A New MCMC Framework with Applications to Protein Bioinformatics

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In the past two decades, statisticians and other quantitative researchers have begun to appreciate the power of Monte Carlo integration and optimization methods. This proposal focuses on the development of a novel Markov chain Monte Carlo (MCMC) framework, which promises to greatly enhance our capability of and flexibility in designing effective Monte Carlo algorithms. More precisely, the investigator proposes a unifiedframework to generalize the standard Metropolis-Hastings approach to design Markov chains and shows its deep relationship with a few existing MCMC methods, such as multigrid Monte Carlo, configurational-bias Monte Carlo, and orientational-bias Monte Carlo. The investigator will also focus on one of the fastest growing application areas, protein bioinformatics (encompassing multiple sequence alignments, protein function annotation, and protein-protein interactions, and protein structural modeling, etc.), which serves both as an important application and as a great source of significant challenges to existing MCMC methods. On one hand, the investigator seeks to apply the new MCMC framework to design novel protein structure and sequence analysis tools; on the other hand, the challenging problems encountered during such endeavors will motivate and steer the investigator to develop new MCMC strategies. With the ever growing need of quantitative (statistical) analysis of very large datasets with complex structures (such as genomics data, consumer goods data, internet data, etc.), the need for designing more efficient computational methods to analyze these data and to make useful predictions is also strong. This proposal has three inter-related themes: to develop a novel Monte Carlo framework, which can be generally understood as a new way of utilizing computer-generated random numbers to approximately solve an optimization or integration problem, to develop novel statistical models for biological sequence and proteinstructure analysis, and to apply these new computational methods and statistical models to infer molecular mechanisms of protein functions and to predict protein structures. The proposed research will not only significantly advance the Monte Carlo methodology and computational statistics theory, which are applicable to a wide range of optimization and simulation problems in different application areas, but will also bring the power of these new methods and theory to bear on one of the most important application areas, computational biology. It will particularly advance the modeling, analysis, and computational techniques in protein bioinformatics. It will help educators revise and generate new courses on computational biology and Monte Carlo methodologies for both undergraduate and graduate students. It will also provide interdisciplinary research opportunities for such students, and will result in software and methodologies that may be of interest to the pharmaceutical industry.