Bayesian forecasting of recurrent earthquakes and predictive performance for a small sample size

This paper presents a Bayesian method of probability forecasting for a renewal of earthquakes. When only limited records of characteristic earthquakes on a fault are available, relevant prior distributions for renewal model parameters are essential to computing unbiased, stable time-dependent earthquake probabilities. We also use event slip and geological slip rate data combined with historical earthquake records to improve our forecast model. We apply the Brownian Passage Time (BPT) model and make use of the best fit prior distribution for its coefficient of variation (the shape parameter, alpha) relative to the mean recurrence time because the Earthquake Research Committee (ERC) of Japan uses the BPT model for long-term forecasting. Currently, more than 110 active faults have been evaluated by the ERC, but most include very few paleoseismic events. We objectively select the prior distribution with the Akaike Bayesian Information Criterion using all available recurrence data including the ERC datasets. These data also include mean recurrence times estimated from slip per event divided by long-term slip rate. By comparing the goodness of fit to the historical record and simulated data, we show that the proposed predictor provides more stable performance than plug-in predictors, such as maximum likelihood estimates and the predictor currently adopted by the ERC.