Statistical multiple integration via Monte Carlo importance sampling

Man-Suk Oh, Purdue University

Abstract

This thesis is concerned with Monte Carlo importance sampling as used for statistical multiple integration. Several issues are considered. First, the effect of dimension on the accuracy of importance sampling is studied. For this, the behavior of variances of importance sampling estimates, as a function of dimension p, is investigated. Second, adaptive importance sampling is developed as a mechanical, yet flexible, way of dealing with the selection of the parameters of the importance function. Third, importance sampling is compared with the accept-reject scheme of Monte Carlo integration. The asymptotic variances and costs of both schemes are considered and a criterion where one scheme is better than the other is given. Finally, we consider using a mixture of density functions as an importance function when the integrand is multimodal.

Degree

Ph.D.

Advisors

Berger, Purdue University.

Subject Area

Statistics

COinS