{ "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", "< [11.0 Predictive Models Informed by Simulation, Measurement, and Surrogates](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.00-Predictive-Models-Informed-by-Simulation-Measurement-and-Surrogates.html) | [Contents](toc.html) | [11.2 Markov Chain Monte Carlo Examples](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html)
"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1-Gibbs-Sampling-to-Approximate-Bayes'-Integral)",
"section": "11.1 Gibbs Sampling to Approximate Bayes' Integral"
}
},
"source": [
"# 11.1 Gibbs Sampling to Approximate Bayes' Integral"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1-Gibbs-Sampling-to-Approximate-Bayes'-Integral)",
"section": "11.1 Gibbs Sampling to Approximate Bayes' Integral"
}
},
"source": [
"Created by Pedro Amorim (pamorimv@nd.edu)"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1-Gibbs-Sampling-to-Approximate-Bayes'-Integral)",
"section": "11.1 Gibbs Sampling to Approximate Bayes' Integral"
}
},
"source": [
"The following text, examples, and codes were adapted from these sources:\n",
"* McClarren, Ryan G (2018). Uncertainty Quantification and Predictive Computational Science: A Foundation for Physical Scientists and Engineers, Chapter 8: Reliability Methods for Estimating the Probability of Failure, Springer, https://doi.org/10.1007/978-3-319-99525-0_8\n",
"* McClarren, Ryan G (2018). Uncertainty Quantification and Predictive Computational Science: A Foundation for Physical Scientists and Engineers, Chapter 11: Predictive Models Informed by Simulation, Measurement, and Surrogates, https://link.springer.com/chapter/10.1007/978-3-319-99525-0_11\n",
"* Yildirim, Ilke (2012). Bayesian Inference: Gibbs Sampling, http://www.mit.edu/~ilkery/papers/GibbsSampling.pdf"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1-Gibbs-Sampling-to-Approximate-Bayes'-Integral)",
"section": "11.1 Gibbs Sampling to Approximate Bayes' Integral"
}
},
"source": [
"Models can be used to fuse experimental and simulation data, as long as we attend to the dissonances between those two. To do that, we can use calibration techniques to account for those dissonances. One of the ways to combine simulation and experimental, or, better saying deterministic and stochastic data to use Bayes' rule."
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1-Gibbs-Sampling-to-Approximate-Bayes'-Integral)",
"section": "11.1 Gibbs Sampling to Approximate Bayes' Integral"
}
},
"source": [
"$$\\pi(t,\\epsilon | y,x) = \\frac{f(y|x,t,\\epsilon)\\pi(t)\\pi(\\epsilon)}{\\int dt \\int d \\epsilon f(y|x,y,\\epsilon)\\pi(t)\\pi(\\epsilon)}$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1-Gibbs-Sampling-to-Approximate-Bayes'-Integral)",
"section": "11.1 Gibbs Sampling to Approximate Bayes' Integral"
}
},
"source": [
"The likelihood, if assumed to be normal (for example), can be solved. This way we will have a closed form for the prior."
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1-Gibbs-Sampling-to-Approximate-Bayes'-Integral)",
"section": "11.1 Gibbs Sampling to Approximate Bayes' Integral"
}
},
"source": [
"$$f(y|x,t,\\epsilon) = \\frac{1}{2\\pi^{N/2}\\sigma^N} exp{\\left[ -\\frac{1}{2\\sigma^2} \\sum_{i=1}^{N} (y(x_i) - \\eta(x_i,t_i))^2\\right]}$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1-Gibbs-Sampling-to-Approximate-Bayes'-Integral)",
"section": "11.1 Gibbs Sampling to Approximate Bayes' Integral"
}
},
"source": [
"But if you don't know the measurement error, you will have to evaluate the denominator of Bayes' rule, and after each step re-evaluate your QoI. This process can become not only very tedious, but also very expensive as your model becomes more complex. To avoid this numerical integration, you can approximate your integral via several methods. **The one discussed in this notebook will be Gibbs Sampling**, although other methods such as Markov Chain Monte Carlo."
