Probability of chance correlations of earthquakes with predictions in areas of heterogeneous seismicity rate: The VAN Case
Evaluations of 22 claims of successful earthquake predictions in Greece by Varotsos and Lazaridou  were performed using the Ms (surface wave) as well as the ML (local) magnitude scales. If we assume that the predicted magnitudes were Ms (the scale was not specified in the prediction telegrams), and use the Preliminary Determinations of Epicenters (PDE) to estimate the seismicity rate expected at random, we find that 74% were false (they did not correlate with an earthquake as specified), 9% correlated by chance (probability, p, of one or more earthquakes at random >.50), and 17% are uncertain (0.15 < p < 0.40). There were no successes above the 85% confidence level. If we assume that the magnitude scale for predictions and seismicity rate was M(VAN)=ML(ATH)+0.5, and use the Monthly Bulletin of the Seismological Institute, National Observatory Athens (SI-NOA), for estimating the seismicity rate, we find that 12 of 23 claims were false and that the rest, except for one, most likely correlated by chance with earthquakes. The missed earthquakes eligible for prediction numbered 35 and 456, respectively, using the two data sets. The probability that the observed correlation of predictions with earthquakes (6 and 11 respectively, out of 23 attempts) was due to chance is estimated as 69% and 96%, respectively, by summing the products of the individual probabilities for success and all the permutations of m successes out of n attempts. The probabilities of individual predictions to be fulfilled by chance were estimated based on the declustered catalogs for each prediction area separately, except for predictions during aftershock periods. For these the average seismicity rate during one month after the mainshock was used. We conclude that the various hypotheses of Varotsos et al. [1981a,b,c, 1982a,b, 1983, 1993a,b, 1996] and Varotsos and Lazaridou  (these references will be referred to as VAN) relating seismic electrical signals (SES) to earthquakes, are invalid.