A New MCMC Framework with Applications to Protein Bioinformatics

在过去的二十年里，统计学家和其他定量研究人员已经开始欣赏蒙特卡罗积分和优化方法的力量。 该建议的重点是发展一种新的马尔可夫链蒙特卡罗（MCMC）框架，这将大大提高我们的能力和灵活性，在设计有效的蒙特卡罗算法。更确切地说，研究者提出了一个统一的框架来推广标准的Metropolis-Hastings方法来设计马尔可夫链，并显示了它与一些现有的MCMC方法的深刻关系，如多重网格蒙特卡罗，配置偏置蒙特卡罗和定向偏置蒙特卡罗。研究者还将专注于增长最快的应用领域之一，蛋白质生物信息学（包括多序列比对，蛋白质功能注释，蛋白质-蛋白质相互作用和蛋白质结构建模等），这既是一个重要的应用，也是对现有MCMC方法的重大挑战的巨大来源。一方面，研究者试图应用新的MCMC框架来设计新的蛋白质结构和序列分析工具;另一方面，在这种努力中遇到的挑战性问题将激励和引导研究者开发新的MCMC策略。随着对具有复杂结构的非常大的数据集（例如基因组学数据、消费品数据、互联网数据等）的定量（统计）分析的需求不断增长，设计更有效的计算方法来分析这些数据并做出有用的预测的需求也很强烈。该提案有三个相互关联的主题：开发一种新的蒙特卡罗框架，其通常可以被理解为利用计算机生成的随机数来近似地解决优化或整合问题的新方式，开发用于生物序列和蛋白质结构分析的新的统计模型，并应用这些新的计算方法和统计模型来推断蛋白质功能的分子机制和预测蛋白质结构。这项研究不仅将大大推进蒙特卡罗方法和计算统计理论，适用于不同应用领域的广泛优化和模拟问题，而且还将使这些新方法和理论的力量影响到最重要的应用领域之一，计算生物学。它将特别推进蛋白质生物信息学中的建模、分析和计算技术。它将帮助教育工作者为本科生和研究生修订和生成关于计算生物学和蒙特卡罗方法的新课程。它还将为这些学生提供跨学科的研究机会，并将产生制药行业可能感兴趣的软件和方法。

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.