### Simulation III: Monte Carlo and Markov Chain Monte Carlo (Introduction to Statistical Computing)

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.

Update, 22 December: If you do read Geyer, it's also worth reading two posts
by Andrew Gelman
(A Centipede Many
Times Over
and A
Tale of Two Discussion Papers), and Gelman and Rubin's "Inference from
Iterative Simulation Using Multiple Sequences"
(Statistical
Science **7** (1992): 457--472). Thanks to Andy for
reminding me (politely!) about these pieces.

Introduction to Statistical Computing

Posted at October 21, 2013 13:58 | permanent link