Inference for Diffusions and Related Processes

Lead Research Organisation: Lancaster University
Department Name: Mathematics and 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
 
Description Monte Carlo methods are commonplace in statistics. Standard Monte Carlo methods are based around discrete-time stochastic processes.
We have discovered a new class of Monte Carlo algorithms which work in continuous-time. The motivation for this was to allow inference for continuous-time stochastic models, such as diffusion processes. However it has the potential to be used much more widely.
Exploitation Route This continuous-time Monte Carlo algorithm has the potential to perform Bayesian analysis in a way that scales better to Big Data. This idea is currently being developed as part of the EPSRC funded grant on intractable likelihood. This shows great promise, and has potential impact across a wide-range of areas (where there is a need to perform Bayesian inference for large data). There is an technical report available at https://arxiv.org/abs/1609.03436; and a more informal overview of this area is available at https://arxiv.org/abs/1611.07873. The latter paper has appeared in Statistical Science.
Sectors Digital/Communication/Information Technologies (including Software)

 
Description EPSRC
Amount £2,400,000 (GBP)
Funding ID EP/K014463/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 01/2013 
End 12/2017