BAYESIAN ESTIMATION FOR A PARAMETRIC MARKOV RENEWAL MODEL APPLIED TO SEISMIC DATA

Abstract. This paper presents a complete methodology for the Bayesian inference of a semi-Markov process, from the elicitation of the prior distribution, to the computation of posterior summaries, including a guidance for its JAGS implementation. The inter-occurrence times (conditional on the transition between two given states) are assumed to be Weibull-distributed. We examine the elicitation of the joint prior density of the shape and scale parameters of the Weibull distributions, deriving in a natural way a specific class of priors, along with a method for the determination of hyperparameters based on “historical data ” and moment existence conditions. This framework is applied to data of earthquakes of three types of severity (low, medium and high size) occurred in the central Northern Apennines in Italy and collected by the CPTI04 (2004) catalogue. 1