STA 293 Syllabus

STA 293 MCMC and Spatial Modeling

Instructor: Dave Higdon, 216 Old Chem, higdon@stat.duke.edu

Meeting Times: Tues and Thurs, 3:50 - 5:05, 025 Old Chem

KDI Seminar Times: Wed, 4:00 - 5:00, 127 Physics

MCMC Texts that may be of use:

Bayesian Data Analysis by Gelman, Carlin, Stern and Rubin 1996, Chapman & Hall.
Markov Chain Monte Carlo in Practice by Gilks, Richardson, and Spiegelhalter 1996, Chapman & Hall.
Monte Carlo Statistical Methods by Robert and Casella 1999, Springer-Verlag.

Probability and Markov chain Texts that may be of use:

Probability and Random Processes by Grimmett and Stirzaker 1992, Oxford.
Probability by Shiryayev 1984, Springer-Verlag.
Probability: Theory and Examples by Durrett 1991, Wadsworth.
An Introduction to Stochastic Modeling, 3rd Edition by Taylor and Karlin 19??.

mc1.ps Class notes on Markov chains

Course Topics

	basic Markov chain theory for MCMC
	MCMC
	Bayesian inference via MCMC
	Spatial applications
	Inversion problems
	Non-spatial applications

Course Work

	computing as well as some paper based homework assignments
	course project

Code

C code for the ising model MetropIs.zip

Homework

Create some realizations from the ising model using the above code. Try out different values of beta. For beta near zero, pixel values are essentially independent; for large beta (1 is large), nearly all the pixels have the same value. Can you determine the critical value for beta for this example where realizations are neither pixelwise independent nor predominantly a single value?