TY - JOUR
T1 - Gaussian process modelling in approximate bayesian computation to estimate horizontal gene transfer in Bacteria
AU - Järvenpää, Marko
AU - Gutmann, Michael U.
AU - Vehtari, A. K.I.
AU - Marttinen, Pekka
PY - 2018/12/1
Y1 - 2018/12/1
N2 - 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.
AB - 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.
KW - Approximate bayesian computation
KW - Gaussian process
KW - Input-dependent noise
KW - Intractable likelihood
KW - Model selection
UR - http://www.scopus.com/inward/record.url?scp=85057174949&partnerID=8YFLogxK
U2 - 10.1214/18-AOAS1150
DO - 10.1214/18-AOAS1150
M3 - Article
VL - 12
SP - 2228
EP - 2251
JO - Annals of Applied Statistics
JF - Annals of Applied Statistics
SN - 1932-6157
IS - 4
ER -