrNIB7qfihrxdLWtVs5peOUE+qFg4mD6qBiCuKIw7tOehdvXPXGdFn3cDdfeeYr9I711rFnhmHUg3kuIIoxUp/4FU0VbmP/4H7uefWe9PFrF7+WC5dfmLcPoY4O8J3jkv39aCKRt16tEBHetPpNvPOkd5Jar9U73sstz97CsdFjde2bYRi1ZV4LiKKSBU1TxZRwE/zgpR+kI6qubl3NO056R0EPaQmHCbX7MZFUSfbVZqnrVLxu6et4/8b3ExJvFddAfIDtz27n6Ej5aV4Nw5gdzGsBUShZUDkqpge7H+TI6BEAIk6E3z7ltyeNxgozNz/1xs6NfGDTB9Ihwocmhrjl2Vs4NHyozj0zDKMWzG8BUWiZ6ySe1JAjIAJ1j40e4xddv0gfv3n1m1kQWzBlP7JWMs0gAQGez8Y1m64h6njfz0hihO3Pbqd7qCYZYQ3DqCPzW0DE80dznSwWE+S3Qagq33/p++lMcCtbVnLB8guK6kdwJVPieO2c5YplbdtaPnj6B4mFYoCXX+LW525l/+D+OvfMMIxqMq8FRKGMcsFZgRM+0XaQzw/iscOP8ergq941OLzzpHcWnZQnuJIp2TMzVwutbl3Ntadfm05dOp4c5z+f+09e6X+lvh0zDKNqzFsBoYkEJH1BEHKQcMZOkJUsaCoVU8JlID6QtWrp9Stfz7LmZUX3JbQw4AtRJ2e5Yljespxtp29L55aIu3G+/sLX2dt/YqpUwzBmP/NXQBRIFgSF81Gny3JWMf3o5R8xnvTa64x1csmqS6bVl1BHwEjd24u65WWqqyZLm5ey7YxttEa8+E0T7gRff/7rvNz/cp17ZhhGpZm3AqJQsiAoYplrQGgc6D/IC70vpI/fddK70qt+isWJRnFaW/ybuzNmqWshFjctzgryl9AEtz1/Gy/1vVTnnhmGUUnmrYDIWuKaM4Mo1lEu6SZ47sjz6fJzl5zLuvZ1JfUnvDgT9nti/8w3/i5qXMS207fRFm0DfCHxwm2WU8Iw5hAmIMg2UEPxjnKHhg8R9wP+tURaeOvat5bcn+i6den9+CuvlNxOLVnYuJBtZ2SERFKT3L7rdst1bRhzhPkrIII2iEAcJtdVXD8JkACOk2cVU9ghnoxzZOQIkvS+wreve3t6hU8pNKxfn94fnyUCAjyby3VnXMeCBs/fI6lJ7th1B7t6dtW5Z4ZhlMu8FRDF5YJw8obICEccDg5146KQdFjZspLTF55eVn8iK1emV1Ilj/eQ7J89OaI7Yh1sO30bHQ2esT0lJJ499myde2YYRjnUXECIyGoR+bmIPC8iz4rIH/nlnSKyQ0R2+9uOqdoqBy1gpJ7K/gBwfOIYx8c8hzZJOly65tKCsZaKRcJhImtWp49ni5opxYLYAradkRESLi7f3v1tnjzyZJ17ZhhGqdRjBpEA/kRVNwEXAn8oIqcDNwD3quoG4F7/uGroeBFxmPLYHwDuO3AfKV/r9kg761rXVaRPWWqmvbPPt6C9oZ3rzrwunfNCUe566S7Lc20Ys5SaCwhVPaiqj/v7g8DzwErgSmC7X2078O6q9iOYCyKaWZY61Qzi1YFXebFvF4S8eitbVhaVl7oYZqOhOpe2aBvXnXEdS5uWpsvu3ns3D3Y/WMdeGYZRCnW1QYjIOuAc4GFgqaoeBE+IAEsKXPMREdkpIjuPHi099HTBXBCTRHJV1bTHtIZcFsY6aYw0TZmXuliy7BA9vbPKDhGkOdLMtjO2ZeW53rFvB/fvvx9VneRKwzBmEnUTECLSAnwb+GNVHSj2OlW9SVU3q+rmxQHfgelSjJE6N8zGi70vpgPUSQhWNK844ZpykHCY6No16eP4LFQzpWgMN/K7p/8ua1vXpsvu67qPe169x4SEYcwS6iIgRCSCJxy+pqrf8YsPi8hy//xy4Eg1+6C+/wJk2yAKhdlw1eXeV+9NH69sX0407F1XqRkEZKuZZtNy13w0hBq4ZtM1nNx+crrswe4HuXPPnSTdZB17ZhhGMdRjFZMANwPPq+o/Bk59D9jm728D7qpmP7JyQUQCfhAFjNRPHX2Ko6OeSqsh1MDJC09Kn8uXdrRUogFDdXzvKxVrt15EQhGuOu0qNnZsTJc9dewpbnvhtnT8KsMwZib1mEFcBPwu8BYRedL/XA58HtgqIruBrf5x1cj2pM4IiHwziAl3gp/v/3m6fMvyLTQ2xNLHlVIxAURWrEAintE82ds74+MyFUPYCfO+je/j3CXnpste6n+J7c9uZyg+VMeeGYYxGfVYxfSAqoqqnq2qr/U/d6vqcVW9VFU3+Nuqxr0uKlmQP4N49NCjDMQ9M0lzuJktK7ZMmpe6HCQcJjqL/SEK4YiXI+NNq96ULjs4fJCvPPMVjo0eq1/HDMMoyPz1pC4iWVAoLEy4EzzU/VC67I2r30g0FC2YdrQSRLP8IV6paNv1RER44+o38s6T3ongORb2jvfy1We+StdgV517ZxhGLvNWQGQ5yk2yiunJI08yNOGpQdqibZyz5Jz0uXzXVIK54A8xGa9b+jrev/H9hMVb0pvKc/3MsWfq3DPDMILMXwFRaAYRHOwdshy8tqzYQtjxBrXgDKKSRmo40Q6R6J2ZaUjLYWPnRq49I5PCNKEJvr372+zYtwNXZ27CJMOYT8xfAVHIDyIw2O8dfpm+cc9I3BRuyjKy5stLXSly7RAT+/ZVtP2ZwurW1Vx/5vUsjGVSrj7Y/SBfe/5rjEyM1LFnhmHAPBUQ6rpeTmoAkfTbOgQGe4Unjz+RLr9g+QVEQxlBUk0BAXPXDpHLosZF/N5Zv8epHaemy17uf5kvP/1lDg8frmPPDMOYnwIiZ/YQjMSaGuz7xvvomfBW1zSEGjhv2XlZbVTTSA25/hCz16O6GGLhGFdtvIpLVmZyefeO9/KVZ77Cc8efq2PPAqiC60JyAhLjmc/EWPYnMQ6JuFcvmfCuMc9xY5YSrncH6kF2HKbsdKOJCRcUDg0fRP2AfOctPe+EZEBBI3WlbRCQsUPoxATJvj4Svb2EO6oaAb2uiAhvXvNmljUv4849dxJ348TdON988Zuct/Q8tq7dSiSUJ9e3m4SJUUiMwcSIP0j7A3VyPLOfGPcH7bj3cROB/aR3TpNeuRvYqut9KHeQF3BCXowWJwTieB8n7H1CEa/ciWSOQxEIRb2y1H4oCuEohBoC29Qn5m8bITQv/2sbFWZe/ooKxWECz5N6ID7AcGIEQkpYwlyw/IIT2qj2DEJCIaJr1zC+5yXAW800lwUEAMkJNjUuZeGat/GNl+6kZ/Q4JCd4tHcfL7/4fX679VRWSBjiwxlhMGu8sdUTOiSgFlFGnHC2wIjEINIIkSavPNLof5q9bbTJO5f6mIAxmKcCIisOUzQnH/WEcmj4kFfPcTl36WZaoi0ntFFtGwR4y13TAmLvKzSdc05V7lN1kgkY64PRPhjr9/bHB/x9fzs+mB7slwC/p0m+N36IF5LeEuPjwM19e3ljZCEXRxbilJmgqSRSb/0IiHjb9DnJqJJSMw5Vf1uHVVluAuJD3qcUQg0QbfYFR7O/n/q0ZG8bWrx9J1TZZzDqzjwVEPlnEKpK38gAgxODgPd737J8S942qj2DgBw7xEz1h3BdGO+H0V7/05fZTwmFEgapRgnxvoaVPJno58fxI8RxcVF+PnGMPclh/kvDcjqcKCDeG3A45r/9xgJvzjFfJeMfp1Q0WeqblHrHV/U4IW+bVgWl1EEpoVDG96TJgNrK33eT4E74Kq1ERt3lTvgqsYBaLLifVqHFPTVa0t+mVGxa5jQlOQ6j4zA6jYAGkSZPUKQERkNr5rihFRraMuWRxvK+T6MmzFMBkT8Ok+sqB4cO+ieUs5eezYLYgrxtZNkgqjSDiKxYgUSjaDxePzuEqjfADx+DkR4YOQ4jx/xtjycEKvWGLCF/cGmFhlakoYVzos2sFfjusSfoiveBE2Z/KMy/hRu5dO1WNq/YgjMb3lwdB3A8YVQLkglIjPoCI7gNfkYC