Collaborative Research: Sequential Monte Carlo Methods and Their Applications

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Sequential Monte Carlo (SMC) methodology recently emerged in statistics and engineering fields promises to solve a wide class of nonlinear filtering and optimization problems, opening up new frontiers for cross-fertilization between statistics and many areas of applications. A distinctive feature of SMC is its ability to adapt to the dynamics of the underlying stochastic systems via recursive simulation of the variables involved. Although special forms of SMC date back to 1950s, the general use of the method appeared only recently and its many key properties have yet been well understood. This research group will focus on three major theoretical issues regarding the design of effective SMC-based computational tools and three important application areas, namely, wireless communications, computational biology, and business data analysis. In the theory part, they will study approaches of generating better Monte Carlo samples for tracking system dynamics; investigate roles of resampling which is critical to the effectiveness of SMC; and propose system reconfiguration strategies for more efficient SMC algorithms. In the application part, they plan to design novel signal processing and network control algorithms for wireless multimedia communications; develop better multiple sequence alignment models and SMC-based optimization method for protein structures; and build SMC-based modeling and analysis tools for business data. It is anticipated that the proposed research will culminate in the formulation of novel SMC methodologies and will bring the promise of the SMC paradigm into the practical arena of many emerging applications.Stochastic dynamic systems are routinely used in many application fields such as automatic control, engineering, and finance. The statistical analyses of these systems are crucial. However, except for a few special cases, quantitative analyses of these systems still present major challenges to researchers. Sequential Monte Carlo (SMC) technique recently emerged in the field of statistics and engineering shows a great promise on solving a wide class of nonlinear filtering, prediction, and optimization problems, providing us with many exciting new research opportunities. The name "Monte Carlo" was coined in 1940s by scientists involved in designing atomic bombs and it refers to a technique in which computer is used to simulate and study a complex stochastic system. The technique was named after the famed gambling resort because its procedures incorporate the element of chance. A distinctive feature of SMC is its ability to sequentially simulate the system by considering one variable at a time. The general use of SMC appeared recently and its invasion into many fields of science and engineering has just begun. Researchers including people in this research group have demonstrated that SMC can be successfully adapted to solve chemistry, engineering, and statistical problems. Understanding its theoretical properties and extending the use of SMC to other fields are the main focuses of this project. More specifically, this research group will focuse on three major theoretical issues regarding the design of effective SMC-based computational tools and three important application areas including wireless communications, computational biology, and business data analysis. These applications are not only important by their own merits, but also essential as the test ground for the new theories being developed and as the sources of stimulation for new research directions for SMC. It is anticipated that this research will culminate in the formulation of novel SMC methodologies and will bring the promise of the SMC paradigm into the practical arena of many emerging applications. In particular, this research will bear fruits in the following areas: novel designs of signal processing and network control algorithms for wireless multimedia communications; developments of better algorithms analyzing biological sequence and structure data; and a SMC-based tool for business data analysis and prediction.