Collaborative Research: Advanced Sequential Monte Carlo Methods and Applications

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Proposal IDs: DMS-0244638, DMS-0244583 and DMS-0244541PIs: Jun Liu, Xiaodong Wang, and Rong ChenTitle: FRG Collaborative Research: Advanced Sequential Monte Carlo MethodsAbstractSequential Monte Carlo (SMC) can be loosely defined as a family of techniques that use Monte Carlo simulations to solve on-line estimation and prediction problems in stochastic dynamic systems. By recursively generating random samples of the state variables, SMC adapts flexibly to the dynamics of underlying stochastic systems. In this FRG project, the investigators and their colleagues will develop a few advanced SMC methods, including novel operations in SMC (pilot exploration, flexible resampling, tempered SMC, etc.) and the nonparametric SMC framework. To demonstrate their wide applicabilities in solving scientific problems, they will apply the developed methodologies to a wide spectrum of problems found in computational biology (e.g., the discovery of cis-regulatory binding motif modules, progressive multiple sequence alignment, the inference for gene relationships, and chain polymer analyses) and wireless information networks (e.g., the design of adaptive nonparametric receivers in various wireless channels, mobility tracking in wireless networks, handoff the design of adaptive nonparametric receivers in various wireless channels, mobility tracking in wireless networks, handoff management and admission control in cellular networks). The proposed research will significantly enrich and advance the statistical modeling methodology and statistical computation theory and is expected to culminate in the formulation of novel modeling, analysis, and computation techniques in computational biology and wireless information networks.Stochastic modeling is essential in many application fields ranging from computer vision and engineering to molecular biology and statistical physics. But statistical analyses of these models often pose significant challenges to researchers. The sequential Monte Carlo (SMC) methodology recently emerged in the fields of statistics and engineering has shown great promise in solving a large class of highly complex inference and optimization problems regarding stochastic models, opening up new frontiers for cross-fertilization between statistical science and many application areas. The investigators have been working closely in the past on both theoretical developments of SMC and applications of SMC in computational biology and telecommunications, and have made significant impacts. In the meantime, many aspects of SMC theory are yet to be explored; and new challenges arising from applications in these two areas demand novel SMC strategies to be developed. For example, computational biology and wireless communications are two fronts of vital importance in modern science and engineering. With the explosive growth of research and development in these two areas, efficient and accurate statistical methods that can cope with nonlinear, non-Gaussian, and nonstationary features are in urgent need. It is thus important to continue the interdisciplinary research that has been carried out by the investigators to further advance the SMC theory and to bring this powerful statistical paradigm into the most exciting areas of today's scientific and engineering research and development. In this project, the investigators and their colleagues will continue to develop novel SMC methods and to investigate their theoretical properties. They will also apply the developed methods to a wide spectrum of problems found in computational biology and wireless information networks. The proposed research is expected to culminate in the formulation of novel modeling, analysis, and computation techniques in computational biology and wireless information networks.