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June 2019 Efficient Acquisition Rules for Model-Based Approximate Bayesian Computation
Marko Järvenpää, Michael U. Gutmann, Arijus Pleska, Aki Vehtari, Pekka Marttinen
Bayesian Anal. 14(2): 595-622 (June 2019). DOI: 10.1214/18-BA1121

Abstract

Approximate Bayesian computation (ABC) is a method for Bayesian inference when the likelihood is unavailable but simulating from the model is possible. However, many ABC algorithms require a large number of simulations, which can be costly. To reduce the computational cost, Bayesian optimisation (BO) and surrogate models such as Gaussian processes have been proposed. Bayesian optimisation enables one to intelligently decide where to evaluate the model next but common BO strategies are not designed for the goal of estimating the posterior distribution. Our paper addresses this gap in the literature. We propose to compute the uncertainty in the ABC posterior density, which is due to a lack of simulations to estimate this quantity accurately, and define a loss function that measures this uncertainty. We then propose to select the next evaluation location to minimise the expected loss. Experiments show that the proposed method often produces the most accurate approximations as compared to common BO strategies.

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Marko Järvenpää. Michael U. Gutmann. Arijus Pleska. Aki Vehtari. Pekka Marttinen. "Efficient Acquisition Rules for Model-Based Approximate Bayesian Computation." Bayesian Anal. 14 (2) 595 - 622, June 2019. https://doi.org/10.1214/18-BA1121

Information

Published: June 2019
First available in Project Euclid: 18 September 2018

zbMATH: 07045444
MathSciNet: MR3934099
Digital Object Identifier: 10.1214/18-BA1121

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Vol.14 • No. 2 • June 2019
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