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The conditional intensity function of a point process is a useful tool for generating probability forecasts of earthquakes. The epidemic-type aftershock sequence (ETAS) model is defined by a conditional intensity function, and the corresponding point process is equivalent to a branching process, assuming that an earthquake generates a cluster of offspring earthquakes (triggered earthquakes or so-called aftershocks). Further, the size of the first-generation cluster depends on the magnitude of the triggering (parent) earthquake. The ETAS model provides a good fit to standard earthquake occurrences. However, there are nonstandard earthquake series that appear under transient stress changes caused by aseismic forces such as volcanic magma or fluid intrusions. These events trigger transient nonstandard earthquake swarms, and they are poorly fitted by the stationary ETAS model. In this study, we examine nonstationary extensions of the ETAS model that cover nonstandard cases. These models allow the parameters to be time-dependent and can be estimated by the empirical Bayes method. The best model is selected among the competing models to provide the inversion solutions of nonstationary changes. To address issues of the uniqueness and robustness of the inversion procedure, this method is demonstrated on an inland swarm activity induced by the 2011 Tohoku-Oki, Japan earthquake of magnitude 9.0., Comment: Published in at http://dx.doi.org/10.1214/14-AOAS759 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Earthquakes occur because of abrupt slips on faults due to accumulated stress in the Earth's crust. Because most of these faults and their mechanisms are not readily apparent, deterministic earthquake prediction is difficult. For effective prediction, complex conditions and uncertain elements must be considered, which necessitates stochastic prediction. In particular, a large amount of uncertainty lies in identifying whether abnormal phenomena are precursors to large earthquakes, as well as in assigning urgency to the earthquake. Any discovery of potentially useful information for earthquake prediction is incomplete unless quantitative modeling of risk is considered. Therefore, this manuscript describes the prospect of earthquake predictability research to realize practical operational forecasting in the near future., Comment: Published in at http://dx.doi.org/10.1214/13-STS439 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)