Statistical Problems in Hidden Markov Modeling for Biology and Chemistry

点击翻译按钮获取中文摘要

Proposal ID: DMS-0204674PI: Jun S. LiuTitle: Statistical problems in hidden Markov modeling for biology and chemistryAbstractWith the completion of genomes of many species and the advances of microarray technologies, biological researchers begin to possess a tremendous amount of data --- but these "raw products" are still far from usable. One of the most challenging problems of this century is to decipher this huge amount of biological information, turning the data into knowledge. Simultaneously, there also has been a revolution in chemistry research: scientists can now use advanced technology to make observations on single-molecule dynamics, which promises to rewrite some fundamental laws in physics and chemistry derived from traditional ensemble-averaged experiments. As the data concerning molecular movements are inherently noisy, the development of advanced statistical tools for handling such data is a pressing need. The past decade has witnessed the power of formal statistical modeling, especially the use of hidden Markov models, in revolutionizing the field of computational biology. It is the investigators' belief that using proper statistical models to describe the underlying chemical processes and to derive efficient inference methods can also greatly strengthen the data analysis in single-molecule studies. For the biological information analysis, the investigators describe a few problems related to the statistical models used for finding motifs, whose solutions can deepen the understanding of a few popular Bioinformatics algorithms for sequence analysis. The investigators show that these algorithms are based on special hidden Markov or semi-Markov models and can be generalized to accommodate more detailed biology knowledge. For single-molecule data analysis, the investigators outline an efficient likelihood-based approach for inferring quantities of special interests in single-molecule studies. The form of the observed data naturally calls for a data augmentation framework, which is a promising means for solving the computational difficulty. In single-molecule studies, besides the problem of model inference, model selection is also an important and difficult task, as it is often the case that there are competing models describing one chemical reaction, making it necessary to use the experimental data to choose the appropriate model. The investigators, using a data augmentation approach, propose a few generalized methods for choosing among different chemical models.