Three-Toed Sloth

Simulation II: Markov Chains (Introduction to Statistical Computing)

Lecture 15: 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.

Readings: Handouts on Markov chains and Monte Carlo

Introduction to Statistical Computing