2xGIj2T2S/mbpq4dLiIQsxPOCItYu7cfa/MFiS9MGtq8snDD1O0ZVWF+CogCNojuvoP0x/0kPSHlopUXFWwjqGJyqzSDkFCI6Jo1jO/ZA8DY00/TcsklU1xVIskJTwgMHYahI/72MAwf9d5Iy0K8QaBxgbdNfxZkBoGGtoJvlZ3Ah/RKHjjwAPfvvx8Xlzjwo/338tjxp7l8/eWsbVt7wnXzmlAYQv5gO11UM4IjPpyx+cSHMsfjg5n9VPl0DPmur3Yc64P+/VM8S0NGcKR+K7F2X4gEyhpabVZSYeangCiQTe6hrl+n9zubO9K5lfPhhLxoQgokXUVdRZzK/zhjp29KC4ihX/ySxnPPJdRyok2kaFzXmwEMdMPgIRjshoGDniAodaVOtAUaOwKfBd7gn9pvaPffoEvHEYdLVl3CyQtO5ru7v8vxseMAHBk5wi3P3sJZi87irWvfSlu0raz7GHiDbLTJ+zQX/j+QhevCxDCM+8JifMATHONDvjAZ9Lap4+ksLkiOw8i497udtN9OZvaREiCxtjzb8n+P84V5KSDcrDhMnoA4NnqMF4/uJobnwbyuY03ea9PXiRAKO2n1UiLhEolWXtXReO65DD/0axJHj6LxOIP33MOCd0+Rrjsx7r39p1RCo70ZldDIcU+/PR3CMWhaBE2d3oDRtDDzaeyondoELwf4R1/zUR7qfohfHvglE/6zPH3saXb17OKNq97I+cvPT4dEMWqE42Te8oshEfcFxoC/Hcw5HvAWMIwPFv97Vddf+NA/xaxEPON6bEEeAdIemJG0zfvVXPPy6fMZqX914Fdo0psBtEfbWNDcPmU7oUhGQCQnqiMgxHFou+zt9Nz6HwCMPvEkzeefT2TFCu+tbfgoDByAwYP+rOCgJwSmfydPALQshZYl3rZ5ibc/w6buYSfMG1a9gbMXn82OfTt49vizAMTdODte3cEjhx7h4pUX89olrzVBMVMJRyG8EJoXTl5P1VNxpoTFuL/yLS1A/PKxfk8NVhSaWeE1VbLjaMuJM5Cs2YkvUGr4klRL5uX/nlwjdd9YH08dfQpxvSRAy5qXZ61SKkQo4sCot1+tlUwADaecQsOpGxh/7hmIDzFwy/+h85I1yECXt3pl2g22QdsKaF0GrSugbTm0LPP+084i2hvaee+p7+Xc/nP58d4fpzP+9cf7+eHeH/KLA7/g4hUXc87Sc4g4c/M/8JxHJOOz0bp08rrJiYywSAmQ4H5qafV0VtWlBMlg9+T1wo0nzkZSBvigrSTSNKNetqZifgqIgJHaaWjgwe4HcXEJJYXWSAst0RZC4an/iFX1pk7EvWly717o2UtbbBdHu3/jvfwchbGOHhpXFdC3iwPNizNqoaaFge1C7z/bHOKk9pP4/bN/n0cPP8oDXQ8wnBgGYDA+yI9e+RG/PPBLXr/i9bxu6euy4mkZc4xQxP+dd05ez03mCI2BbL+c9CxlkKLtcolRGBr1VLuT4YTzr9TKWsXlb2fA6q15KSCCntSjkuTxI48DIEmHZc3LgexVSoXI8oUoZ6mrqmcn6N0Lva9Az15PbRRYahhugOZTOhne7a1LH3z6MLHlLUhzR2YW0LrCmxm0LJ13utOQE+LC5Rdy7pJzeezwYzzY/WA6j8fQxBA/3fdT7u+6n7MWncXrlr6OZc3L6txjo244ocyCislwXc+4foIAyZ2ZDBbvd+ImMn5CUxFqCPiQBARHNFDWusyzp1SJ+TWK+AQ9qZ8eeJ5kzPvjLoouTq+CKUrFVKqzXHB20LvP244PTnlZy1mrGD0iuMRIRlsYbrmclrdeVvx95wHRUJQtK7awedlmnjj8BA90P8Bg3Ptux5Pj7Dy8k52Hd7KieQXnLDmHsxafRUOo/m9qxgzEcTJLsidDNbNyK20XybWR+PvTWTKeXr01iU3xnGth1euKb3OazE8B4c8gEm6Cp/tfgJincjmz4yzivuNo0TYIn6wZhOtC3z7o7zrxB5L64RQzdW1