Gaussian process modelling in approximate bayesian computation to estimate horizontal gene transfer in Bacteria

Marko Järvenpää, Michael U. Gutmann, A. K.I. Vehtari, Pekka Marttinen

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)
146 Downloads (Pure)

Abstract

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.

Original languageEnglish
Pages (from-to)2228-2251
Number of pages24
JournalAnnals of Applied Statistics
Volume12
Issue number4
DOIs
Publication statusPublished - 1 Dec 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • Approximate bayesian computation
  • Gaussian process
  • Input-dependent noise
  • Intractable likelihood
  • Model selection

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