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Piecewise Approximate Bayesian Computation: fast inference for discretely observed Markov models using a factorised posterior distribution

White, S. R.; Kypraios, T.; Preston, S. P.

Authors

S. R. White

SIMON PRESTON simon.preston@nottingham.ac.uk
Professor of Statistics and Applied Mathematics



Abstract

© 2013, The Author(s). Many modern statistical applications involve inference for complicated stochastic models for which the likelihood function is difficult or even impossible to calculate, and hence conventional likelihood-based inferential techniques cannot be used. In such settings, Bayesian inference can be performed using Approximate Bayesian Computation (ABC). However, in spite of many recent developments to ABC methodology, in many applications the computational cost of ABC necessitates the choice of summary statistics and tolerances that can potentially severely bias the estimate of the posterior. We propose a new “piecewise” ABC approach suitable for discretely observed Markov models that involves writing the posterior density of the parameters as a product of factors, each a function of only a subset of the data, and then using ABC within each factor. The approach has the advantage of side-stepping the need to choose a summary statistic and it enables a stringent tolerance to be set, making the posterior “less approximate”. We investigate two methods for estimating the posterior density based on ABC samples for each of the factors: the first is to use a Gaussian approximation for each factor, and the second is to use a kernel density estimate. Both methods have their merits. The Gaussian approximation is simple, fast, and probably adequate for many applications. On the other hand, using instead a kernel density estimate has the benefit of consistently estimating the true piecewise ABC posterior as the number of ABC samples tends to infinity. We illustrate the piecewise ABC approach with four examples; in each case, the approach offers fast and accurate inference.

Citation

White, S. R., Kypraios, T., & Preston, S. P. (2015). Piecewise Approximate Bayesian Computation: fast inference for discretely observed Markov models using a factorised posterior distribution. Statistics and Computing, 25(2), 289-301. https://doi.org/10.1007/s11222-013-9432-2

Journal Article Type Article
Acceptance Date Oct 24, 2013
Online Publication Date Nov 29, 2013
Publication Date 2015-03
Deposit Date Oct 10, 2017
Publicly Available Date Oct 10, 2017
Journal Statistics and Computing
Print ISSN 0960-3174
Electronic ISSN 1573-1375
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 25
Issue 2
Pages 289-301
DOI https://doi.org/10.1007/s11222-013-9432-2
Keywords Approximate Bayesian Computation, Simulation, Stochastic Lotka–Volterra
Public URL https://nottingham-repository.worktribe.com/output/984874
Publisher URL https://link.springer.com/article/10.1007%2Fs11222-013-9432-2

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0





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