Multi-step analysis of seismic hazard through point processes

In this article the seismic hazard assessment is the final goal of a multi-step procedure in which the reliability of the final result depends strongly on the answers given to the intermediate issues. The first problem consists in analyzing the completeness of the sequences of earthquakes drawn from the Italian catalog dating back several centuries. The issue is tackled as a problem of identification, in the Bayesian framework, of the change-point between two Poisson processes. The part considered as complete of the data set is then analyzed through a new self-correcting-type point process that compares the expected and the observed displacement obtained respectively by the unknown slip rate and by the sum of the slips caused by every earthquake. The difference D(t) between these displacements turns out the level of the physical process controlling the rate of the point process proposed, having a stepwise exponentially increasing intensity function. Estimation is performed through MCMC methods.