Probabilities and information gain for earthquake forecasting
The paper discusses some issues arising out of attempts to calculate and score regular regional forecasts for earthquake probabilities. Given a conditional intensity model for earthquake occurrence, the model is first used to simulate occurrence patterns over the forecast interval. Then the simulations are used to estimate the required occurrence probabilities. A simple binomial score is suggested for monitoring and evaluating the performance of the probability forecasts. It is shown that an upper bound for the average score is provided by the information (or entropy) rate of the model. Similarly the improvement in the score over a standard model (constant rate Poisson with independent magnitudes) is limited from above by the entropy gain. Rates can be per unit time or per event. The performances of the ETAS and Stress Release models are described, and used to illustrate how the efficiency of the forecasts depends on the type of model, the timing of the forecasts and the choice of forecast interval.