Details of Grant 

EPSRC Reference:	EP/G026521/1
Title:	Inference for Diffusions and Related Processes
Principal Investigator:	Roberts, Professor G O
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Statistics
Organisation:	University of Warwick
Scheme:	Standard Research
Starts:	01 November 2009	Ends:	31 October 2012	Value (£):	311,940
EPSRC Research Topic Classifications:	Mathematical Analysis Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:	EP/G028745/1
Panel History:	Panel Date Panel Name Outcome 03 Dec 2008 Mathematics Prioritisation Panel Announced
Summary on Grant Application Form
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.
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Organisation Website:	http://www.warwick.ac.uk