Effective Bayesian Modeling of Large Spatiotemporal Count Data Using Autoregressive Gamma Processes

2025-07-26

AI Summary

Bayesian modeling of large-scale spatiotemporal count data is hindered by the non-conjugacy between standard log-Gaussian process priors and Poisson likelihoods, leading to inefficient variational inference or MCMC. Method: We propose an Auto-Regressive Gamma Process (ARGP)-based fully conjugate framework that induces a temporally stationary and spatially sparse spatiotemporal structure, ensuring exact conjugacy between the latent process prior and Poisson observations. This enables efficient Gibbs sampling with linear computational complexity. By decomposing Poisson latent variables and modeling them via ARGP, the approach achieves both interpretability and scalability. Results: Experiments on synthetic and real-world datasets demonstrate substantial improvements in parameter estimation accuracy, posterior convergence speed, and out-of-sample predictive performance—particularly for generalization to novel spatiotemporal locations.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial random effects, where the latter is typically assumed to follow a latent Gaussian process, the conditional autoregressive model, or the intrinsic conditional autoregressive model. Since log-Gaussian is not conjugate to Poisson, such implementations must resort to either approximation methods like INLA or Metropolis moves on latent states in MCMC algorithms for model fitting and exhibit several approximation and posterior sampling challenges. Instead of modeling logarithms of spatiotemporal frailties jointly as a Gaussian process, we construct a spatiotemporal autoregressive gamma process guaranteed stationary across the time dimension. We decompose latent Poisson variables to permit fully conjugate Gibbs sampling of spatiotemporal frailties and design a sparse spatial dependence structure to get a linear computational complexity that facilitates efficient posterior computation. Our model permits convenient Bayesian predictive machinery based on posterior samples that delivers satisfactory performance in predicting at new spatial locations and time intervals. We have performed extensive simulation experiments and real data analyses, which corroborated our model's accurate parameter estimation, model fitting, and out-of-sample prediction capabilities.

Problem

• Develops Bayesian model for large spatiotemporal count data
• Enables efficient posterior sampling via conjugate Gibbs sampling
• Improves prediction accuracy at new locations and times

Innovation

• Autoregressive gamma process for spatiotemporal data
• Fully conjugate Gibbs sampling for efficient computation
• Sparse spatial dependence for linear complexity