A rare event approach to high-dimensional approximate Bayesian computation

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

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.

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

• Journal Article Type: Article
• Acceptance Date: Jul 4, 2017
• Online Publication Date: Jul 11, 2017
• Deposit Date: Jul 7, 2017
• Publicly Available Date: Jul 11, 2017
• Journal: Statistics and Computing
• Print ISSN: 0960-3174
• Electronic ISSN: 1573-1375
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 28
• Issue: 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
• Public URL: https://nottingham-repository.worktribe.com/output/872136
• Publisher URL: https://link.springer.com/article/10.1007/s11222-017-9764-4