Title: Distributed Bayesian inference for varying coefficient spatiotemporal models
Authors: Cheng Li - National University of Singapore (Singapore) [presenting]
Rajarshi Guhaniyogi - University of California Santa Cruz (United States)
Terrance Savitsky - US Bureau of Labor Statistics (United States)
Sanvesh Srivastava - The University of Iowa (United States)
Abstract: Bayesian varying coefficients modeling is popular in many disciplines due to its flexibility and interpretability. Markov chain Monte Carlo methods used to fit these models are inefficient in moderately large data. We address this problem by developing a generalization of this class of models using linear mixed effects modeling, where the random effects are modeled by Gaussian processes. Computationally, we use parameter expansion to develop an efficient and stable data augmentation-type algorithm for fitting these models under the Bayesian framework, which can be scaled to millions of observations using the divide-and-conquer technique. Theoretically, we derive the convergence rates of Bayes risks for the divide-and-conquer posterior distributions of parameters, and show that the rates can be tuned to nearly optimal when the true underlying function is assumed to lie in some general functional classes. We demonstrate that our method yields smaller mean square errors, shorter credible intervals, and better frequentist coverage for the model parameters than its competitors, using several numerical experiments and real data applications.