MCMC-Free Uncertainty Quantification for Deep Generative Inference for Spatially Varying Coefficient Models at Scale
Abstract
Varying coefficient (VC) regression models have become indispensable tools in spatial data analysis, providing unmatched flexibility in capturing complex, nonlinear relationships and spatially-varying effects of predictors on responses. Although hierarchical Bayesian approaches offer a rigorous probabilistic framework for uncertainty quantification in VC modeling, their practical application to large-scale spatial datasets remains severely hindered by the scalability limitations of Markov chain Monte Carlo (MCMC) algorithms. In response, the past decade has seen substantial advances in developing more efficient hierarchical Bayesian VC models, primarily through substituting traditional Gaussian processes (GP) with computationally efficient stochastic surrogates for estimating unknown coefficient functions. This article introduces a fundamentally different approach: the Geostatistical Variational Auto-Encoder (GeoVAE), a hierarchical deep generative framework built specifically for joint estimation of multiple spatially varying coefficient functions. GeoVAE departs from both classical GP-based Bayesian models and standard variational auto-encoders (VAEs) in two key ways. First, it constructs a coefficient-specific auto-encoder for each coefficient function, allowing each to capture its own spatial resolution and smoothness. Second, a hierarchical synthesis layer integrates information across these auto-encoders to a shared auto-encoder, explicitly modeling cross-coefficient dependencies arising from the shared spatial domain. This design enables GeoVAE to recover complex spatial patterns at computational cost that scales favorably with sample size, without MCMC or explicit GP covariance representations. We characterize the advantages and limitations of GeoVAE relative to hierarchical Bayesian spatial models, demonstrating its strong potential for large-scale spatial analysis.
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BibTeX
@misc{jeon2026mcmcfree,
title = {{MCMC-Free Uncertainty Quantification for Deep Generative Inference for Spatially Varying Coefficient Models at Scale}},
author = {Yeseul Jeon and Aaron Scheffler and Rajarshi Guhaniyogi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36325},
eprint = {2609.36325},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36325},
}
RIS
TY - UNPB
TI - MCMC-Free Uncertainty Quantification for Deep Generative Inference for Spatially Varying Coefficient Models at Scale
AU - Yeseul Jeon
AU - Aaron Scheffler
AU - Rajarshi Guhaniyogi
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36325
UR - https://arxiv.org/abs/2609.36325
AB - Varying coefficient (VC) regression models have become indispensable tools in spatial data analysis, providing unmatched flexibility in capturing complex, nonlinear relationships and spatially-varying effects of predictors on responses. Although hierarchical Bayesian approaches offer a rigorous probabilistic framework for uncertainty quantification in VC modeling, their practical application to large-scale spatial datasets remains severely hindered by the scalability limitations of Markov chain Monte Carlo (MCMC) algorithms. In response, the past decade has seen substantial advances in developing more efficient hierarchical Bayesian VC models, primarily through substituting traditional Gaussian processes (GP) with computationally efficient stochastic surrogates for estimating unknown coefficient functions. This article introduces a fundamentally different approach: the Geostatistical Variational Auto-Encoder (GeoVAE), a hierarchical deep generative framework built specifically for joint estimation of multiple spatially varying coefficient functions. GeoVAE departs from both classical GP-based Bayesian models and standard variational auto-encoders (VAEs) in two key ways. First, it constructs a coefficient-specific auto-encoder for each coefficient function, allowing each to capture its own spatial resolution and smoothness. Second, a hierarchical synthesis layer integrates information across these auto-encoders to a shared auto-encoder, explicitly modeling cross-coefficient dependencies arising from the shared spatial domain. This design enables GeoVAE to recover complex spatial patterns at computational cost that scales favorably with sample size, without MCMC or explicit GP covariance representations. We characterize the advantages and limitations of GeoVAE relative to hierarchical Bayesian spatial models, demonstrating its strong potential for large-scale spatial analysis.
ER -