Sequential Monte Carlo Methods for Computationally Intensive Problems

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Sequential Monte Carlo methods provide a versatile and powerful tool forsolving complex statistical inference problems. The objective of thisproposal is to develop sequential Monte Carlo techniques in threeimportant areas: conditional inference on multiway tables, likelihoodinference in population genetics, and adaptive control of nonlinearstochastic systems. A common theme in these applications is computationalcomplexity. The investigator develops efficient proposal distributionsand resampling techniques to improve current methods in these threeapplications. New theories arising from these applications shed light onseveral fundamental issues related to the implementation of sequentialMonte Carlo methods, in particular, the decomposition of a highdimensional problem into small components so that each component is easyto handle and the sequential nature of the problem can be utilized, andthe choice of the proposal distribution so that it is easy to sample andclose enough to the true underlying distribution.The investigator develops innovative sequential Monte Carlo techniques inthree important areas. The first area is conditional inference onmultiway contingency tables. Such tables arise very often from social andmedical sciences, including large survey data and grouped case-controldata with several risk factors. The second area is likelihood-basedinference in population genetics, which is motivated by the interest ininferring key biological characteristics of the major pathogenic serotypesof Cryptococcus neoformans, an agent of serious respiratory disease inhumans. The third area is on-line identification and adaptive control ofnonlinear stochastic systems. The investigator improves the current methodsused in these three applications and develops a systematic theory thatprovides insight into general strategies for applying sequential MonteCarlo methods. New theories arising from these applications are ofinterest across a broad range of areas in statistics, science and beyond. The proposed research has significant impact on education throughinvolvement of Ph.D. students directly in the proposed research andincorporation of results into undergraduate and graduate courses.