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On the testing of seismicity models

Molchan G.

Acta Geophysica

2012

Vol. 60, no. 3

624-637

Recently a likelihood-based methodology has been developed by the Collaboratory for the Study of Earthquake Predictability (CSEP) with a view to testing and ranking seismicity models. We analyze this approach from the standpoint of possible applications to hazard analysis. We arrive at the conclusion that model testing can be made more efficient by focusing on some integral characteristics of the seismicity distribution. This can be achieved either in the likelihood framework but with economical and physically reasonable coarsening of the phase space or by choosing a suitable measure of closeness between empirical and model seismicity rate in this space.

Efficient testing of earthquake forecasting models

Rhoades D.A., Schorlemmer D., Gerstenberger M.C., Christophersen A., Zechar J.D., Imoto M.

Acta Geophysica

2011

Vol. 59, no. 4

728-747

Computationally efficient alternatives are proposed to the likelihood- based tests employed by the Collaboratory for the Study of Earthquake Predictability for assessing the performance of earthquake likelihood models in the earthquake forecast testing centers. For the conditional L-test, which tests the consistency of the earthquake catalogue with a model, an exact test using convolutions of distributions is available when the number of earthquakes in the test period is small, and the central limit theorem provides an approximate test when the number of earthquakes is large. Similar methods are available for the R-test, which compares the likelihoods of two competing models. However, the R-test, like the N-test and L-test, is fundamentally a test of consistency of data with a model. We propose an alternative test, based on the classical paired t-test, to more directly compare the likelihoods of two models. Although approximate and predicated on a normality assumption, this new T-test is not computer-intensive, is easier to interpret than the R-test, and becomes increasingly dependable as the number of earthquakes increases.