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The Area Skill Score Statistic for Evaluating Earthquake Predictability Experiments

Jeremy D. Zechar, & Thomas H. Jordan

Accepted 2010, SCEC Contribution #1216

Rigorous predictability experimentation requires a statistical characterization of the performance metric used in experimental evaluation. Here we explore the statistical properties of the area skill score metric proposed by Zechar & Jordan (2008) and consider issues related to experimental discretization. For the case of continuous alarm functions and continuous observations, we present exact analytical solutions describing the distribution of the area skill score for unskilled predictors, and the approximation of this distribution by a Gaussian with known mean and variance. We also quantify the deviation of the exact area skill score distribution from the Gaussian approximation by specifying the kurtosis excess as a function of the number of observed earthquakes. For predictability experiments involving discretization of the study region, we analyze simulation procedures for estimating the area skill score distribution, and we present efficient algorithms for various experimental scenarios. When more than one of the observed target earthquakes occurs within the same space/time/magnitude cell, the probabilities of predicting these events are not independent, which requires special consideration.

Zechar, J. D., & Jordan, T. H. (2010). The Area Skill Score Statistic for Evaluating Earthquake Predictability Experiments. Pure and Applied Geophysics, (accepted).