Structured Bayesian Inference for Spatio-Temporal Systems with Applications in Remote Sensing

Abstract

Satellite-based remote sensing observing systems are a key source of information for understanding Earth system dynamics. Bayesian inference provides a principled framework for retrieving physical parameters from satellite observations while quantifying uncertainty. However, the high dimensionality and spatio-temporal complexity of remote sensing problems pose major computational challenges for traditional inference methods. This thesis develops scalable algorithms for Bayesian inference for remote sensing systems by leveraging low-rank structure and sparse conditional dependence structure. The resulting methods enable accurate and efficient posterior characterization at scales relevant for modern satellite missions. The first theme of this thesis is identifying low-rank structure in problems where the scientific goal is to estimate a small number of quantities of interest (QoIs) that are a function of the unknown parameters. Using a gradient-based dimension reduction framework, we construct informative subspaces of the observation space that are tailored to specific QoIs. This framework is integrated with transport maps to enable simulation-based inference directly for the QoIs, without the need to recover the full posterior of the high-dimensional parameters. We demonstrate this approach on imaging spectroscopy data from NASA’s upcoming Surface Biology and Geology (SBG) mission and show that it achieves inference accuracy comparable to Markov chain Monte Carlo (MCMC) while requiring orders of magnitude less computational time. In addition, we examine the role of preconditioning in dimension reduction and demonstrate that the optimal choice of preconditioner depends on the nonlinearity of the forward model. Next, we explore how conditional independence structure can be used to improve the scalability of inference algorithms relevant to remote sensing systems. We first consider a single-pixel setting and exploit within-state conditional independence to build sparse transport maps for hyperspectral retrievals. These sparse maps reduce computation over standard nonGaussian inference methods while preserving accuracy. Extending beyond individual pixels, we develop an information filter that leverages spatio-temporal conditional independencies in satellite observing systems. By incorporating sparse inverse covariance structure into the filtering equations, we achieve significant improvements in both scalability and inference accuracy on data relevant to NASA’s OCO-2, EMIT, and SBG missions. Building on this structure, this thesis also explores extensions of large-scale spatio-temporal inference to the continuous non-Gaussian setting using measure transport. Drawing inspiration from belief propagation algorithms for Gaussian graphical models, we construct decomposed transport maps tailored to spatio-temporal graphical structures. These methods enable scalable inference while capturing non-Gaussian features of the posterior. We demonstrate their application to spatio-temporal systems, providing a viable framework for high-fidelity uncertainty quantification.