Department of Biostatistics Seminar/Workshop Series

Kernel mixtures of Gaussian Processes

Richard F. MacLehose, MS, PhD

National Institute of Environmental Health Sciences, North Carolina

Wednesday, February 6, 1:30-2:30pm, MRBIII Conference Room 1220

Intended Audience: Persons interested in applied statistics, statistical theory, epidemiology, health services research, clinical trials methodology, statistical computing, statistical graphics, R users or potential users

In many applications, there is interest in estimating a collection of related functions. For example, in epidemiology these functions may correspond to dose-response curves for an environmental exposure at different lag times or spatial locations. Our focus is on estimating the dose-response effects of chrysotile asbestos exposure during multiple previous times on current mortality. Data come from an occupational cohort study of textile workers in South Carolina. We focus on Bayesian nonparametric methods for incorporating dependence in collections of related functions through an appropriate prior. The standard choice in such settings is a Gaussian process (GP) with a separable covariance function. We propose a more general class of kernel mixtures of Gaussian processes (KMGP), which induces flexible dependence in random functions. Some theoretical properties of the KMGP are formalized. We use the KMGP to develop a class of generalized additive distributed lag models, which are useful in assessing time-varying effects of predictors. Efficient MCMC algorithms are developed for posterior inference. The methods are illustrated using simulations, and an application to the occupational cohort study examining the health effects of asbestos exposure.