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Bayesian Non‐Parametric Estimation of Smooth Hazard Rates for Seismic Hazard Assessment
Author(s) -
ROCCA LUCA LA
Publication year - 2008
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2008.00595.x
Subject(s) - mathematics , statistics , kernel density estimation , markov chain monte carlo , bayesian probability , hazard , econometrics , poisson distribution , parametric statistics , bayes estimator , estimator , chemistry , organic chemistry
. Hazard rate estimation is an alternative to density estimation for positive variables that is of interest when variables are times to event. In particular, it is here shown that hazard rate estimation is useful for seismic hazard assessment. This paper suggests a simple, but flexible, Bayesian method for non‐parametric hazard rate estimation, based on building the prior hazard rate as the convolution mixture of a Gaussian kernel with an exponential jump‐size compound Poisson process. Conditions are given for a compound Poisson process prior to be well‐defined and to select smooth hazard rates, an elicitation procedure is devised to assign a constant prior expected hazard rate while controlling prior variability, and a Markov chain Monte Carlo approximation of the posterior distribution is obtained. Finally, the suggested method is validated in a simulation study, and some Italian seismic event data are analysed.