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Bayesian Variable Selection for Multi-Dimensional Semiparametric Regression Models

Wednesday, December 6, 2017 2:00 pm– 3:0 0 pm
Purvis Hall, 1020 Pine Ave. West, Room 25

ALL ARE WELCOME
Abstract

Humans are routinely exposed to mixtures of chemical and other environmental factors, making the quantification
of health effects associated with environmental mixtures a critical goal for establishing environmental policy
sufficiently protective of human health. The quantification of the effects of exposure to an environmental mixture
poses several statistical challenges. It is often the case that exposure to multiple pollutants interact with each
other to affect an outcome.

Further, the exposure -response relationship between an outcome and some exposures, such as some metals, can exhibit complex, nonlinear forms, since some exposures can be beneficial and detrimental at different ranges of exposure. To estimate the health effects of complex mixtures we propose
sparse tensor regression, which uses tensor products of marginal basis functions to approximate complex functions. We induce sparsity using multivariate spike and slab priors on the number of exposures that make up the tensor factorization. We allow the number of components required to estimate the health effects of multiple
pollutants to be unknown and estimate it from the data. The proposed approach is interpretable, as we can use the posterior probabilities of inclusion to identify pollutants that interact with each other.

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