Statistical Estimation of the Efficiency of Earthquake Prediction Under Uncertain Identification of Target Events

The efficiency of earthquake prediction is often expressed in terms of the success and alarm rates, determined by the ratio of the number of successful predictions to the total number of predictions and to the number of events which should be predicted, respectively. We consider here a predicting system that aims at events of magnitude above a given threshold value. System indications are assumed to be univocal “yes” or “no.” For such a system the observation error of magnitude of events used to determine the prediction rates of the system causes an increase of number of identified prediction targets and a decrease of number of identified prediction successes. In effect when the uncertainty of event magnitude is ignored the prediction rates can be significantly underestimated. This could result in rejecting a valuable predicting system or in underestimating of the actual seismic risk. A method of estimation of prediction rates is given, which accounts for the error of observed magnitude of any symmetric, independent of magnitude distribution. The uncertainty of target identification is expressed as the result of the probabilistic transition from the actual to observed magnitude classes. This problem of prediction rates estimation is solved by an analysis of the prediction and transition processes, given the prediction efficiency parameters, the incidental connection rate, and the transition probabilities. Numerical tests and Monte Carlo simulations of the prediction/transition processes, assuming the normal distribution of observation error, appear to confirm that the solution is correct. Manuscript received 23 June 1998.