Dr. Mark Huber ( Department of Mathematics, Claremont McKenna College )

Title: Randomized adaptive cooling schedules for Monte Carlo Integration

Abstract: Cooling schedules have long been a staple of Markov chain methods: they form the basis of simulated annealing and tempering. These schedules are not only useful for generating random variates, they also yield a powerful technique for using the samples to estimate the integrals of interest. The advantage of these estimation methods is that the standard deviation of the estimate can be bounded a priori. A drawback to these methods is the need to come up with the cooling schedule in the first place.

In this talk I will discuss a new method for creating cooling schedules on the fly. The resulting randomized adaptive cooling schedules (RACS) have provably nice properties and can lead to estimation of high dimensional integrals that are both provably good and much faster than existing methods. I will illustrate these methods with several applications.