UCSC-SOE-22-10: Bayesian Data Sketching for Spatial Regression Models

Rajarshi Guhaniyogi, Laura Baracaldo and Sudipto Banerjee
05/31/2022 09:40 AM
We introduce Bayesian data sketching for spatial regression models to obviate computational challenges presented by large numbers of spatial locations. To address the challenges of analysing very large spatial data, we compress spatially oriented data 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 analysing large spatial data in that it requires neither the development of new models or algorithms nor any specialised computational hardware while delivering fully model-based Bayesian inference. Well-established methods and algorithms for spatial regression models can be applied to the compressed data. We establish posterior contraction rates for estimating the spatially varying coefficients and predicting the outcome at new locations under the randomly compressed data model. We use simulation experiments and conduct a spatial analysis of remote sensed vegetation data to empirically illustrate the inferential and computational efficiency of our approach.