Three Case Studies of Two-stage MCMC for Fast Bayesian Inference of Large Spatio-temporal Data

2026-09-13

AI Summary

本文通过使用两阶段MCMC算法，以较低的计算成本解决高维时空模型的计算限制问题，展示了该方法在三种不同模型中的应用及效率提升。

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.

Problem

• spatio-temporal models
• computational limitations
• two-stage MCMC
• Bayesian inference
• large datasets

Innovation

• Two-stage MCMC
• Bayesian Inference
• Spatio-temporal Data
• Computational Efficiency