Multivariate Bayesian hypothesis testing for ground motion model selection

In this paper, the Bayesian hypothesis testing basis is proposed for selecting, ranking, and assigning weights to ground motion prediction equations that fits perfectly on the classical definition of a logic tree. The posterior probability of a model being the best model describing the data is calculated, and the definition of Bayes factors is used for selecting and weighting prediction models. Accounting for data correlation is important in model ranking and combination which is missing from the commonly used scoring procedures such as the median likelihood, average log-likelihood, Euclidean distance ranking, and the Bayesian information criterion methods. The proposed method considers data correlation (i.e., within event and between event correlation and correlation between ordinates) by utilizing a multivariate likelihood function. While the proposed procedure is mostly objective and data-driven, the Bayesian updating rule allows for consideration of expert’s judgment by using prior probabilities. The proposed method is applied to subsets of the NGA-West2 dataset, and five selected NGA-West2 models are ranked and weighted in different magnitude and period ranges according to available data.