# An Introduction to Markov Chain Monte Carlo

Instructor:
Prof. Carlos C. Rodriguez
Office Hours:
Tues., Wed. and Thurs. after lectures or by appointment on Weds..
Text:
Radford M. Neal, 1993. Probabilistic Inference Using Markov Chain Monte Carlo Methods. Available online at https://omega0.xyz/omega8008/neal.pdf and https://omega0.xyz/omega8008/neal-review.ps

#### Software:

Neal's MCMC package is now installed and accessible from any Unix machine with access to the /home part of the tree directory. To access the programs from your account just add the directory:
/home/cr569/mcmcbin
to your search path. There is an extensive documentation with examples, available online. Use this User Friendly Window for 1D Metropolis.
A Virtual Monte Carlo Summer at State College, PA

### If you don't get the fonts for the equations click here

• Lecture I:
Introduction, the basics of Monte Carlo Integration, and the elements of statistical physics (part 1).
[.html] [.pdf] [.ps] [.tex]
• Lecture II:
Statistical Physics (part 2), the original Metropolis Algorithm, Simulated Annealing.
[.html] [.pdf] [.ps] [.tex]
• Lecture III:
Bringing Metropolis to Statistics, Hastings generalization, Component-wise Metropolis, Gibbs Sampler.
[.html] [.pdf] [.ps] [.tex]
Links: [Gaussian sampler with Unif(x-1,x+1) proposal]
• Lecture IV:
Being Exact: The essential Rejection Method and the Acceptance Complement Method
[.html] [.pdf] [.ps] [.tex]
Links: [Ke's Javascript with histogram] [See the source and use his histogram()]
• Lecture V:
Examples of Applications of MCMC: Statistical Inference and Combinatorial Optimization. Reconstruction of a binary Image. Nonparametric Denstity Estimation.
[.html] [.pdf] [.ps] [.tex]
• Lecture VI:
MCMC Application: Neural Networks as a way to specify nonparametric regression and classification models.
[.html] [.pdf] [.ps] [.tex]
Links: [10 Lectures] by Kevin Gurney [gurney10.tar.gz] [Brian Ripley's 8 year old but still cool paper]
• Lecture VII:
The Hybrid Monte Carlo Method: Hamiltonian Dynamics, Liouville's Theorem, Leap-frog Discretization. The Non-Reversible Directed Metropolis.
[.html] [.pdf] [.ps] [.tex]
• Lecture VIII:
Using the exponential and mixture connections in the space of distributions for sampling. Appications: Thermodynamic integration, The half Monty-Carlos Method for sampling from one distribution by generating from another.
[.html] [.pdf] [.ps] [.tex]
• In the Oven... IX,...,to be continued...?:
Overview of the theory of Markov Chains: Basic definitions, Invariant Distributions, Ergodicity, Reversibility, Continuous Time Chains, Coupling, examples. Convergence Theorems, examples. Propp and Wilson Algorithm and Perfectly Random Sampling. The full Monty-Carlos.
EVALUATION
Based on attendance and on a computer project assigned individually during the first week of class and due before the end of the course.

JAVASCRIPT and HTML resources:
• Netscape HTML Tag Reference
• Netscape JavaScript Referenc
• Netscape JavaScript Guide
• HTML Goodies
• JAVA Goodies

File translated from TEX by TTH, version 1.95.
On 7 Jun 1999, 16:53.