A0500
Title: Distributed Bayesian varying coefficient modeling using a Gaussian process prior
Authors: Sanvesh Srivastava - The University of Iowa (United States) [presenting]
Abstract: The divide-and-conquer technique is used to address inefficient inference in Varying coefficient models (VCMs) based on Gaussian process (GP) priors. Our proposal has three steps. The first step creates many data subsets with much smaller sample sizes by sampling without replacement from the full data. The second step formulates VCM as a linear mixed-effects model and develops a data augmentation (DA)-type algorithm for obtaining MCMC draws of the parameters and predictions on all the subsets in parallel. The DA-type algorithm appropriately modifies the likelihood such that every subset posterior distribution accurately approximates the corresponding true posterior distribution. The third step develops a combination algorithm for aggregating MCMC-based estimates of the subset posterior distributions into a single posterior distribution called the Aggregated Monte Carlo (AMC) posterior. The AMC posterior has minimax optimal posterior convergence rates in estimating the varying coefficients and the mean regression function.
