Particle filters and extensions

粒子过滤器和扩展

• 批准号: 2585619
• 金额: --
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2585619
• 关键词: Particle; filters; extensions

State-space models are a popular and flexible class of statistical models widely used in signal processing, physics, Bayesian inference, economics, and other fields to describe systems which change over time. The state of the system is modelled as a Markov process for which only some partial and noisy information is available via some observation process, and the goal is often to approximate the distribution of the current state given the observables available - the so-called "filtering distributions". Unfortunately, except in simple settings, this distribution is often not available in analytical form. Particle filters are a very popular class of algorithms used in these settings (and in others as well) that - under some conditions - are able to approximate sequentially the sequence of filtering distributions. The performance of this algorithm depends crucially on the particular filter used - and unfortunately those which are theoretically the most efficient are not always implementable in practice. This project, spanning from mathematical and computational statistics to applied probability, will investigate some methods to extend the applicability of particle filters - for instance by considering Markov Chain Monte Carlo based steps within the algorithm. The project, in line with the EPSRC strategic delivery plan for the 2022-25 period, aims to study these issues and methodology from both a theoretical and mathematical point of view by studying the convergence of such schemes, and a practical one.

州空间模型是一种流行且灵活的统计模型类别，广泛用于信号处理，物理，贝叶斯推断，经济学和其他领域，以描述随着时间的推移而变化的系统。该系统的状态被建模为马尔可夫过程，仅通过某些观察过程才能获得某些部分和嘈杂的信息，并且该目标通常是近似于可观察到的可观察到的当前状态的分布 - 所谓的“过滤分布”。不幸的是，除了简单的设置以外，此分布通常不以分析形式获得。粒子过滤器是在这些设置（以及其他情况下）中使用的一种非常流行的算法类别，在某些条件下 - 能够顺序近似过滤分布的序列。该算法的性能取决于所使用的特定过滤器 - 不幸的是，从理论上讲最有效的过滤器在实践中并不总是可以实现的。从数学和计算统计到应用的概率，该项目将研究一些方法以扩展粒子过滤器的适用性 - 例如，考虑Markov Chain Chain Monte Carlo基于算法中的步骤。该项目符合2022-25时期的EPSRC战略交付计划，旨在通过研究此类方案的融合以及实际情况来研究这些问题和方法。