The Area Skill Score Statistic for Evaluating Earthquake Predictability Experiments

Rigorous predictability experimentation requires a statistical characterization of the performance metric used to evaluate the participating models. We explore the properties of the area skill score measure and consider issues related to experimental discretization. For the case of continuous alarm...

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Bibliographic Details
Published in:Pure and applied geophysics 2010-08, Vol.167 (8-9), p.893-906
Main Authors: Zechar, J. Douglas, Jordan, Thomas H.
Format: Article
Language:English
Subjects:
Alarm systems
Algorithms
Approximation
Discretization
Earth and Environmental Science
Earth Sciences
Earthquake prediction
Earthquakes
Experiments
Geophysics/Geodesy
Mathematical analysis
Mathematical models
Predictions
Seismic activity
Seismic phenomena
Skills
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Summary:Rigorous predictability experimentation requires a statistical characterization of the performance metric used to evaluate the participating models. We explore the properties of the area skill score measure and consider issues related to experimental discretization. For the case of continuous alarm functions and continuous observations, we present exact analytical solutions that describe the distribution of the area skill score for unskilled predictors, and we also describe how a Gaussian distribution with known mean and variance can be used to approximate the area skill score distribution. We quantify the deviation of the exact distribution from the Gaussian approximation by specifying the kurtosis excess as a function of the number of observed target earthquakes. For numerical earthquake predictability experiments that involve discretization of the study region and observations, we explore simulation procedures for estimating the area skill score distribution, and we present efficient algorithms for various experimental scenarios. When more than one target earthquake occurs within a given space/time/magnitude bin, the probabilities of predicting individual events are not independent, and this requires special consideration. Having presented the statistical properties of the area skill score, we describe and illustrate a preliminary procedure for comparing earthquake prediction strategies based on alarm functions.
ISSN:0033-4553
1420-9136
DOI:10.1007/s00024-010-0086-0