ZBh3roHM9LFiL07KUlmU7GfjhDwEY+vXjNF5wMaHWEta6z3EiToTzl5/PuUvP5ckjT/LQwYfoGct4BXcPd9O9t5sd+3ZwWudpbFq4iZPbT84fENAwJkGBRLiJpNNIomEJyaQy4bokXSXhKsmkknBdbz8+ho4PoanwMmMDSHwQGR/AiQ8i8SGc+CChiSE0mUCBpmiI1liYpmiYE1bSl+LnMg3mp4CY8Ay7R0ePMhbyPKWXNC5hOSvYhzeITFvFNDYG3Xvh8DNw5Pnph5cIx2DBWuhYCx3rvW2eqWPTeZsZefRREkeOeMte77136mWv85iwE2bzss28bunr2Dewj8ePPM5zx58j6asE4m6cp449xVPHniIsYU5ecDIbOzdyasepNEeqN3U3ikfVH2j9T3DfO3ZxXbytXzeR9M+rXydwnEi6J7SVcBXXzQzs6Wv86yeSLm5O/XR5Se5DIWCB/wngADGgQYnoOA3JYRrcERrGhmkdH2VlY4KVTUmWNMTpCI0Raswf6aFSzEsB4Y6Pk9Qkh0cOk4x4y+wuWnkRyX2Zv/SUM4hkgvD4Meg/DGN9JH79Iiw+VHwnUrOD1KdlaVHOO+llr9tvBbxlr7FNm4ht3Fj8vechIsK69nWsa1/H29e9naeOPcUTh5/gyGgmLERCE+zq3cWu3l0IwsqWlaxrW8eatjWsbl1NLByr4xOUh6riqufU6WpmsHSDg61f7rqk91Of3GtSA2pisnbUG2RTg7YbGFy99iDpv1m7qcE72G763vX+9uqACBMSY8KJMURmKfAugBHvE3aEyw+H2FKG3+xUzEsBoeNxjo0cI+kmcSMOHQ0dnLnoTF58KbMCIUtAqHqqod5XMkbk/v2EDi6EPs/YOTAcw10oOI7/a25ohcWneauGggamWLu3LUOV0XDyyTRsPJXxXS+CKr1f+zqxs86k7bLLyvOynic0RZq4cPmFXLDsArqHu3mh5wV29ezi6MhRFG8wVZR9/fvZ278fVUUQFsYWs6J5NcubV7EotoSWyAJQxxsg/UEydxB2NTgYKqr+gKpkBlXNDJAFy9Nl+PcJlpO3biKrH/X+1uc2YUcIOeJtQ9427DiEHcFxhEhICPnHqXrhkONv/escJ7DvXZ90lf29I7xybJjekWyHwYSrdDRXVyU6LwVEcnyMwyOeMEhGQly08iIccTxDczIBEyOEjh2FscO+A9pBL4xADg2RjA/CscF2njjwOs54/SJia0+HBWuqut657bLLON51AHfY69fY088wvns3rZe+labzNiNTzEZU1UuSlhqUso69Mg2cc3Pru95xUtWvF6jr5mvPr+9mt51Mn8u8uao/oJ54XeaeqQE5FerEDQycmX5kBl0NDJTBwdtreylJXcJYsp8Bdx8D7j6G3SOcaCfqBV5MHwkhGqWTmNNBTDqJSQdRp50IzVlZCo3ySQ2a6UHY/ziSPSiHHIeQ4NULOYTEvybkX5N17A/g4g3gjpM9OAfvlbo+VR4JBe7tSFX/3lv8GUTvcJxXjg/zyvFh9h4d5thwnLWd1VWDzjsBMREf57mDA/SPxQi7A+jxbpY+9SCHx++m/8V2xgc9g/WguwenpT89Rnhvlv6+egPTWGyC5IJGekcWkoi20+1G2fVrobVPiSw6nB4ElcwglTsoEzgO1ksNfpnBNHWO9IAqZ7yNJY8/QPu+3ek+sftrDN+xg1fPvYSRBQsnGfxr/93PdBqcdhY7Z7OYs0noKMPuIYbdwwy7hxjV4+QKDCXJiB5lJHk0q1wIEZUWotKa/kSkmbA0EaaRiDTiEK25EHH8gdMR7xNy8AZUB0LiDZCpbXAQTl0THGBDTqZ+VjuO47fhtRlOD6ROoD0yZaHsNkMiWWVhR/xI6yZwO5qjdDRHOWeNtzx3JJ6gsQrRG4KIzrCRQkTeDvwTnhXny6r6+UJ1N2/erDt37pxW+737nuOuv7qDpERAlORal7WRURob+ugZWMd43FvmumzhM8QaMn74SYnSH1nM8YZVHI+uoCe6knioCVRp6Jmg8XB28LHxziijS6KcuOyg8rQf6WL9bx4gNpTprwqMtSxgpL2TkbZOhtsWMtreyXhjy6zy5Kw1wUFUhPRA5TLBiHuYIfcQw8mjjLq9TDBCKm2QiHhZRfEKBO96xzvAP42IF+Qx5IRoDDUTCzXREIoRC8eIhWI0hGI0hGM0hmJEQ1GioSgNgW0s3EDEiRANh2lwIoRDofSbcnCAD6X3M89gg6yRQkQeU9XNU9WbUTMIEQkBXwS2Al3AoyLyPVWtWOb63xzs9oQDgDi0jXXSNyb0Da5JdYK4NHCo6SSGW9oZDC9kILKYkVBb/oFVhPGFURKNIZoPjOJMeAK3oSdOeCRBMuZJeK3i/804i3jx9CvoPPgKCw7tw0kpnEegcSRO48FDLMQzoLshh2Q4ijoOGgrhOiEIhdBQOJ0URwAcQZD0VsAf6AL7ZN7sxB9Q03nWHPH3M+XZ1wgOmcRswcEz1WZKtkpgwM3cIzjwSrodJ3XObyc9YOe0kbp/6lxqIM/KEpeXxf4HEm6ckYlRRpOjjEyMMJoYJZ4cJ+4mivzLJYFB/5PBBYb9TzE4Ijg4XpY9Ee9ZEERSe076LTz93ZARGMGy1ONL4N9gnfSxZM7ko5if+/QFlgm4XF5z+cWsO+PMqrU/owQEcD6wR1VfBhCR24ErgYoJiI3LT+doy/fpdduIOEtJtK4mGYriOg3+J+xFaj2zk5amCK0CK0VwhPRbpfjHgr9NTYHPUgaf72X82HjmLRII/L/LHtDSZZJzPqdcMv9hcwdbIJN+89QzYc0G3AP7cQe8MAGSapRJ/nspUHBM89Nm1pDU3WqRurkyhInSRhRv9qkoSU3iqusthNAkSXU9FaLrernxqjhz15xtJWoaM5Pe7sPzSkCsBIJxeruAC4IVROQjwEcA1qyZPCR3PpavXcHv/Ms/MeFOEB9NMHR0gt6Dw/QcHGZ81Bslo7EwWy5ehxOafsx4PXsZ+5/v4eUnj1V1EChIpAlO2whJF3d01PuMjKCjo7ijI2hi9gy7sxVBCEvYk8gFf0LqCQ31UqmmVk656vr7LurbpTRwXv081+l/bWw3qshMExD5XnKz/guo6k3ATeDZIEq9UcSJEGmO0NzcyNJ1bagqIwNxhnrHaV/cWJJwAO+tf83pC1m0qpW+IyNpa7DW/kX8BBRFx8bRxAQ6kUATCTQxAYmkt/Wt16lByBuFskOIZAk9G5xmBKnZiidAPGex1Cwl9XFxgdRyV6+O/8vM/EZTgifrxSZVmr1QI3g+s5tpZ5JaRgVZdvL6qrY/0wREF/gZezxWAVPE2a0MIkJzewPN7ZWJy9PUFqWpzSKHGoYxe5lpefceBTaIyHoRiQJXAd+rc58MwzDmJTNqBqGqCRH5b8BP8Ja5fkVVn61ztwzDMOYlM0pAAKjq3cDd9e6HYRjGfGemqZgMwzCMGYIJCMMwDCMvJiAMwzCMvJiAMAzDMPIy44L1TQcROQrsK/HyRcCxCnZnNmDPPD+wZ54flPPMa1V18VSVZrWAKAcR2VlMNMO5hD3z/MCeeX5Qi2c2FZNhGIaRF6XX2BgAAATCSURBVBMQhmEYRl7ms4C4qd4dqAP2zPMDe+b5QdWfed7aIAzDMIzJmc8zCMMwDGMSTEAYhmEYeZmTAkJE3i4iu0Rkj4jckOd8g4h8wz//sIisC5z7lF++S0TeVst+l0OpzywiW0XkMRF52t++pdZ9L5Vy/s7++TUiMiQif1qrPpdLmb/ts0XkIRF51v97x2rZ91Ip47cdEZHt/rM+LyKfqnXfS6GI571ERB4XkYSIvDfn3DYR2e1/tpXdmWDWqbnwwQsT/hJwEhAFfgOcnlPnD4B/8/evAr7h75/u128A1vvthOr9TFV+5nOAFf7+mcCBej9PtZ85cP7bwDeBP63389Tg7xwGngJe4x8vnAe/7Q8At/v7TcArwLp6P1MFnncdcDZwK/DeQHkn8LK/7fD3O