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Efficient testing of earthquake forecasting models

David A. Rhoades, Danijel Schorlemmer, Matthew C. Gerstenberger, Annemarie Christophersen, & Jeremy D. Zechar

Published 2010, SCEC Contribution #1456

Computationally efficient alternatives are proposed to the likelihood-based tests employed by the Collaboratory for the Study of Earthquake Predictability (CSEP) for assessing the performance of regional 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 “T-test” is not computer-intensive, is easier to interpret than the R-test, and becomes increasingly dependable as the number of earthquakes increases.

Key Words
models, precursors, testing, earthquakes, earthquake prediction, seismic risk

Rhoades, D. A., Schorlemmer, D., Gerstenberger, M. C., Christophersen, A., & Zechar, J. D. (2010). Efficient testing of earthquake forecasting models. Acta Geophysica, 59(4), 728-747. doi: 10.2478/s11600-011-0013-5.