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A rare event approach to high-dimensional approximate Bayesian computation

Prangle, Dennis; Everitt, Richard G.; Kypraios, Theodore

Authors

Dennis Prangle

Richard G. Everitt

Theodore Kypraios theodore.kypraios@nottingham.ac.uk



Abstract

Approximate Bayesian computation (ABC) methods permit approximate inference for intractable likelihoods when it is possible to simulate from the model. However they perform poorly for high dimensional data, and in practice must usually be used in conjunction with dimension reduction methods, resulting in a loss of accuracy which is hard to quantify or control. We propose a new ABC method for high dimensional data based on rare event methods which we refer to as RE-ABC. This uses a latent variable representation of the model. For a given parameter value, we estimate the probability of the rare event that the latent variables correspond to data roughly consistent with the observations. This is performed using sequential Monte Carlo and slice sampling to systematically search the space of latent variables. In contrast standard ABC can be viewed as using a more naïve Monte Carlo estimate. We use our rare event probability estimator as a likelihood estimate within the pseudo-marginal Metropolis-Hastings algorithm for parameter inference. We provide asymptotics showing that RE-ABC has a lower computational cost for high dimensional data than standard ABC methods. We also illustrate our approach empirically, on a Gaussian distribution and an application in infectious disease modelling.

Journal Article Type Article
Journal Statistics and Computing
Print ISSN 0960-3174
Electronic ISSN 1573-1375
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 28
Issue 4
APA6 Citation Prangle, D., Everitt, R. G., & Kypraios, T. (in press). A rare event approach to high-dimensional approximate Bayesian computation. Statistics and Computing, 28(4), https://doi.org/10.1007/s11222-017-9764-4
DOI https://doi.org/10.1007/s11222-017-9764-4
Keywords ABC, Markov chain Monte Carlo, Sequential Monte Carlo, Slice sampling, Infectious disease modelling
Publisher URL https://link.springer.com/article/10.1007/s11222-017-9764-4
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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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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