Bayesian Inference for Spatial-Temporal Non-Gaussian Data Using Predictive Stacking

Area of Science:

• Statistics
• Computational Biology
• Ecological Modeling

Background:

• Analyzing non-Gaussian spatial-temporal data presents challenges in generalized linear models due to difficulties in analytically integrating random effects.
• Standard inference methods struggle with convergence for weakly identified parameters in these models.

Purpose of the Study:

• To develop a novel Bayesian inference method for non-Gaussian spatial-temporal data.
• To improve computational efficiency and overcome convergence issues in complex statistical models.
• To apply the method to real-world ecological data, specifically avian count data.

Main Methods:

• Devised Bayesian inference using predictive stacking to assimilate information from analytically tractable conditional posterior distributions.
• Expanded on Diaconis-Ylvisaker conjugate priors and utilized generalized conjugate multivariate (GCM) distribution theory for exponential families.
• Enabled exact sampling from posterior distributions conditional on process parameters and assimilated inference over parameter ranges.

Main Results:

• The proposed method demonstrates effective inferential performance on simulated data.
• Comparison with full Bayesian inference using Markov chain Monte Carlo (MCMC) shows comparable results.
• Successfully applied to analyze spatially-temporally referenced avian count data from the North American Breeding Bird Survey.

Conclusions:

• Bayesian inference with predictive stacking offers a viable and efficient approach for non-Gaussian spatial-temporal data analysis.
• The method addresses limitations of traditional inference, particularly convergence issues.
• Provides a robust framework for analyzing complex ecological datasets with spatial and temporal dependencies.