Sequential Monte Carlo Methods for Computationally Intensive Problems

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

Sequential Monte Carlo methods provide a versatile and powerful tool for solving complex statistical inference problems. The objective of this proposal is to develop sequential Monte Carlo techniques in three important areas: conditional inference on multiway tables, likelihood inference in population genetics, and adaptive control of nonlinear stochastic systems. A common theme in these applications is computational complexity. The investigator develops efficient proposal distributions and resampling techniques to improve current methods in these three applications. New theories arising from these applications shed light on several fundamental issues related to the implementation of sequential Monte Carlo methods, in particular, the decomposition of a high dimensional problem into small components so that each component is easy to handle and the sequential nature of the problem can be utilized, and the choice of the proposal distribution so that it is easy to sample and close enough to the true underlying distribution. The investigator develops innovative sequential Monte Carlo techniques in three important areas. The first area is conditional inference on multiway contingency tables. Such tables arise very often from social and medical sciences, including large survey data and grouped case-control data with several risk factors. The second area is likelihood-based inference in population genetics, which is motivated by the interest in inferring key biological characteristics of the major pathogenic serotypes of Cryptococcus neoformans, an agent of serious respiratory disease in humans. The third area is on-line identification and adaptive control of nonlinear stochastic systems. The investigator improves the current methods used in these three applications and develops a systematic theory that provides insight into general strategies for applying sequential Monte Carlo methods. New theories arising from these applications are of interest across a broad range of areas in statistics, science and beyond. The proposed research has significant impact on education through involvement of Ph.D. students directly in the proposed research and incorporation of results into undergraduate and graduate courses.