Hybrid kernel estimates of space–time earthquake occurrence rates using the epidemic-type aftershock sequence model

Abstract

Bandwidths, Shape parameters, Cross-validation, ETAS models, Intensity function, Kernel estimates, Space–time point processes, Space–time ETAS model, Transformation of time,

Forward likelihood‐based predictive approach for space–time point processes

“…Therefore, the complex estimation issue of a particular point process now reduces to the simple estimation of the intensity function (9) of an inhomogeneous Poisson process identified by a space-time Gaussian kernel density (Adelfio and Ogata, 2010). A power-law kernels based approach has been proposed by Kagan and Jackson (2000); in Adelfio et al (2006b) the seismicity of the Southern Tyrrhenian Sea is described by the use of Gaussian kernels and the optimum value of h is chosen such as to minimize the MISE of the estimatorf ðÁÞ: in particular the authors used the value h opt obtained minimizing the MISE off ðÁÞ assuming multivariate normality (see Silverman, 1986, p. 86).…”

Kernel estimation and display of a five-dimensional conditional intensity function

“…Introducing the estimator defined in (5), the estimation of a complex intensity function dependent on the past history of the process as in (2) now reduces to the estimation of the intensity function of an inhomogeneous Poisson process, independent of the past history and identified by a space-time Gaussian kernel intensity (Adelfio and Ogata, 2010); this result provides useful directions for a simpler estimation approach in describing very complex phenomena such as the seismic one. Separability of time and space kernel densities is here assumed for computational convenience, because of the high dimensional issue, although tests to assess this assumption could be used (Schoenberg, 2004).…”

Comparative seismic hazard analysis of two Spanish regions

“…It is important to highlight that nonparametric methods can be valuable supplements to several conventional parametric approaches, and they can also be a good first step in an exploratory data analysis. Nowadays, there exist a lot of references related to nonparametric estimation applied to earthquake data [18][19][20][21][22][23][24].…”