Open Access
2014 Bayesian estimation for a parametric Markov Renewal model applied to seismic data
Ilenia Epifani, Lucia Ladelli, Antonio Pievatolo
Electron. J. Statist. 8(2): 2264-2295 (2014). DOI: 10.1214/14-EJS952


This paper presents a complete methodology for Bayesian inference on a semi-Markov process, from the elicitation of the prior distribution, to the computation of posterior summaries, including a guidance for its 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 a specific class of priors in a natural way, along with a method for the determination of hyperparameters based on “learning data” and moment existence conditions. This framework is applied to data of earthquakes of three types of severity (low, medium and high size) that occurred in the central Northern Apennines in Italy and collected by the CPTI04(2004) catalogue. Assumptions on two types of energy accumulation and release mechanisms are evaluated.


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Ilenia Epifani. Lucia Ladelli. Antonio Pievatolo. "Bayesian estimation for a parametric Markov Renewal model applied to seismic data." Electron. J. Statist. 8 (2) 2264 - 2295, 2014.


Published: 2014
First available in Project Euclid: 31 October 2014

zbMATH: 1317.60116
MathSciNet: MR3273626
Digital Object Identifier: 10.1214/14-EJS952

Primary: 60K20 , 62F15 , 62M05 , 86A15
Secondary: 65C05

Keywords: Bayesian inference , earthquakes , Gibbs sampling , Markov renewal process , predictive distribution , semi-Markov process , Weibull distribution

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 2 • 2014
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