Exact Inference in Functional Regression: Estimating Hydrological Controls on Ecosystem Dynamics in an Antarctic Lake

• Activity Number: 216 - Modern Bayesian Computing in Ecology
• Type: Invited
• Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Radu Herbei* and Corey J. Smith
• Companies: The Ohio State University and The Ohio State University
• Keywords: Exact inference; MCMC; functional regression

Abstract

Many of the modern-day statistical inference problems address the issue of estimating an infinite dimensional parameter (a function or a surface). Given that one can only store a finite representation of these objects on a computer, the typical approach is to employ some dimension-reduction strategy and proceed with a statistical inference procedure in a multivariate setting. We introduce an exact inference procedure for functional parameters in a Bayesian regression setting. By "exact" we mean that the MCMC sampler used to explore the constructed posterior distribution uses no dimension reduction. Rather we use a technique based on a randomized acceptance probability to ensure that the sampler targets the correct distribution. We apply our method to the problem of estimating the association between stream discharge and physical, chemical, and biological processes within an Antarctic lake system.