Three Case Studies of Two-stage MCMC for Fast Bayesian Inference of Large Spatio-temporal Data
Abstract
High dimensional spatio-temporal models can quickly run up against computational limitations. Recursive or multi-stage Bayesian algorithms are one way to address this computational challenge. Here we consider an increasingly used two-stage algorithm. The first stage models locations independently and in parallel across space. Resampling particles from this stage-one model with Metropolis-within-Gibbs methods and suitably computed acceptance ratios can impose spatial dependence across locations at a low computational cost, while targeting the same posterior distribution as the single-stage MCMC algorithm at a fraction of the overall computational cost. In this paper we show three complete examples of how two-stage MCMC algorithms can be used to efficiently fit Bayesian spatio-temporal models to large datasets. Specifically, we consider: a spatio-temporal self-exciting count model on areal data utilizing intrinsic conditional autoregressive (ICAR) prior distributions; a spatio-temporal model of point-referenced data using a stationary, isotropic distance-based covariance function; and a binary model fit to data on a spatial lattice utilizing a latent Gaussian process to capture all spatio-temporal dependence. In each example, we define the model and describe the corresponding two-stage MCMC approach. We then compare the resulting posterior samples and computational efficiency with those obtained using a standard single-stage MCMC algorithm. While varying across the three examples and numerous parameters, the two-stage approach often achieves roughly an order of magnitude higher computational efficiency, with the two-stage and single-stage algorithms producing closely agreeing posterior samples.
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BibTeX
@misc{shams2026three,
title = {{Three Case Studies of Two-stage MCMC for Fast Bayesian Inference of Large Spatio-temporal Data}},
author = {Mostafa Shams and Robert Erhardt and Staci Hepler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14774},
eprint = {2609.14774},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14774},
}
RIS
TY - UNPB
TI - Three Case Studies of Two-stage MCMC for Fast Bayesian Inference of Large Spatio-temporal Data
AU - Mostafa Shams
AU - Robert Erhardt
AU - Staci Hepler
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14774
UR - https://arxiv.org/abs/2609.14774
AB - High dimensional spatio-temporal models can quickly run up against computational limitations. Recursive or multi-stage Bayesian algorithms are one way to address this computational challenge. Here we consider an increasingly used two-stage algorithm. The first stage models locations independently and in parallel across space. Resampling particles from this stage-one model with Metropolis-within-Gibbs methods and suitably computed acceptance ratios can impose spatial dependence across locations at a low computational cost, while targeting the same posterior distribution as the single-stage MCMC algorithm at a fraction of the overall computational cost. In this paper we show three complete examples of how two-stage MCMC algorithms can be used to efficiently fit Bayesian spatio-temporal models to large datasets. Specifically, we consider: a spatio-temporal self-exciting count model on areal data utilizing intrinsic conditional autoregressive (ICAR) prior distributions; a spatio-temporal model of point-referenced data using a stationary, isotropic distance-based covariance function; and a binary model fit to data on a spatial lattice utilizing a latent Gaussian process to capture all spatio-temporal dependence. In each example, we define the model and describe the corresponding two-stage MCMC approach. We then compare the resulting posterior samples and computational efficiency with those obtained using a standard single-stage MCMC algorithm. While varying across the three examples and numerous parameters, the two-stage approach often achieves roughly an order of magnitude higher computational efficiency, with the two-stage and single-stage algorithms producing closely agreeing posterior samples.
ER -