{ "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) |
"
]
},
{
"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": [
{
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\n",
"text/plain": [
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]
}
],
"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
}