Tuesday, January 12, 2016

MCMC Class Lecture Notes

In the fall of 2015, I taught an applied introductory course in Markov-Chain Monte Carlo Methods targeted to graduate students from scientific computing, engineering, math, and computer science.

Here's the blurb I put out for the course:
Markov Chain Monte Carlo (MCMC) is one the most powerful and versatile methods developed in the 20th century. It uses a sequence of random numbers to solve important problems in physics, computational biology, econometrics, political science, Bayesian inference, machine learning, data science, optimization, etc. For many of these problems, simple Monte Carlo ("integration by darts") is inefficient. Often, MCMC is the answer. 
Broadly speaking, MCMC is collection of sampling methods that allows us to solve problems of integration, optimization, simulation in high dimensional spaces. In this course, we will look at the foundations of Monte Carlo and MCMC, introduce and implement different sampling algorithms, and develop statistical concepts and intuition to analyze convergence and error in the simulation. Assignments and labs will consider illustrative examples from statistics, material science, physics, economics, optimization, and Bayesian inference.
The complete set of lecture notes may be downloaded from my Google Sites webpage.

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