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Testing long-term earthquake forecasts: likelihood methods and error diagrams

Yan Y. Kagan

Published 2009, SCEC Contribution #1252

We propose a new method to test the performance of a spatial <br/>point process forecast based on a log-likelihood score for <br/>predicted point density and the information gain for events <br/>that actually occurred in the test period. <br/>The method largely avoids simulation use and allows us to <br/>calculate the information score for each event or set of <br/>events as well as the standard error of each forecast. <br/>As the number of predicted events increases, the score <br/>distribution approaches the Gaussian law. <br/>The degree of its similarity to the Gaussian distribution can <br/>be measured by the computed coefficients of skewness and <br/>kurtosis. <br/>To display the forecasted point density and the point events, <br/>we use an event concentration diagram or a variant of the <br/>Error Diagram (ED). <br/>We find forward relation between the error diagram curve and <br/>the information score as well as inverse relation for one <br/>simple model of point spatial fields. <br/>We again show that the error diagram is more informative than <br/>the likelihood ratio.<br/><br/>We demonstrate the application of the method by using our <br/>long-term forecast of seismicity in two western Pacific <br/>regions. <br/>We compare the ED for these regions with simplified diagrams <br/>based on two-segment approximations. <br/>Since the earthquakes in these regions are concentrated in <br/>narrow subduction belts, using the forecast density as a <br/>template or baseline for the ED is a more convenient display <br/>technique. <br/>We also show, using simulated event occurrence, that some <br/>proposed criteria for measuring forecast effectiveness at EDs <br/>would be strongly biased for a small event number. <br/> <br/>

Kagan, Y. Y. (2009). Testing long-term earthquake forecasts: likelihood methods and error diagrams. Geophysical Journal International, 177(2), 532-542.