A Bayesian spatial–temporal model with latent multivariate log‐gamma random effects with application to earthquake magnitudes. Issue 1 (23rd March 2018)

• Record Type: Journal Article
• Authors: Hu, Guanyu; Bradley, Jonathan
• Is Part Of: Stat. Volume 7:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-03-23
• Subjects: earthquake magnitudes -- multivariate log‐Gamma process -- Pareto regression; Statistics -- Periodicals; 519.2
• DOI: 10.1002/sta4.179
• Languages: English
• ISSNs: 2049-1573

Abstract

Abstract : We introduce a Bayesian spatial–temporal model for analyzing earthquake magnitudes. Specifically, we define a spatial–temporal Pareto regression model with latent multivariate log‐Gamma random vectors to analyze earthquake magnitudes. This represents a marked departure from the traditional spatial generalized linear regression model, which uses latent Gaussian random effects. The multivariate log‐Gamma distribution results in a full‐conditional distribution that can be easily sampled from, which leads to a fast mixing Gibbs sampler. Thus, our proposed model is a computationally efficient approach for modelling Pareto spatial data. The empirical results suggest similar estimation properties between the latent Gaussian model and latent multivariate log‐Gamma model, but our proposed model has stronger predictive properties. Additionally, we analyze a small US earthquake data set as an illustration of the effectiveness of our approach. Copyright © 2018 John Wiley & Sons, Ltd.