The Likelihood for a Model of Continuous Rate Density Distribution
Rodolfo Console, Maura Murru, Giuseppe Falcone · 2017
The statistical procedures taken into account are the uncertainty in the measurements and the imperfect specificity in the definition of the hypothesis. This leads to formulating the hypothesis of occurrence in terms of continuous variables, as a function of the distance from earlier seismic events or of the localization of preceding geophysical anomalies. The model considered here is, where the rate density changes from point to point, while the occurrence rate in an infinitesimal volume surrounding the point is still modeled as a stationary random process, is called the generalized Poisson process. The case of time independence is mainly relevant to the null hypothesis. The result can be obtained by computing the average magnitude of the events exceeding the magnitude threshold m0. Rate density for the epidemic model expression is used to compute the log-likelihood observation of a set of seismic events.