Collaborative Research: Advanced Sequential Monte Carlo Methods and Applications

提案编号：DMS-0244638，DMS-0244583和DMS-0244541 PIS：刘军，王晓东，陈荣标题：FRG协作研究：高级序贯蒙特卡罗方法摘要序贯蒙特卡罗可以松散地定义为使用蒙特卡罗模拟解决随机动态系统中的在线估计和预测问题的一族技术。通过递归地产生状态变量的随机样本，SMC能够灵活地适应底层随机系统的动态。在这个FRG项目中，研究人员和他们的同事将开发一些先进的SMC方法，包括SMC中的新操作(试验勘探、灵活重采样、回火SMC等)。和非参数SMC框架。为了展示它们在解决科学问题中的广泛应用，他们将把开发的方法应用于计算生物学(例如，发现顺式结合基序模块、渐进多序列比对、基因关系推断和链聚合物分析)和无线信息网络(例如，各种无线信道中的自适应非参数接收器的设计、无线网络中的移动性跟踪、各种无线信道中的自适应非参数接收器的设计、无线网络中的移动性跟踪、切换管理和蜂窝网络中的接纳控制)中的广泛问题。这项研究将极大地丰富和发展统计建模方法和统计计算理论，并有望在计算生物学和无线信息网络中形成新的建模、分析和计算技术。随机建模在从计算机视觉和工程到分子生物学和统计物理的许多应用领域都是必不可少的。但对这些模型的统计分析往往会给研究人员带来重大挑战。最近在统计和工程领域出现的序贯蒙特卡罗(SMC)方法在解决一大类关于随机模型的高度复杂的推理和优化问题方面显示出巨大的潜力，为统计科学和许多应用领域的交叉开辟了新的前沿。过去，研究人员在SMC的理论发展以及SMC在计算生物学和电信领域的应用方面进行了密切的合作，并产生了重大影响。同时，SMC理论的许多方面仍有待探索；在这两个领域的应用带来的新挑战要求开发新的SMC策略。例如，计算生物学和无线通信是现代科学和工程中至关重要的两个前沿。随着这两个领域研究和开发的爆炸性增长，迫切需要能够处理非线性、非高斯和非平稳特征的高效、准确的统计方法。因此，重要的是继续由研究人员进行的跨学科研究，以进一步推进SMC理论，并将这一强大的统计范式带入当今科学和工程研究和开发的最令人兴奋的领域。在这个项目中，研究人员和他们的同事将继续开发新的SMC方法，并研究它们的理论性质。他们还将把开发的方法应用于计算生物学和无线信息网络中发现的一系列问题。这项拟议的研究有望在计算生物学和无线信息网络中形成新的建模、分析和计算技术。

Proposal IDs: DMS-0244638, DMS-0244583 and DMS-0244541PIs: Jun Liu, Xiaodong Wang, and Rong ChenTitle: FRG Collaborative Research: Advanced Sequential Monte Carlo MethodsAbstractSequential Monte Carlo (SMC) can be loosely defined as a family of techniques that use Monte Carlo simulations to solve on-line estimation and prediction problems in stochastic dynamic systems. By recursively generating random samples of the state variables, SMC adapts flexibly to the dynamics of underlying stochastic systems. In this FRG project, the investigators and their colleagues will develop a few advanced SMC methods, including novel operations in SMC (pilot exploration, flexible resampling, tempered SMC, etc.) and the nonparametric SMC framework. To demonstrate their wide applicabilities in solving scientific problems, they will apply the developed methodologies to a wide spectrum of problems found in computational biology (e.g., the discovery of cis-regulatory binding motif modules, progressive multiple sequence alignment, the inference for gene relationships, and chain polymer analyses) and wireless information networks (e.g., the design of adaptive nonparametric receivers in various wireless channels, mobility tracking in wireless networks, handoff the design of adaptive nonparametric receivers in various wireless channels, mobility tracking in wireless networks, handoff management and admission control in cellular networks). The proposed research will significantly enrich and advance the statistical modeling methodology and statistical computation theory and is expected to culminate in the formulation of novel modeling, analysis, and computation techniques in computational biology and wireless information networks.Stochastic modeling is essential in many application fields ranging from computer vision and engineering to molecular biology and statistical physics. But statistical analyses of these models often pose significant challenges to researchers. The sequential Monte Carlo (SMC) methodology recently emerged in the fields of statistics and engineering has shown great promise in solving a large class of highly complex inference and optimization problems regarding stochastic models, opening up new frontiers for cross-fertilization between statistical science and many application areas. The investigators have been working closely in the past on both theoretical developments of SMC and applications of SMC in computational biology and telecommunications, and have made significant impacts. In the meantime, many aspects of SMC theory are yet to be explored; and new challenges arising from applications in these two areas demand novel SMC strategies to be developed. For example, computational biology and wireless communications are two fronts of vital importance in modern science and engineering. With the explosive growth of research and development in these two areas, efficient and accurate statistical methods that can cope with nonlinear, non-Gaussian, and nonstationary features are in urgent need. It is thus important to continue the interdisciplinary research that has been carried out by the investigators to further advance the SMC theory and to bring this powerful statistical paradigm into the most exciting areas of today's scientific and engineering research and development. In this project, the investigators and their colleagues will continue to develop novel SMC methods and to investigate their theoretical properties. They will also apply the developed methods to a wide spectrum of problems found in computational biology and wireless information networks. The proposed research is expected to culminate in the formulation of novel modeling, analysis, and computation techniques in computational biology and wireless information networks.