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

TL;DR

This paper develops a Bayesian inference methodology for semi-Markov processes with Weibull-distributed holding times, applied to seismic data to analyze earthquake severity and energy mechanisms.

Contribution

It introduces a natural class of priors for Weibull parameters and provides a practical guide for Bayesian analysis using JAGS, applied to real earthquake data.

Findings

Effective Bayesian inference framework for seismic semi-Markov models

Prior elicitation method based on learning data and moment conditions

Application to earthquake data reveals insights on energy mechanisms

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 JAGS implementation. The holding 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 \cite{CPTI04} catalogue. Assumptions on two types of energy accumulation and release mechanisms are evaluated.