Statistical methods and various models in time-space-magnitude parameter space of earthquakes are being developed to analyze seismic activity based on earthquake hypocenter catalogs that are routinely accumulated. Considering complex geophysical environments and uncertainties, we seek proper stochastic modeling that depends on the history of earthquake occurrences and relevant geophysical information for describing and forecasting earthquake activity. Also, we need empirical Bayesian models with many parameters in order to describe nonstationary or nonhomogeneous seismic activity. This review is concerned with earthquake predictability research aimed at realizing practical operational forecasting. In particular, uncertainty lies in identifying whether abnormal phenomena are precursors to large earthquakes. The predictability of such models can be examined by certain statistical criteria.


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