Inference for Diffusions and Related Processes

Lead Research Organisation: University of Warwick
Department Name: Statistics

Abstract

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.

Publications

10 25 50

publication icon
Latuszynski K (2011) CLTs and Asymptotic Variance of Time-Sampled Markov Chains in Methodology and Computing in Applied Probability

publication icon
Latuszynski K (2011) Simulating events of unknown probabilities via reverse time martingales in Random Structures & Algorithms

 
Description 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 discretise 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 extended the above framework to a very rich and diverse class of stochastic processes. The main output is a novel Monte Carlo approach for calculating properties of any continuous-time stochastic process in a way that avoids any time-discretisation error. Other work includes approaches to inference for diffusions that uses a computationally-efficient approximation: which has been successfully applied to models used within systems biology and epidemics.
Exploitation Route Our work is foundational work on how to perform Bayesian inference for stochastic processes. Since the award, its ideas have been taken up by more applied researchers in application areas, including epidemiology, finance and others. The methodological work of this grant continues in other projects such as the ilike EPSRC programme grant.
Sectors Aerospace, Defence and Marine,Chemicals,Energy,Financial Services, and Management Consultancy

 
Description Intractablelikelihood: New challenges from modern applications (i-like)
Amount £2,369,503 (GBP)
Funding ID EP/K014463/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Academic/University
Country United Kingdom
Start 01/2013 
End 12/2017