Nonparametric Aftershock Forecasts Based on Similar Sequences in the Past

The basic premise behind aftershock forecasting is that sequences in the future will be similar to those in the past. Most forecasts use empirically tuned parametric distributions to approximate the behavior of past sequences and project those distributions into the future. Although parametric models do a good job of capturing the average behavior in a population, they are not explicitly designed to capture the full range of variability between sequences, and sometimes suffer from instabilities or inaccuracies due to overtuning of the model. Here, we present a nonparametric forecast method that cuts out the parametric “middleman” between training data and forecast. The forecast is drawn directly from past outcomes of sequences that appear similar to the target sequence, with similarity defined as the Poisson probability that the event count in a past sequence comes from the same underlying intensity as the event count to-date in the target sequence. The forecast is just the distribution of previously observed event counts, weighted by their similarity. The similarity forecast is only marginally less accurate than the parametric Reasenberg and Jones (1989; hereafter RJ89) method. The rate of severe underpredictions, however, is much lower for the similarity forecast. Although 10% of observed sequences exceed the upper 2.5% range of the RJ89 forecast range, only 3% exceed this range for the similarity forecast. Given an adequate database of past events, the similarity method makes overtuning impossible, minimizes the rate of surprises, and serves as a useful benchmark for more precisely tuned parametric forecasts