Department of Statistics, The Ohio State University
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 posterior distribution over the functional parameter is unaffected by the fact that only finite dimensional objects are used during the simulation procedure. We use techniques based on randomized acceptance probabilities and Bernoulli factories 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.
This talk is free and open to the public.