8rpz1ycQZwP7FHVl1U1DtwOXJlT50pgu7//LeBSERG//HZVHVfVvcAev72ZTsnPrKpPqGoqa9+zQExEKpNWr7qU83dGRN6N9x9oNuUbKeeZfwt4SlV/A6Cqx1V1NiQoL+eZFWgWkTDQCMSBgdp0u2SmfF5VfUVVnwLcnGvfBuxQ1R5V7QV2AG8vpzNzUUCsBPYHjrv8srx1VDUB9OO9URVz7UyknGcO8h7gCVUdr1I/K0nJzywizcAngRtr0M9KUs7f+VRAReQnvnriz2rQ30pQzjN/CxgGDgKvAv+gqj3V7nCZlDMGVXz8mnEJgyqA5CnLXctbqE4x185Eynlm76TIGcDf4b1pzgbKeeYbgS+o6pA/oZgtlPPMYeBi4DxgBLhXRB5T1Xsr28WKU84znw8kgRV4Kpdfisg9qvpyZbtYUcoZgyo+fs3FGUQXsDpwvAroLlTHn362Az1FXjsTKeeZEZFVwHeBa1X1par3tjKU88wXAH8vIq8Afwx82k91O9Mp97d9v6oeU9URvKyN51a9x+VTzjN/APixqk6o6hHgV8BMj9dUzhhU+fGr3kaZKhh5wni65fVkjDxn5NT5Q7KNWnf4+2eQbaR+mdlhyCvnmRf49d9T7+eo1TPn1Pkss8dIXc7fuQN4HM9YGwbuAd5R72eq8jN/Evgq3pt1M/AccHa9n6nc5w3UvYUTjdR7/b91h7/fWVZ/6v2FVOlLvhx4EW81wJ/7ZX8NXOHvx/BWr+wBHgFOClz75/51u4DL6v0s1X5m4C/w9LRPBj5L6v081f47B9qYNQKi3GcGPohnlH8G+Pt6P0u1nxlo8cuf9YXD/6z3s1Toec/Dmy0MA8eBZwPXXu9/D3uAD5XbFwu1YRiGYeRlLtogDMMwjApgAsIwDMPIiwkIwzAMIy8mIAzDMIy8mIAwDMMw8mICwjAMw8iLCQjDMAwjLyYgDKOCiMh5IvKUiMREpNnPvXBmvftlGKVgjnKGUWFE5G/wvHsbgS5V/Vydu2QYJWECwjAqjIhEgUeBMeD1OjvyLhjGCZiKyTAqTydeHKBWvJmEYcxKbAZhGBVGRL6HlwlsPbBcVWdDKHHDOIG5mDDIMOqGiFwLJFT16yISAh4Ukbeo6s/q3TfDmC42gzAMwzDyYjYIwzAMIy8mIAzDMIy8mIAwDMMw8mICwjAMw8iLCQjDMAwjLyYgDMMwjLyYgDAMwzDy8v8DlTJsNEkeNSMAAAAASUVORK5CYII=\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.stats import ksone\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "x = np.linspace(0,0.1)\n", "for n in [10,100,1000,10000,100000]:\n", " plt.plot(x, ksone.pdf(x, n), lw=3, alpha=0.6,label=str(n))\n", "plt.title('Kolmogorov Distribution')\n", "plt.ylabel('Density')\n", "plt.xlabel('x')\n", "plt.legend()\n", "plt.show()\n", "a=[]\n", "for n in [10,100,1000,10000,100000]:\n", " a.append(ksone.ppf(0.95, n))\n", "plt.plot([10,100,1000,10000,100000],a)\n", "plt.plot([20,20],[0,0.29],'r')\n", "plt.text(20,0.31,'N = 20', fontsize=12)\n", "plt.xscale('log')\n", "plt.title('95th Percentile Value')\n", "plt.ylabel('x (0.95)')\n", "plt.xlabel('Sample size')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "nbpages": { "level": 