Details of Grant 

EPSRC Reference:	GR/S61584/01
Title:	Bayesian inference for discretely observed continuous-time processes
Principal Investigator:	Godsill, Professor S
Other Investigators:	Roberts, Professor G O
Researcher Co-Investigators:	Professor P Dellaportas Professor N Friel Dr M Pitt Professor G O Roberts Professor N Shephard
Project Partners:	Nuffield College
Department:	Engineering
Organisation:	University of Cambridge
Scheme:	Standard Research (Pre-FEC)
Starts:	01 January 2004	Ends:	31 December 2006	Value (£):	81,681
EPSRC Research Topic Classifications:	Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:	Communications Financial Services
Related Grants:	GR/S61577/01
Panel History:
Summary on Grant Application Form
Although it is often natural to model observed stochastic phenomena in continuous time, observed data is always discrete. Moreover, unlike the continuous-time likelihood, the likelihood of the discrete skeleton chain is very often unavailable. Where data is observed on a sufficiently fine grid of times, likelihood-based inference is straightforward since accurate approximations to the continuous-time likelihood are available. When data is not sufficiently fine, a Bayesian approach using MCMC requires the imputation of additional data. However, for many stochastic process models such as diffusions, this is not a routine application of data-augmentation since the dependence between missing data and volatility is arbitrary large leading to extremely poor convergence of the obvious algorithm. This project will develop methodology for effective data-augmentation for these models. Generic model types such as diffusion processes with parameterised families of drift and diffusion coefficients will be studied. However other more specific model types where data-augmentation encounters particular problems, will also be analysed, including CTAR models, jump-diffusion models, and stochastic volatility models. Substantial application areas in the analysis of audio signals and financial time series will be considered.
Key Findings
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Organisation Website:	http://www.cam.ac.uk