Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models

Martin, Gael M, McCabe, Brendan PM ORCID: 0000-0002-9731-1766, Frazier, David T, Maneesoonthorn, Worapree and Robert, Christian P (2019) Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models. Journal of Computational and Graphical Statistics, 28 (3). pp. 508-522.

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Official URL: http://dx.doi.org/10.1080/10618600.2018.1552154

Abstract

A new approach to inference in state space models is proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation of an intractable likelihood by matching summary statistics computed from observed data with statistics computed from data simulated from the true process, based on parameter draws from the prior. Draws that produce a 'match' between observed and simulated summaries are retained, and used to estimate the inaccessible posterior; exact inference being feasible only if the statistics are sufficient. With no reduction to sufficiency being possible in the state space setting, we pursue summaries via the maximization of an auxiliary likelihood function. We derive conditions under which this auxiliary likelihood-based approach achieves Bayesian consistency and show that, in the limit, results yielded by the auxiliary maximum likelihood estimator are replicated by the auxiliary score. In multivariate parameter settings a separate treatment of each parameter dimension, based on integrated likelihood techniques, is advocated as a way of avoiding the curse of dimensionality associated with ABC methods. Three stochastic volatility models for which exact inference is either challenging or infeasible, are used for illustration.

Item Type:	Article
Additional Information:	This paper is a revision of arXiv:1604.0794. It also supersedes the earlier arXiv paper "Approximate Bayesian Computation in State Space Models" (arXiv:1409.8363)
Uncontrolled Keywords:	stat.CO, stat.CO, math.ST, stat.ME, stat.TH
Depositing User:	Symplectic Admin
Date Deposited:	16 Aug 2019 14:48
Last Modified:	19 Jan 2023 00:30
DOI:	10.1080/10618600.2018.1552154
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3051724