Bounded relative variance estimators for Monte Carlo

Mark Huber. Dept of Mathematics & Statistics, Claremont McKenna College

The standard Monte Carlo approach is to draw samples, then use the samples to estimate the mean and variance of the output. For problems where the mean might be exponentially large in the input, it is important to have a small relative variance. In this talk, I discuss ways to avoid having to estimate the relative variance. I will present two recently developed methods, the Paired Product Estimator (PPE) and the Gamma Bernoulli Approximation Scheme (GBAS) where the relative variance of the estimate is already bounded. The PPE was developed to handle the problem of estimating the partition function of a Gibbs distribution, which comes up in work that I did with Robert on the stationary Matern type III processes. The GBAS estimate for the mean of a Bernoulli has the unique property that the relative error in the estimate does not depend at all on the parameter being estimated!