Details of Grant 

EPSRC Reference:	GR/T19698/01
Title:	Perfect & direct simulation for missing data problems
Principal Investigator:	Roberts, Professor G O
Other Investigators:	Fearnhead, Professor P
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics and Statistics
Organisation:	Lancaster University
Scheme:	Standard Research (Pre-FEC)
Starts:	01 October 2004	Ends:	31 March 2008	Value (£):	242,805
EPSRC Research Topic Classifications:	Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:	Financial Services
Related Grants:
Panel History:
Summary on Grant Application Form
The use of MCMC to perform Bayesian inference is now commonplace. However, practical problems with implementing MCMC still exist, including diagnosing converge of the Markov chain, and designing Markov chains which mix well for complex models. We will address these two problems for an important class of models, missing data problems, using methods for exact simulation. We will focus on two approaches to exact simulation, the first based on the perfect simulation methodology of Propp and Wilson, and the second based on recursive methods for direct simulation. Where applicable exact simulation avoids any problem with diagnosing convergence of a Markov chain, as it allows for independent draws from the Markov chain's stationary distribution. For more complicated missing data problems, we will use exact simulation within a larger MCMC algorithm in order to efficiently update the missing data conditional on the parameter values. Unfortunately, current methods for exact simulation can only be applied to a limited range of problems. We will extend these methods, focussing on applications to mixture models, hidden Markov models, and stochastic volatility models. We will compare different approaches to exact simulation; explore approximate versions of direct simulation and their relationship to particle filters; and produce practical guidelines for implementing exact simulation within larger MCMC algorithms.
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Organisation Website:	http://www.lancs.ac.uk