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December 2020 Identifying main effects and interactions among exposures using Gaussian processes
Federico Ferrari, David B. Dunson
Ann. Appl. Stat. 14(4): 1743-1758 (December 2020). DOI: 10.1214/20-AOAS1363


This article is motivated by the problem of studying the joint effect of different chemical exposures on human health outcomes. This is essentially a nonparametric regression problem, with interest being focused not on a black box for prediction but instead on selection of main effects and interactions. For interpretability we decompose the expected health outcome into a linear main effect, pairwise interactions and a nonlinear deviation. Our interest is in model selection for these different components, accounting for uncertainty and addressing nonidentifiability between the linear and nonparametric components of the semiparametric model. We propose a Bayesian approach to inference, placing variable selection priors on the different components, and developing a Markov chain Monte Carlo (MCMC) algorithm. A key component of our approach is the incorporation of a heredity constraint to only include interactions in the presence of main effects, effectively reducing dimensionality of the model search. We adapt a projection approach developed in the spatial statistics literature to enforce identifiability in modeling the nonparametric component using a Gaussian process. We also employ a dimension reduction strategy to sample the nonlinear random effects that aids the mixing of the MCMC algorithm. The proposed MixSelect framework is evaluated using a simulation study, and is illustrated using data from the National Health and Nutrition Examination Survey (NHANES). Code is available on GitHub.


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Federico Ferrari. David B. Dunson. "Identifying main effects and interactions among exposures using Gaussian processes." Ann. Appl. Stat. 14 (4) 1743 - 1758, December 2020.


Received: 1 November 2019; Revised: 1 April 2020; Published: December 2020
First available in Project Euclid: 19 December 2020

MathSciNet: MR4194246
Digital Object Identifier: 10.1214/20-AOAS1363

Keywords: Bayesian modeling , chemical mixtures , Gaussian process , interaction selection , semiparametric , strong heredity , Variable selection

Rights: Copyright © 2020 Institute of Mathematical Statistics


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Vol.14 • No. 4 • December 2020
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