Title: Bayesian Data Sketching for Varying Coefficient Regression Models

Abstract: Varying coefficient models are popular tools in estimating nonlinear regression functions in functional data models. Their Bayesian variants have received limited attention in large data applications, primarily due to the prohibitively slow posterior computations using Markov chain Monte Carlo (MCMC) algorithms. We introduce Bayesian data sketching for varying coefficient models to obviate computational challenges presented by large sample sizes. To address the challenges of analyzing large data, we compress functional response vector and predictor matrix by a random linear transformation to achieve dimension reduction and conduct inference on the compressed data. Our approach distinguishes itself from several existing methods for analyzing large functional data in that it requires neither the development of new models or algorithms nor any specialized computational hardware while delivering fully model-based Bayesian inference. Well-established methods and algorithms for varying coefficient regression models can be applied to the compressed data. We establish posterior contraction rates for estimating the varying coefficients and predicting the outcome at new locations under the randomly compressed data model. We use simulation experiments and conduct a spatially varying coefficient analysis of remote sensed vegetation data to empirically illustrate the inferential and computational efficiency of our approach.

Bio: Dr. Laura Baracaldo Lancheros is a Visiting Assistant Professor in the Department of Statistics and Applied Probability at the University of California, Santa Barbara. Dr. Baracaldo received her Ph.D. in Statistical Science in 2022 at the University of California, Santa Cruz, and her M.S. and B.S. in Statistics in 2015 and 2012 respectively at the National University of Colombia. Her research interests include Bayesian High Dimensional Spatio-Temporal modeling, Bayesian High Dimensional Structured Variable Selection with applications in Ecology, Neurosciences, Epidemiology, Genomics and Social Sciences.