Exact and approximate Bayesian inference for low count time series models with intractable likelihoods

Drovandi, Christopher C., Pettitt, Anthony N., & McCutchan, Roy A. (2016) Exact and approximate Bayesian inference for low count time series models with intractable likelihoods. Bayesian Analysis, 11(2), pp. 325-352.

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In this paper we present a new simulation methodology in order to obtain exact or approximate Bayesian inference for models for low-valued count time series data that have computationally demanding likelihood functions. The algorithm fits within the framework of particle Markov chain Monte Carlo (PMCMC) methods. The particle filter requires only model simulations and, in this regard, our approach has connections with approximate Bayesian computation (ABC). However, an advantage of using the PMCMC approach in this setting is that simulated data can be matched with data observed one-at-a-time, rather than attempting to match on the full dataset simultaneously or on a low-dimensional non-sufficient summary statistic, which is common practice in ABC. For low-valued count time series data we find that it is often computationally feasible to match simulated data with observed data exactly. Our particle filter maintains $N$ particles by repeating the simulation until $N+1$ exact matches are obtained. Our algorithm creates an unbiased estimate of the likelihood, resulting in exact posterior inferences when included in an MCMC algorithm. In cases where exact matching is computationally prohibitive, a tolerance is introduced as per ABC. A novel aspect of our approach is that we introduce auxiliary variables into our particle filter so that partially observed and/or non-Markovian models can be accommodated. We demonstrate that Bayesian model choice problems can be easily handled in this framework.

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ID Code: 60032
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: Approximate Bayesian computation, INARMA model, Markov process, particle filter, particle Markov chain Monte Carlo, renewal process
DOI: 10.1214/15-BA950
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 > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2015 International Society for Bayesian Analysis
Deposited On: 22 May 2013 23:31
Last Modified: 13 Mar 2016 14:21

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