Earthquake prediction: Simple methods for complex phenomena
Earthquake predictions are often either based on stochastic models, or tested using stochastic models. Tests of predictions often tacitly assume predictions do not depend on past seismicity, which is false. We construct a naive predictor that, following each large earthquake, predicts another large earthquake will occur nearby soon. Because this "automatic alarm" strategy exploits clustering, it succeeds beyond "chance" according to a test that holds the predictions fixed.
Some researchers try to remove clustering from earthquake catalogs and model the remaining events. There have been claims that the declustered catalogs are Poisson on the basis of statistical tests we show to be weak. Better tests show that declustered catalogs are not Poisson. In fact, there is evidence that events in declustered catalogs do not have exchangeable times given the locations, a necessary condition for the Poisson.
If seismicity followed a stochastic process, an optimal predictor would turn on an alarm when the conditional intensity is high. The Epidemic-Type Aftershock (ETAS) model is a popular point process model that includes clustering. It has many parameters, but is still a simplification of seismicity. Estimating the model is difficult, and estimated parameters often give a non-stationary model. Even if the model is ETAS, temporal predictions based on the ETAS conditional intensity are not much better than those of magnitude-dependent automatic (MDA) alarms, a much simpler strategy with only one parameter instead of five. For a catalog of Southern Californian seismicity, ETAS predictions again offer only slight improvement over MDA alarms.