The Stochastic Area Metric for the Selection and Ranking of Ground-Motion Models.

Abstract:

The predictive capability of a ground motion model (GMM) and the selection of the best GMM for a given application from the growing suite of predictive models poses many challenges. Typically, for instance, model testing and ranking do not appropriately account for uncertainties, thus leading to improper ranking. We introduce the cumulative distribution area metric (AM) as a scoring metric for the GMM, which not only informs the user of the degree to which observed or test data fit with the model but also considers the uncertainties without the assumption of how data are distributed. The proposed method is advantageous in many ways as it assesses the whole distribution with equal importance, retains the physical units of the data and can be unbounded. The best fit model for a given dataset would be the one that gives the minimum area value. We apply this metric along with existing testing methods to recent and commonly used European ground motion prediction equations - Bindi et al. (2014, B014), Akkar et al. (2014, A014) and Cauzzi et al. (2015, C015), to rank them and to analyze their performance using the European Engineering Strong Motion (ESM) dataset. We focus on the ranking of models for ranges of magnitude and distance with sparse data, which pose a specific problem with other statistical testing methods. Performance of models in different ranges of data analyzed using AM revealed the importance of considering specific models for certain ranges of data. We find the A014 model displays good performance with complete dataset while B014 appears to be suitable for ranges of small magnitudes and distance. This metric is shown to be convenient and robust in the process of selection and ranking of GMMs for various applications.