{ "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", "< [11.1 Gibbs Sampling to Approximate Bayes' Integral](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.01-Gibbs-Sampling.html) | [Contents](toc.html) | [11.3 The Kennedy-O’Hagan Predictive Model](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.03-Contributed-Example.html)
"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "bdNm3J0HWYcB",
"nbpages": {
"level": 1,
"link": "[11.2 Markov Chain Monte Carlo Examples](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2-Markov-Chain-Monte-Carlo-Examples)",
"section": "11.2 Markov Chain Monte Carlo Examples"
}
},
"source": [
"# 11.2 Markov Chain Monte Carlo Examples"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "izBlOg3zWYcE",
"nbpages": {
"level": 1,
"link": "[11.2 Markov Chain Monte Carlo Examples](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2-Markov-Chain-Monte-Carlo-Examples)",
"section": "11.2 Markov Chain Monte Carlo Examples"
}
},
"source": [
"Created by Xinhong Liu (xliu27@nd.edu)\n",
"\n",
"\n",
"This example was adapted from:\n",
"\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, Springer, https://link.springer.com/chapter/10.1007%2F978-3-319-99525-0_11\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"colab": {},
"colab_type": "code",
"id": "wvSaZPPuWYcG",
"nbpages": {
"level": 1,
"link": "[11.2 Markov Chain Monte Carlo Examples](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2-Markov-Chain-Monte-Carlo-Examples)",
"section": "11.2 Markov Chain Monte Carlo Examples"
}
},
"outputs": [],
"source": [
"## import all needed Python libraries here\n",
"import numpy as np\n",
"import scipy.stats as stats\n",
"import math\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 2,
"link": "[11.2.1 Markov Chain](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.1-Markov-Chain)",
"section": "11.2.1 Markov Chain"
}
},
"source": [
"## 11.2.1 Markov Chain\n",
"A Markov Chain is a sequence ${x_1,x_2,...x_t}$ for a random variable $X$ that satisfies the following property\n",
"\n",
"\\begin{equation}\n",
"p(x_{t+1}|x_t,x_{t-1},...x_1) = p(x_{t+1}|x_t)\n",
"\\end{equation}\n",
"\n",
"which means given the present state, the probability model for the future state is independent of the past states if $t$ is large enough\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "dJuJ7c2rW8gg",
"nbpages": {
"level": 2,
"link": "[11.2.2 Metropolis-Hastings for MCMC](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2-Metropolis-Hastings-for-MCMC)",
"section": "11.2.2 Metropolis-Hastings for MCMC"
}
},
"source": [
"## 11.2.2 Metropolis-Hastings for MCMC\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 2,
"link": "[11.2.2 Metropolis-Hastings for MCMC](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2-Metropolis-Hastings-for-MCMC)",
"section": "11.2.2 Metropolis-Hastings for MCMC"
}
},
"source": [
"The Metropolis-Hastings algorithm (MH) enable us to evaluate the product of the prior and the likelihood function without calculating the normalization constant. It is a rejection sampling technique that uses a distribution that is not the target distribution to generate proposed samples\n",
"\n",
"\\begin{equation}\n",
"\\hat{p}(x_{t+1}) = \\int_X p(x_{t+1}|x_t) p(x_t) dx_t\n",
"\\end{equation}\n",
"\n",
"### Algorithm\n",
"1. Choose initial state $x_0$ and a proposal density $q(x_{t+1}|x_t)$\n",
"2. Randomly simulate candidate sample $y$ from $q(x_{t+1}|x_t)$ and $u$ from $U(0,1)$\n",
"3. Calculate the acceptance ratio\n",
"\n",
"\\begin{equation}\n",
"\\alpha(x_t,y) = min \\left(1, \\frac{\\hat{p}(y) q(x_t|y)}{\\hat{p}(x_t) q(y|x_t)}\\right)\n",
"\\end{equation}\n",
"\n",
"4. Set $x_{t+1} = y$ if $\\alpha(x_t,y) \\geq u$, $x_{t+1} = x_t$ otherwise\n",
"\n",
"Then the stationary pdf for the Markov Chain is the target probability"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 3,
"link": "[11.2.2.1 Implemention](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2.1-Implemention)",
"section": "11.2.2.1 Implemention"
}
},
"source": [
"### 11.2.2.1 Implemention\n",
"\n",
"Following example is using MCMC to approximate a Beta distribution with a proposal density $N(2,1)$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"nbpages": {
"level": 3,
"link": "[11.2.2.1 Implemention](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2.1-Implemention)",
"section": "11.2.2.1 Implemention"
}
},
"outputs": [],
"source": [
"def beta_mcmc(N, x0, sigma, a, b):\n",
" '''\n",
" Use Markov Chain Monte Carlo to approximate a Beta distribution with a proposal density N(x0,1).\n",
" \n",
" Arguments:\n",
" N: total number of samples needed\n",
" a,b: alpha and beta values for beta distribution\n",
" \n",
" Returns:\n",
" states: stable\n",
" acc: acceptance rate\n",
" \n",
" '''\n",
" states = []\n",
" acc = 0 # number of accepted samples\n",
" x = x0 # initial state - starting point for Markov chain\n",
" for i in range(0,N):\n",
" states.append(x) # append state vector\n",
" y = proposal_dist(x,sigma) # candidate sample\n",
" alpha = min(beta_dist(y,a,b)/beta_dist(x,a,b),1) # acceptance probability\n",
" u = np.random.uniform(0,1) # generate uniform random number\n",
" # check if sample is accepted\n",
" if u <= alpha:\n",
" x = y # generated sample=candidate sample\n",
" acc = acc + 1 # update accepted candidate sample count\n",
" acc_ratio = acc/(N-1)\n",
" return states, acc_ratio \n"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 3,
"link": "[11.2.2.1 Implemention](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2.1-Implemention)",
"section": "11.2.2.1 Implemention"
}
},
"source": [
"*Note*: The cell below can take a few minutes to evaluate. Adjust $N$ (number of samples) to explore the trade-off between accuracy and run time."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"nbpages": {
"level": 3,
"link": "[11.2.2.1 Implemention](https://ndcbe.github.io/cbe67701-uncertainty-quantification/11.02-Contributed-Example.html#11.2.2.1-Implemention)",
"section": "11.2.2.1 Implemention"
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:20: RuntimeWarning: divide by zero encountered in double_scalars\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of samples = 5000\n",
"Acceptance ratio = 0.27645529105821165\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"
"
]
}
],
"metadata": {
"colab": {
"name": "11.02-Contributed-Example.ipynb",
"provenance": []
},
"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": 1
}