Bayesian indirect inference using a parametric auxiliary model

Drovandi, Christopher C., Pettitt, Anthony N., & Lee, Anthony (2015) Bayesian indirect inference using a parametric auxiliary model. Statistical Science, 30(1), pp. 72-95.

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Abstract

Indirect inference (II) is a methodology for estimating the parameters of an intractable (generative) model on the basis of an alternative parametric (auxiliary) model that is both analytically and computationally easier to deal with. Such an approach has been well explored in the classical literature but has received substantially less attention in the Bayesian paradigm. The purpose of this paper is to compare and contrast a collection of what we call parametric Bayesian indirect inference (pBII) methods. One class of pBII methods uses approximate Bayesian computation (referred to here as ABC II) where the summary statistic is formed on the basis of the auxiliary model, using ideas from II. Another approach proposed in the literature, referred to here as parametric Bayesian indirect likelihood (pBIL), we show to be a fundamentally different approach to ABC II. We devise new theoretical results for pBIL to give extra insights into its behaviour and also its differences with ABC II. Furthermore, we examine in more detail the assumptions required to use each pBII method. The results, insights and comparisons developed in this paper are illustrated on simple examples and two other substantive applications. The first of the substantive examples involves performing inference for complex quantile distributions based on simulated data while the second is for estimating the parameters of a trivariate stochastic process describing the evolution of macroparasites within a host based on real data. We create a novel framework called Bayesian indirect likelihood (BIL) which encompasses pBII as well as general ABC methods so that the connections between the methods can be established.

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3 citations in Web of Science®

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ID Code: 63767
Item Type: Journal Article
Refereed: Yes
Keywords: approximate Bayesian computation, likelihood-free methods, Markov jump processes, Quantile distributionssimulated likelihood, simulated likelihood
DOI: 10.1214/14-STS498
ISSN: 0883-4237
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 > QUT Faculties and Divisions > Science & Engineering Faculty
Funding:
Copyright Owner: Copyright 2014 Institute of Mathematical Statistics
Deposited On: 27 Oct 2013 22:31
Last Modified: 14 Aug 2015 22:41

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