Sequential Importance Sampling with Resampling and Its Applications

摘要：时序重要性抽样（SIS）的蒙特卡罗方法为解决复杂的统计推理问题提供了一个通用的、强大的工具。为了使该方法得到更广泛的应用，关于该方法的一些基本问题仍有待解决：如何选择建议分布以在计算复杂性和统计效率之间取得适当的平衡？重采样的作用是什么，重采样计划的选择是什么？本提案的目标是通过对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。研究将制定SIS的重采样计划和建议分布，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。变化点问题可以看作是隐马尔可夫模型的一个特例，它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抽样方法，并通过将这种重新抽样策略与适当选择的提案分布相结合，加强目前可用的SIS方法。最后一个研究领域是关于偶然性和0 - 1表的条件推理。从这些应用中产生的新理论将在广泛的领域引起兴趣。时序重要抽样的蒙特卡罗方法已经成功地应用于广泛的科学问题，包括模拟分子，滤波和平滑工程和经济中的时间序列，以及贝叶斯统计推断。但是，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，如何在实现该方法的计算复杂性和统计效率之间取得适当的平衡，以及对该方法进行各种增强的作用是什么。本研究将通过为三个重要应用领域开发更有效的顺序重要性采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，这在通信信号处理中有重要的应用。第二个领域是对家谱树的统计推断。生物技术的最新进展提供了大量关于种群内DNA遗传变异的数据。这些数据通常会带来计算上具有挑战性的统计推断问题，但它们可以揭示种群的进化过程，并为定位导致遗传疾病的基因提供重要信息。第三个应用领域是对偶然性和0 - 1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与物种间竞争关系的理论的兴趣。本研究将改进这三个应用中使用的顺序重要性抽样方法，并努力发展一个系统的理论，为应用顺序重要性抽样的一般策略提供见解

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