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.

中文翻译：

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地面运动模型选择的多元贝叶斯假设检验

在本文中，提出了贝叶斯假设检验基础，用于选择，排序和分配权重至完全符合逻辑树经典定义的地震动预测方程。计算出作为描述数据的最佳模型的模型的后验概率，并且使用贝叶斯因子的定义来选择和加权预测模型。在模型排序和组合中，数据相关性的计算很重要，而这些评分方法通常缺少诸如中位数似然，平均对数似然，欧几里得距离排序和贝叶斯信息准则方法之类的评分程序。所提出的方法通过使用多元似然函数来考虑数据相关性（即，事件内以及事件之间和事件之间的相关性以及纵坐标之间的相关性）。虽然所提出的过程主要是客观的并且由数据驱动，但是贝叶斯更新规则允许通过使用先验概率来考虑专家的判断。所提出的方法被应用于NGA-West2数据集的子集，并根据可用数据对五个选定的NGA-West2模型进行了排序，并在不同的幅度和周期范围内加权。