Mathematical principles of predicting the probabilities of large earthquakes

A multicomponent random process used as a model for space-time earthquake prediction enables the construction of a consistent estimator for conditional probabilities of large earthquakes with known values of the predictor characterizing seismic prehistory. This paper defines tools for the assessment of the prediction efficiency, including separate determinations of the efficiency for time prediction and location prediction: a generalized correlation coefficient and information gain density. A technique for testing a predictor is proposed to determine whether the hypothesis of no prediction can be rejected.