Electronic Journal of Statistics

Bayesian estimation for a parametric Markov Renewal model applied to seismic data

Ilenia Epifani, Lucia Ladelli, and Antonio Pievatolo

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 8, Number 2 (2014), 2264-2295.

Dates
First available in Project Euclid: 31 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1414761923

Digital Object Identifier
doi:10.1214/14-EJS952

Mathematical Reviews number (MathSciNet)
MR3273626

Zentralblatt MATH identifier
1317.60116

Subjects
Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx] 62F15: Bayesian inference 62M05: Markov processes: estimation 86A15: Seismology
Secondary: 65C05: Monte Carlo methods

Keywords
Bayesian inference earthquakes Gibbs sampling Markov Renewal process predictive distribution semi-Markov process Weibull distribution

Citation

Epifani, Ilenia; Ladelli, Lucia; Pievatolo, Antonio. Bayesian estimation for a parametric Markov Renewal model applied to seismic data. Electron. J. Statist. 8 (2014), no. 2, 2264--2295. doi:10.1214/14-EJS952. https://projecteuclid.org/euclid.ejs/1414761923


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