Emulating a Computationally Expensive Likelihood Function: A Sequential Design Approach

• Activity Number: 511
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Antony Overstall*+ and David Woods
• Companies: Southampton Statistical Sciences Research Institute and Southampton Statistical Sciences Research Institute
• Keywords: computationally expensive likelihood ; computer experiments ; sequential design ; emulator

Abstract

The likelihood function plays a crucial role in statistics; both in the classical and Bayesian paradigms. In some cases, the likelihood function can be computationally expensive, making statistical inference time consuming or even impossible.

Our strategy for this problem is to construct a computationally cheap approximation to the likelihood function and use this emulator as a surrogate for the true likelihood in statistical inference. This is an application of computer experiment methodology - a current area of active research.

The emulator is constructed on the basis of a set of evaluations of the likelihood at different points in the parameter space. To select these points we use an iterative sequential design approach which uses the emulator at the current iteration to choose where next to evaluate the likelihood.