Subsampling for spatial models with short- and long-range dependencies in SGMCMC

Develop subsampling-based stochastic gradient MCMC methods that can capture both short- and long-range dependencies in spatial models while providing unbiased or provably controlled-bias gradient estimates, and establish theoretical guarantees for their accuracy and efficiency.

Background

Subsampling enables scalable stochastic gradient MCMC by reducing per-iteration cost, but naïve subsampling introduces bias in models with dependence (e.g., spatial or network data). While progress has been made for temporal (Hidden Markov) and network models, spatial models present the added challenge of jointly capturing short- and long-range dependencies.

The authors explicitly note that designing subsampling schemes that handle spatial dependence structures remains unresolved, highlighting a key obstacle to extending SGMCMC to broader applied domains.