2, "link": "[12.2.2 Example 1: KS Test on Distributions of the Same Mean](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.02-Contributed-Example.html#12.2.2-Example-1:-KS-Test-on-Distributions-of-the-Same-Mean)", "section": "12.2.2 Example 1: KS Test on Distributions of the Same Mean" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "95th percentile = 0.2647335873372445\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.stats import ksone\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "N=20\n", "x = np.linspace(0,.5)\n", "plt.plot(x, ksone.pdf(x, N), lw=3, alpha=0.6,label='20 sample K-distribution')\n", "a=ksone.ppf(.95,N)\n", "print('95th percentile = ',a)\n", "z=x[x" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "p_hat_up=[]\n", "for i in range(len(max)):\n", " b=max[i]+a\n", " if b > 1:\n", " p_hat_up.append(1)\n", " else:\n", " p_hat_up.append(b)\n", "p_hat_down=[]\n", "for i in range(len(max)):\n", " b=min[i]-a\n", " if b < 0:\n", " p_hat_down.append(0)\n", " else:\n", " p_hat_down.append(b)\n", "\n", "plt.figure(figsize=(9, 6))\n", "plt.plot(r, norm.cdf(r, -0.168, 1.25),'r',lw=3,label='True CDF')\n", "plt.plot(r, max,'C0-',label='max',lw=3)\n", "plt.plot(r, min,'C0-',label='min',lw=3)\n", "plt.plot(r, p_hat_up,'k--',label='$\\hat{P}_{upper}$(x)',lw=3)\n", "plt.plot(r, p_hat_down,'k--',label='$\\hat{P}_{lower}$(x)',lw=3)\n", "plt.title('Analogue of Figure 12.11:\\nKolmogorov-Smirnov 95% Confidence Interval with 20 Samples')\n", "plt.text(-1,0.8,'$\\hat{P}_{upper}$(x)', fontsize=12)\n", "plt.text(0.7,0.3,'$\\hat{P}_{lower}$(x)', fontsize=12)\n", "plt.ylabel('F(x)')\n", "plt.xlabel('x')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [12.1 Predictions under epistemic uncertainty with p-boxes](https://ndcbe.github.io/cbe67701-uncertainty-quantification/12.01-Epistemic-uncertainty-with-p-boxes.html) | [Contents](toc.html) |

\"Open

\"Download\"" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }