Information Criterion of Precursors

Abstract

The terms of ldquovalidityrdquo, ldquoreliabilityrdquo and ldquoprobability gainrdquo are usually used to estimate performance of earthquake prediction. Based on information theory, a new scale is proposed in terms of a log likelihood ratio of an uniform Poisson process to an alternative process of earthquake occurrence. As the alternative process, two Poisson rate model is adopted on the assumption that the large earthquakes may be modeled by two Poisson processes with different rates: the higher rate process simulates large earthquakes that occur in the time-space volume when an earthquake alarm has been declared and the lower rate process simulates earthquakes that occur in a non-alarm time-space volume. The performance of an proposed algorithm can be measured in terms of the likelihood ratio of the two Poisson rate model to a uniform Poisson model. A Monte Carlo simulation experiment shows that correction of the likelihood ratio is required depending on both number of adjusted parameters and number of target earthquakes. The proposed scale is powerful not only for judging statistical significance of precursors but also for comparing effectiveness of precursors