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1-Gibbs-Sampling-to-Approximate-Bayes'-Integral)",
"section": "11.1 Gibbs Sampling to Approximate Bayes' Integral"
}
},
"source": [
"Assume that you have a joint distribution of two variables $\\theta_1$ and $\\theta_2$ about and **can** sample the conditional distribution of a bivariate distribution $p(\\theta_1 | \\theta_2)$ and $p(\\theta_2 | \\theta_1)$."
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1-Gibbs-Sampling-to-Approximate-Bayes'-Integral)",
"section": "11.1 Gibbs Sampling to Approximate Bayes' Integral"
}
},
"source": [
"To conduct Gibbs Sampling, you should follow these steps:\n",
"1. Give an initial value for $\\theta_1^{(0)}$ and $\\theta_2^{(0)}$\n",
"2. Sample $\\theta_1^{(j)}$ from the conditional distribution p($\\theta_1|\\theta_2^{(j-1)})$\n",
"3. Sample $\\theta_2^{(j)}$ from the conditional distribution p($\\theta_2|\\theta_1^{(j)})$"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1-Gibbs-Sampling-to-Approximate-Bayes'-Integral)",
"section": "11.1 Gibbs Sampling to Approximate Bayes' Integral"
}
},
"source": [
"Gibbs Sampling is yet another Markov Chain. The Markov characteristic lies on the fact that the the next value for a parameter solely depend on the knowledge of its current value, and not on its previous values. \n",
"**This method will fail if you have independent variables.**\n",
"According to the law of large numbers, and the central limit theorem, the average of the results of this Gibbs Sampling will generate the expectation value of the quantity you are trying to measure."
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 3,
"link": "[11.1.1 Example: Multivariate distribution](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1.1-Example:-Multivariate-distribution)",
"section": "11.1.1 Example: Multivariate distribution"
}
},
"source": [
"### 11.1.1 Example: Multivariate distribution"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 3,
"link": "[11.1.1 Example: Multivariate distribution](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1.1-Example:-Multivariate-distribution)",
"section": "11.1.1 Example: Multivariate distribution"
}
},
"source": [
"Suppose you have a multivariate distribution $\\theta$ ~ $N_2(0,\\Sigma)$ with $\\Sigma =$ $$\\begin{bmatrix} 1 & \\rho \\\\ \\rho & 1 \\end{bmatrix}$$\n",
"\n",
"\n",
"The conditional distribution for each of these variables is given by:\n",
"\n",
"$\\theta_1 | \\theta_2$ ~ $N(\\rho\\theta_2,[1-\\rho^2]$)\n",
"\n",
"$\\theta_2 | \\theta_1$ ~ $N(\\rho\\theta_1,[1-\\rho^2]$)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"nbpages": {
"level": 3,
"link": "[11.1.1 Example: Multivariate distribution](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1.1-Example:-Multivariate-distribution)",
"section": "11.1.1 Example: Multivariate distribution"
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy import stats\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('seaborn-white')"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"nbpages": {
"level": 3,
"link": "[11.1.1 Example: Multivariate distribution](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1.1-Example:-Multivariate-distribution)",
"section": "11.1.1 Example: Multivariate distribution"
}
},
"outputs": [],
"source": [
"mean_x = 0\n",
"variance_x = 1\n",
"cor_xy = 0.3\n",
"\n",
"mean_y = 0\n",
"variance_y = 1\n",
"cor_yx = cor_xy\n",
"\n",
"x = np.linspace(-3,3,1000)\n",
"y = np.linspace(-3,3,1000)\n",
"xgrid,ygrid = np.meshgrid(x,y)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"nbpages": {
"level": 3,
"link": "[11.1.1 Example: Multivariate distribution](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1.1-Example:-Multivariate-distribution)",
"section": "11.1.1 Example: Multivariate distribution"
}
},
"outputs": [],
"source": [
"position = np.empty(xgrid.shape + (2,))\n",
"position[:,:, 0] = xgrid\n",
"position[:,:, 1] = ygrid\n",
"\n",
"gauss2d = stats.multivariate_normal([mean_x, mean_y], [[variance_x, cor_xy], [cor_yx, variance_y]]) "
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"nbpages": {
"level": 3,
"link": "[11.1.1 Example: Multivariate distribution](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html#11.1.1-Example:-Multivariate-distribution)",
"section": "11.1.1 Example: Multivariate distribution"
}
},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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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
}