Optimal Bayesian experimental design for models with intractable likelihoods using indirect inference applied to biological process models

Ryan, Caitriona M., Drovandi, Christopher C., & Pettitt, Anthony N. (2016) Optimal Bayesian experimental design for models with intractable likelihoods using indirect inference applied to biological process models. Bayesian Analysis, 11(3), pp. 857-883.

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Abstract

This paper addresses the problem of determining optimal designs for biological process models with intractable likelihoods, with the goal of parameter inference. The Bayesian approach is to choose a design that maximises the mean of a utility, and the utility is a function of the posterior distribution. Therefore, its estimation requires likelihood evaluations. However, many problems in experimental design involve models with intractable likelihoods, that is, likelihoods that are neither analytic nor can be computed in a reasonable amount of time. We propose a novel solution using indirect inference (II), a well established method in the literature, and the Markov chain Monte Carlo (MCMC) algorithm of Müller et al. (2004). Indirect inference employs an auxiliary model with a tractable likelihood in conjunction with the generative model, the assumed true model of interest, which has an intractable likelihood. Our approach is to estimate a map between the parameters of the generative and auxiliary models, using simulations from the generative model. An II posterior distribution is formed to expedite utility estimation. We also present a modification to the utility that allows the Müller algorithm to sample from a substantially sharpened utility surface, with little computational effort. Unlike competing methods, the II approach can handle complex design problems for models with intractable likelihoods on a continuous design space, with possible extension to many observations. The methodology is demonstrated using two stochastic models; a simple tractable death process used to validate the approach, and a motivating stochastic model for the population evolution of macroparasites.

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ID Code: 73409
Item Type: Journal Article
Refereed: Yes
Keywords: approximate Bayesian computation, Bayesian experimental design, indirect inference, Markov chain Monte Carlo
DOI: 10.1214/15-BA977
ISSN: 1931-6690
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400)
Divisions: Current > Research Centres > ARC Centre of Excellence for Mathematical & Statistical Frontiers (ACEMS)
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2015 International Society for Bayesian Analysis
Deposited On: 07 Jul 2014 22:34
Last Modified: 01 Mar 2017 23:24

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