Title:  Monte Carlo Methods - Sampling Smartly to Get the Accuracy Needed

Speaker: Fred J. Hickernell, Illinois Institute of Technology

Abstract:

Monte Carlo methods are used to compute the means of random variables whose distributions are so complex that direct computation by hand is infeasible.  Often the mean of the random variable can be interpreted as a multivariate integral, and so Monte Carlo methods are prime candidates for numerical integration.  This talk highlights three of my recent research interests in Monte Carlo methods.  One interest is in ensuring that the Monte Carlo method achieves the specified accuracy, i.e., constructing a guaranteed fixed width confidence interval for the mean.  A second interest is in low discrepancy or quasi-random sampling, a form of highly stratified sampling that can sometimes dramatically improve the convergence rate of the Monte Carlo method.  The third interest is in computing expectations that are effectively infinite-dimensional integrals, which must be approximated in a clever way by finite-dimensional integrals.  This talk will explain the ideas behind recent developments in these areas, highlight key theoretical results and open questions, and present some practical examples.