Collabrative Research: Sequential Monte Carlo Methods and Their Applications

合作研究：序贯蒙特卡罗方法及其应用刘军，哈佛大学陈荣，大学。伊利诺伊州芝加哥大学王晓东德克萨斯农工大学摘要(技术)：最近在统计和工程领域出现的序贯蒙特卡罗(SMC)方法有望解决一大类非线性滤波和优化问题，为统计学和许多应用领域之间的交叉培养开辟了新的前沿。SMC的一个显著特征是它能够通过递归模拟所涉及的变量来适应底层随机系统的动态。虽然SMC的特殊形式可以追溯到20世纪50年代，但这种方法的普遍使用是最近才出现的，它的许多关键性质还没有被很好地理解。这个研究小组将集中于三个主要的理论问题，即设计有效的基于SMC的计算工具和三个重要的应用领域，即无线通信、计算生物学和商业数据分析。在理论部分，他们将研究生成更好的蒙特卡罗样本以跟踪系统动态的方法；研究对SMC有效性至关重要的重采样的作用；以及为更有效的SMC算法提出系统重构策略。在应用部分，他们计划设计新的无线多媒体通信信号处理和网络控制算法；开发更好的多序列比对模型和基于SMC的蛋白质结构优化方法；以及构建基于SMC的商业数据建模和分析工具。预计所提出的研究将最终形成新的SMC方法，并将SMC范式的前景带入许多新兴应用的实践领域。随机动态系统经常用于许多应用领域，如自动控制、工程和金融。对这些系统的统计分析是至关重要的。然而，除了少数特殊情况外，对这些系统的定量分析仍然是研究人员面临的主要挑战。最近在统计和工程领域出现的序列蒙特卡罗(SMC)技术在解决一类广泛的非线性滤波、预测和优化问题方面显示出巨大的前景，为我们提供了许多令人振奋的新研究机会。蒙特卡洛这个名字是由参与设计原子弹的科学家在20世纪40年代创造的，它指的是一种利用计算机模拟和研究复杂随机系统的技术。这项技术是以著名的赌博胜地命名的，因为它的程序包含了机会的元素。SMC的一个显著特征是它能够通过一次考虑一个变量来顺序地模拟系统。SMC的广泛应用是最近才出现的，它对许多科学和工程领域的入侵才刚刚开始。包括本课题组成员在内的研究人员已经证明，SMC可以成功地适用于解决化学、工程和统计问题。了解SMC的理论性质，将SMC的应用扩展到其他领域是本项目的主要重点。更具体地说，这个研究小组将专注于关于设计有效的基于SMC的计算工具的三个主要理论问题和三个重要的应用领域，包括无线通信、计算生物学和商业数据分析。这些应用不仅本身的优点很重要，而且作为正在开发的新理论的试验场和SMC新研究方向的刺激来源也是必不可少的。预计这项研究将最终形成新的SMC方法，并将SMC范例的前景带入许多新兴应用的实践领域。特别是，这项研究将在以下方面取得成果：无线多媒体通信信号处理和网络控制算法的新设计；分析生物序列和结构数据的更好算法的开发；以及基于SMC的商业数据分析和预测工具。

Collaborative Research: Sequential Monte Carlo Methods and Their ApplicationsJun Liu, Harvard University Rong Chen, Univ. Illinois at ChicagoXiaodong Wang, Texas A&M UniversityAbstract (Technical):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.