Exact Bayesian Inference for Multivariate Spatial Data of Any Size with Application to Air Pollution Monitoring

TL;DR

This paper introduces SM-EPR, a scalable Bayesian method that enables exact inference on massive multivariate spatial datasets, exemplified by air pollution data from NASA, avoiding traditional MCMC limitations.

Contribution

The paper develops SM-EPR, combining data subset and EPR techniques to perform exact Bayesian inference on extremely large multivariate spatial data without MCMC.

Findings

Successfully applied to 8 million observations from NASA data

Achieved exact Bayesian inference without MCMC for large datasets

Demonstrated effectiveness through simulations and real data application

Abstract

Fine particulate matter and aerosol optical thickness are of interest to atmospheric scientists for understanding air quality and its various health/environmental impacts. The available data are extremely large, making uncertainty quantification in a fully Bayesian framework quite difficult, as traditional implementations do not scale reasonably to the size of the data. We specifically consider roughly 8 million observations obtained from NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) instrument. To analyze data on this scale, we introduce Scalable Multivariate Exact Posterior Regression (SM-EPR) which combines the recently introduced data subset approach and Exact Posterior Regression (EPR). EPR is a new Bayesian hierarchical model where it is possible to sample independent replicates of fixed and random effects directly from the posterior without the use of Markov chain Monte Carlo (MCMC). We extend EPR to the multivariate spatial context, where the multiple variables may be distributed according to different distributions. The combination of the data subset approach with EPR allows one to perform exact Bayesian inference without MCMC for effectively any sample size. Additional motivation is provided via technical results illustrating favorable Kullback-Leibler and covariance properties. We demonstrate SM-EPR using a motivating big remote sensing data application and provide several simulations.