Rao-Blackwellization for Improved Monte Carlo for Stochastic Processes

• Activity Number: 45
• Type: Invited
• Date/Time: Sunday, August 3, 2014 : 4:00 PM to 5:50 PM
• Sponsor: IMS
• Author(s): Gareth Roberts*+
• Companies: University of Warwick
• Keywords: Rao-Blackwellisation ; Simulation of Diffusions ; Monte Carlo ; Discretisation error free methods

Abstract

David Blackwell's celebrated theorem with Rao compares the variance of an estimator $X$ with that of its conditional expectation given a further variable $S$, $Y=E(X|S)$. Blackwell's motivation was to demonstrate that the best estimators should be functions of the simplest sufficient statistic we can find. However The Rao-Blackwell theorem has also found extensive use in computational statistics by providing a powerful and general recipe for improving on Monte-Carlo estimators by so-called Rao-Blackwellisation. This talk will discuss widely adopted simple Rao-Blackwellisations for Markov chain Monte Carlo and Sequential Monte Carlo samplers, as well as more complex random Rao-Blackwellisations for estimation of expectations of functionals of stochastic processes (particularly univariate and multivariate diffusion processes).

The talk will draw on jount research with Alex Beskos, Paul Fearnhead, Krys, Latuszynski, Omiros Papaspiliopoulos, and Giorgos Sermaidis.