### Simulation II: Markov Chains, Monte Carlo, and Markov Chain Monte Carlo (Introduction to Statistical Computing)

Lecture
18: Combing multiple dependent random variables in a simulation; ordering
the simulation to do the easy parts first. Markov chains as a particular
example of doing the easy parts first. The Markov property. How to write a
Markov chain simulator. Verifying that the simulator works by looking at
conditional distributions. Variations on Markov models: hidden
Markov models, interacting processes, continuous time, chains
with complete connections. Asymptotics of Markov chains via linear
algebra; the law of large numbers (ergodic theorem) for Markov chains: we can
approximate expectations as soon as we can simulate.

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. Bayesian inference via MCMC.

*Readings*: Handouts on Markov chains and Monte Carlo and on Markov chain Monte Carlo

Introduction to Statistical Computing

Posted at October 24, 2012 10:30 | permanent link