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Inference for Diffusions and Related Processes

扩散推理及相关过程

基本信息

批准号：
EP/G026521/1
负责人：
Gareth Roberts
金额：
$ 39.75万
依托单位：
University of Warwick
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2009
资助国家：
英国
起止时间：
2009 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FG026521%2F1
关键词：
Inference Diffusions Related Processes

项目摘要

Traditional methods for diffusion simulation and related Monte Carlo methods have relied on time-discretisation techniques. This approach has two significant disadvantages: it is usually approximate, and time increments typically need to be small to ensure adequacy of the approximation, and thus methods can be computationally expensive.Recent new methodology for this problem has circumvented the need to disretise time by the use of a powerful and flexible new simulation idea known as Retrospective Sampling. This methodology produces exact simulations (to the accuracy constraints of any computer used for the experiment) and has remarkable efficiency properties, so that there appears to be no cost for exactness in this case. However the Exact Algorithm (EA) framework can be applied only for certain classes of diffusion processes (although this class essentially includes all one-dimensional non-explosive diffusions)This project aims to extend the framework above to a very rich and diverse class of stochastic processes, such as jump diffusions, hypo-elliptic diffusions and solutions of stochastic partial differential equations). The approach is to work both with pure simulation methodology and also with related (and more flexible) importance sampling techniques.There are many potential applications of these methods in scientific problems. We will focus on two important areas. The use of diffusion-related models in Systems Biology is expanding rapidly, and we will apply our methodology here. Secondly, we will consider the problem of rare event simulation in molecular dynamics simulation.

传统的扩散模拟方法和相关的蒙特卡罗方法依赖于时间离散技术。这种方法有两个显著的缺点：它通常是近似的，并且通常需要较小的时间增量来确保近似的充分性，因此方法在计算上可能是昂贵的。最近针对这个问题的新方法通过使用一种被称为回溯抽样的强大而灵活的新的模拟思想来规避对时间的需求。这种方法产生了精确的模拟(对用于实验的任何计算机的精度约束)，并且具有显著的效率特性，因此在这种情况下似乎不需要花费精确度。然而，精确算法(EA)框架只能应用于某些类型的扩散过程(尽管这类过程本质上包括所有一维非爆炸性扩散)。本项目旨在将上述框架扩展到非常丰富和多样化的一类随机过程，例如跳跃扩散、次椭圆扩散和随机偏微分方程解)。这种方法既使用纯模拟方法，也使用相关的(更灵活的)重要性抽样技术。这些方法在科学问题中有许多潜在的应用。我们将重点抓好两个重要领域。扩散相关模型在系统生物学中的使用正在迅速扩大，我们将在这里应用我们的方法。其次，我们将考虑分子动力学模拟中的稀有事件模拟问题。