Earthquake prediction analysis: The M8 algorithm

The quality of space-time earthquake prediction is usually characterized by a two-dimensional error diagram (n,tau), where 'n' is the rate of failures-to-predict and 'tau' is the normalized measure of space-time alarm. The most interesting space measure for analysis of a prediction strategy is the rate of target events m(dg) in a sub-area 'dg'. In this case the quantity H=1-(n+tau) determines the prediction capability of the strategy. The uncertainty of m(dg) causes difficulties in estimating 'H' and the statistical significance, 'alfa', of prediction results. We investigate this problem theoretically and show how the uncertainty of the measure can be taken into account in two situations, viz., the estimation of 'alfa' and the construction of a confidence zone for (n,tau)-parameters of the random strategies. We use our results to analyse the M8 earthquake prediction algorithm.