The Metropolis-Hastings Algorithm By Example Consider flipping a fair coin 100 times. The probability space has size 2^100, which is on the order of 10^69. Yet we can easily sample from this space: each event occurs with equal probability 0.5^100, and all we have to do is conduct 100 independent Bernoulli experiments with p=0.5. If the coin isn't fair, not all events occur with equal probability. Yet it's still easy to sample from this space: we conduct 100 independent Bernoulli experiments with 0 <= p <= 1. Now suppose the coin flips aren't independent -- they have some peer pressure. This system is called a one-dimensional Ising model and it's non-trivial to sample from this space. I will describe how the Metropolis-Hastings algorithm allows us to conduct experiments using such a model. John Kerl Graduate Probability Seminar February 14, 2008