Sequential Importance Sampling with Resampling and Its Applications

提案ID：0203762PI：陈雨果标题：序贯重要性抽样与重抽样及其应用摘要：序贯重要性抽样的蒙特卡罗方法为解决复杂的统计推断问题提供了一种通用而有力的工具。关于该方法的一些基本问题仍有待解决，以使其更广泛地适用：应如何选择建议分布，以便在计算复杂性和统计效率之间取得适当平衡？重采样的作用是什么？重采样时间表的最佳选择是什么？这项建议的一个目标是通过对SIS在三个重要应用中的详细研究来解决这些问题。第一个领域是时间序列和随机动态系统。研究将为SIS开发重采样调度和建议分布，以解决连续状态隐马尔可夫模型中一些长期存在的滤波和平滑问题。变点问题可以被视为隐马尔可夫模型的特例，将作为新方法的试验场。第二个领域是分子群体遗传学中的统计推断。这一领域的研究将通过开发一种新的重新采样方法，并将这种重新采样策略与适当选择的建议分布相结合，来加强目前可用的SIS方法。最后的研究领域是关于偶然表和零一表的条件推理。序贯重要性抽样的蒙特卡罗方法已成功地应用于许多科学问题，包括模拟分子、对工程和经济学中出现的时间序列进行过滤和平滑以及进行贝叶斯统计推断。然而，需要解决一些基本问题，以使该方法更广泛地适用和有效。例如，在实现该方法时，应该如何在计算复杂性和统计效率之间取得适当的平衡，以及对该方法的各种增强的作用是什么。这项研究将通过开发三个重要应用领域的更有效的序贯重要性抽样技术来解决这些问题。第一个领域是连续状态隐马尔可夫模型的滤波和平滑问题，它在通信信号处理中有重要的应用。第二个领域是关于系谱树的统计推断。生物技术的最新进展为种群内DNA的遗传变异提供了丰富的数据。这些数据经常提出具有计算挑战性的统计推断问题，可以揭示种群的进化过程，并为定位导致遗传病的基因提供重要信息。第三个应用领域是关于偶然性和零一表的条件推理，其动机是心理学对测试Rasch模型的兴趣，以及生态学对测试关于进化和物种间竞争之间关系的理论的兴趣。本研究将改进这三种应用中使用的序贯重要性抽样方法，并努力发展一种系统的理论，为应用序贯重要性抽样的一般策略提供洞察

Proposal ID: 0203762PI: Yuguo ChenTitle: Sequential importance sampling with resampling and its applicationsAbstract:The Monte Carlo method of sequential importance sampling (SIS) provides a versatile and powerful tool for solving complex statistical inference problems. A number of basic issues concerning the method remain to be resolved for it to be more widely applicable: How should the proposal distribution be chosen to strike a proper balance between computational complexity and statistical efficiency? What is the role of resampling and what is a good choice for the resampling schedule? An objective of this proposal is to address these questions through the detailed study of SIS in three important applications. The first area is time series and stochastic dynamic systems. Research will develop resampling schedules and proposal distributions for SIS to solve some long-standing filtering and smoothing problems in continuous-state hidden Markov models.Change-point problems, which can be seen as a special case of hidden Markov models, will serve as a test ground for the new methodology. The second area is statistical inference in molecular population genetics. Research in this area will enhance currently available SIS methodology by developing a new resampling approach, and by combining such resampling strategy with suitably chosen proposal distributions. The final area of research is conditional inference on contingency and zero-one tables. New theories arising from these applications will be of interest across a broad range of areas.The Monte Carlo method of sequential importance sampling has been fruitfully applied to a wide range of scientific problems including simulating molecules, filtering and smoothing time series arising in engineering and economics, and making Bayesian statistical inferences. However, a number of basic issues need to be resolved to make the method more widely applicable and effective. For example, how should a proper balance be struck between computational complexity and statistical efficiency in implementing the method and what is the role of various enhancements to the method. This research will address these issues through the development of more efficient sequential importance sampling techniques for three important areas of application. The first area is filtering and smoothing problems in continuous-state hidden Markov models, which have important applications in communications signal processing. The second area is statistical inference on genealogical trees. Recent advances in biotechnology have provided an abundance of data on the genetic variation of DNA within a population. This data, which often poses computationally challenging statistical inference problems, can shed light on the evolutionary process of a population and yield important information for locating genes that are responsible for genetic diseases. The third area of application is conditional inference on contingency and zero-one tables, which is motivated by the interest in psychology in testing the Rasch model and in ecology in testing theories about the relationship between evolution and the competition among species. This research will improve the sequential importance sampling methods used in these three applications and strive to develop a systematic theory that provides insight into general strategies for applying sequential importance samplin