Open Access
December 2018 Gaussian process modelling in approximate Bayesian computation to estimate horizontal gene transfer in bacteria
Marko Järvenpää, Michael U. Gutmann, Aki Vehtari, Pekka Marttinen
Ann. Appl. Stat. 12(4): 2228-2251 (December 2018). DOI: 10.1214/18-AOAS1150


Approximate Bayesian computation (ABC) can be used for model fitting when the likelihood function is intractable but simulating from the model is feasible. However, even a single evaluation of a complex model may take several hours, limiting the number of model evaluations available. Modelling the discrepancy between the simulated and observed data using a Gaussian process (GP) can be used to reduce the number of model evaluations required by ABC, but the sensitivity of this approach to a specific GP formulation has not yet been thoroughly investigated. We begin with a comprehensive empirical evaluation of using GPs in ABC, including various transformations of the discrepancies and two novel GP formulations. Our results indicate the choice of GP may significantly affect the accuracy of the estimated posterior distribution. Selection of an appropriate GP model is thus important. We formulate expected utility to measure the accuracy of classifying discrepancies below or above the ABC threshold, and show that it can be used to automate the GP model selection step. Finally, based on the understanding gained with toy examples, we fit a population genetic model for bacteria, providing insight into horizontal gene transfer events within the population and from external origins.


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Marko Järvenpää. Michael U. Gutmann. Aki Vehtari. Pekka Marttinen. "Gaussian process modelling in approximate Bayesian computation to estimate horizontal gene transfer in bacteria." Ann. Appl. Stat. 12 (4) 2228 - 2251, December 2018.


Received: 1 October 2016; Revised: 1 November 2017; Published: December 2018
First available in Project Euclid: 13 November 2018

zbMATH: 07029453
MathSciNet: MR3875699
Digital Object Identifier: 10.1214/18-AOAS1150

Keywords: Approximate Bayesian Computation , Gaussian process , input-dependent noise , intractable likelihood , Model selection

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.12 • No. 4 • December 2018
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