Effect of sample size on parameter estimates and earthquake forecasts

The Epidemic Type Aftershock Sequence (ETAS) model is widely used for producing probability forecasts of aftershocks in some space–time–magnitude volume following a major earthquake. It is empirically based, embodying the Omori and Gutenberg–Richter relationships. The model is generally calibrated (parameter estimation) using historical data. If there are insufficient historical data (i.e. sample size), our calibration could be poor. We initially quantify the effect of temporal sample size on the distributional properties of parameter estimates of a spatial ETAS model. Using these distributions, indexed by the temporal sample size, we then determine the effect of parameter uncertainty on earthquake forecast uncertainty.