Spatial Weibull Regression with Multivariate Log Gamma Process and Its Applications to China Earthquake Economic Loss

Bayesian spatial modeling of heavy-tailed distributions has become increasingly popular in various areas of science in recent decades. We propose a Weibull regression model with spatial random effects for analyzing extreme economic loss. Model estimation is facilitated by a computationally efficient Bayesian sampling algorithm utilizing the multivariate Log-Gamma distribution. Simulation studies are carried out to demonstrate better empirical performances of the proposed model than the generalized linear mixed effects model. An earthquake data obtained from Yunnan Seismological Bureau, China is analyzed. Logarithm of the Pseudo-marginal likelihood values are obtained to select the optimal model, and Value-at-risk, expected shortfall, and tail-value-at-risk based on posterior predictive distribution of the optimal model are calculated under different confidence levels.