|NEAL MADRAS, Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada|
|In search of faster simulations|
Markov Chain Monte Carlo has been one of the most active topics in applied probability in recent years. The main idea is that one can generate random samples from a given complicated distribution by first inventing a Markov chain whose equilibrium distribution is the distribution of interest, and then simulating the chain on a computer. Unfortunately, the chain may converge to equilibrium very slowly; for example, this can be the case when the equilibrium distribution is strongly multimodal. One class of remedies involves creating a sequence of overlapping distributions that interpolate between the distribution of interest and some ``easy'' distribution (whose associated Markov chain equilibriates rapidly). These methods have been successful in practice, but the mathematical theory behind them is not yet complete.