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Bayesian Variable Selection for Pareto Regression Models with Latent Multivariate Log Gamma Process with Applications to Earthquake Magnitudes

1
Department of Statistics, Florida State University, Tallahassee, FL 32306, USA
2
Department of Statistics, University of Connecticut, Storrs, CT 06269, USA
*
Author to whom correspondence should be addressed.
Geosciences 2019, 9(4), 169; https://doi.org/10.3390/geosciences9040169
Received: 10 January 2019 / Revised: 3 April 2019 / Accepted: 9 April 2019 / Published: 12 April 2019
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Abstract

Generalized linear models are routinely used in many environment statistics problems such as earthquake magnitudes prediction. Hu et al. proposed Pareto regression with spatial random effects for earthquake magnitudes. In this paper, we propose Bayesian spatial variable selection for Pareto regression based on Bradley et al. and Hu et al. to tackle variable selection issue in generalized linear regression models with spatial random effects. A Bayesian hierarchical latent multivariate log gamma model framework is applied to account for spatial random effects to capture spatial dependence. We use two Bayesian model assessment criteria for variable selection including Conditional Predictive Ordinate (CPO) and Deviance Information Criterion (DIC). Furthermore, we show that these two Bayesian criteria have analytic connections with conditional AIC under the linear mixed model setting. We examine empirical performance of the proposed method via a simulation study and further demonstrate the applicability of the proposed method in an analysis of the earthquake data obtained from the United States Geological Survey (USGS). View Full-Text
Keywords: earthquake hazard; DIC; CPO; model selection earthquake hazard; DIC; CPO; model selection
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Yang, H.-C.; Hu, G.; Chen, M.-H. Bayesian Variable Selection for Pareto Regression Models with Latent Multivariate Log Gamma Process with Applications to Earthquake Magnitudes. Geosciences 2019, 9, 169.

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