Bayesian Variable Selection for Pareto Regression Models with Latent Multivariate Log Gamma Process with Applications...

Area of Science:

• Environmental statistics
• Statistical modeling
• Geostatistics

Background:

• Generalized linear models are common in environmental statistics, including earthquake magnitude prediction.
• Existing Pareto regression models with spatial effects may face variable selection challenges.

Purpose of the Study:

• To propose a Bayesian spatial variable selection method for Pareto regression.
• To address variable selection issues in generalized linear models with spatial random effects.

Main Methods:

• Developed a Bayesian hierarchical latent multivariate log gamma model framework.
• Incorporated spatial random effects to capture spatial dependence.
• Utilized Bayesian model assessment criteria: Conditional Predictive Ordinate (CPO) and Deviance Information Criterion (DIC).

Main Results:

• The proposed Bayesian approach effectively performs spatial variable selection for Pareto regression.
• Demonstrated analytic connections between CPO, DIC, and conditional AIC.
• Simulation studies confirmed the empirical performance of the method.

Conclusions:

• The proposed Bayesian spatial variable selection method is applicable to environmental statistics problems.
• The method enhances earthquake magnitude prediction by improving model selection.
• The approach provides a robust framework for analyzing spatially dependent data.