Simulation III: Monte Carlo and Markov Chain Monte Carlo (Introduction to Statistical Computing)
Three-Toed Sloth 2013-12-20
Summary:
Lecture 16: The Monte Carlo principle for numerical integrals: write your integral as an expectation, take a sample. Examples. Importance sampling: draw from a distribution other than the one you really are want, then weight the sample values. Markov chain Monte Carlo for sampling from a distribution we do not completely know: the Metropolis algorithm. Gibbs sampling. Bayesian inference via MCMC.
Readings: Handouts on Markov Chains and Monte Carlo, and on Markov Chain Monte Carlo
Optional readings: Charles Geyer, "Practical Markov Chain Monte Carlo", Statistical Science 7 (1992): 473--483; "One Long Run"; Burn-In is Unnecessary; On the Bogosity of MCMC Diagnostics