Testing earthquake forecast hypotheses

This paper outlines methodological aspects of the statistical evaluation of earthquake forecast hypotheses. The recent debates concerning predictabili ty of earthquakes clearly show how this problem is centred on the difficult y of systematically testing the numerous methodologies that in the years ha ve been proposed and sustained by the supporters of prediction. This diffic ulty starts, sometimes, from the lack of a quantitative and rigorous defini tion of the concerned precursor, and other times from the lack of continuou s observations, upon which statistical analyses could be based. The application of rigorous statistical methods, with the aim of verifying any prediction method, requires a univocal definition of the hypothesis, or the model, characterising the concerned anomaly or precursor, so as it can be recognised objectively in any circumstance and by any observer. A simpl e definition of an earthquake forecasting hypothesis could consist of the i dentification of particular sub-volumes of the total time-space volume (usu ally named alarm volumes) within which the probability of occurrence of str ong earthquakes is higher than the average. The test of a similar model nee ds the observation of a sufficient number of past cases upon which to carry out a statistical analysis aimed to determine the rate at which the precur sor has been followed (success rate) or not followed (false alarm, rate) by the target seismic event, or the rate at which a target event has been pre ceded (alarm rate) or not preceded (failure rate) by the precursor. A valid forecast hypothesis is expected to maximise success and minimise false ala rms, with regard also to the maximisation of the probability gain. Some geo physicists prefer a statistical approach such as the B ayes criterion, base d on the computation of the likelihood of an observed realisation of seismi c events, and on the comparison of the likelihood obtained under different hypotheses. This method can be extended, as it has recently been the case f or models of earthquake clustering, to algorithms that allow the computatio n of the density distribution of the conditional probability of earthquake occurrence in space, time and magnitude. Another approach to assess the val idity of an earthquake forecast hypothesis could be that of estimating the total cost that the community has to pay in relation to earthquakes, and ch oosing the model that minimise such cost. Whatever method is chosen for building up a new hypothesis, the final asses sment of its validity should be carried out by a test on a new and independ ent set of observations. The implementation of this test could, however, be problematic for seismicity characterised by long-term recurrence. (C) 2001 Elsevier Science B.V. All rights reserved.