Merging data and experts’ knowledge-based weights for ranking GMPEs

Abstract

In this article, Bayes factors (BFs) are used for selecting and weighting the ground motion prediction equations (GMPEs). BFs are defined as the posterior probability of a model being the best model describing data. The Bayesian framework allows for merging information gathered from available seismic data and the experts’ opinion thus allowing for a bridge between data-driven and non-data-driven methods. A multi-dimensional likelihood function is used to account for earthquake-to-earthquake and record-to-record variability. A study is performed to identify the effects of model uncertainty and dataset variations on Bayesian weights by using simulated data. It was found that for a given median prediction, by increasing standard deviation the relative weights increase until it reaches a maximum and then start to decrease. The standard deviation corresponding to the maximum weights corresponds to the scatter of data used for calculating the weights. The method was applied to a local region with nine preselected local and regional GMPEs. The ranking, selection, and weighting are performed using a local dataset and the results are compared with four available ranking methods. While various methods may yield similar or different ranking results, the proposed method is the only one that provides scientific means of selecting appropriate models from a set of initially selected GMPEs.