A Bayesian latent process spatiotemporal regression model for areal count data

Area of Science:

• Statistics
• Spatiotemporal Analysis
• Bayesian Inference

Background:

• Model-based approaches are standard for areal count data analysis in spatiotemporal contexts.
• Bayesian hierarchical models often use conditional autoregressive (CAR) priors for latent processes to capture spatial and temporal dependencies.
• Existing methods primarily rely on CAR priors for modeling latent processes.

Purpose of the Study:

• To propose and evaluate an alternative to CAR-based priors for modeling latent processes in spatiotemporal count data.
• To introduce a spatiotemporal generalization of a latent process Poisson regression model.
• To provide a flexible and effective modeling framework for complex spatiotemporal dependencies.

Main Methods:

• Developed a novel spatiotemporal latent process model generalizing a time series approach.
• Modeled spatiotemporal dependence via the transition matrix of the autoregressive process.
• Specified a structured covariance matrix for the error term.
• Implemented Bayesian inference using Markov Chain Monte Carlo (MCMC) techniques.

Main Results:

• The proposed model effectively captures spatiotemporal dependencies in areal count data.
• Parameterizations were successfully fitted using MCMC methods.
• Empirical results demonstrate the proposed approach is as effective as traditional CAR-based models.
• The new method offers a viable alternative for spatiotemporal count data analysis.

Conclusions:

• The proposed spatiotemporal latent process model provides a competitive alternative to CAR-based approaches.
• This method offers flexibility in modeling complex spatiotemporal structures.
• The findings support the utility of this novel approach in real-world spatiotemporal analyses.