This paper introduces for the first time the concept of Bayesian model averaging (BMA) with multiple prior structures, for rainfall‐runoff modeling applications. The original BMA model proposed by Raftery et al. (2005, https://doi.org.10.1175/MWR2906.1) assumes that the prior probability density function (pdf) is adequately described by a mixture of Gamma and Gaussian distributions. Here we discuss the advantages of using BMA with fixed and flexible prior distributions. Uniform, Binomial, Binomial‐Beta, Benchmark, and Global Empirical Bayes priors along with Informative Prior Inclusion and Combined Prior Probabilities were applied to calibrate daily streamflow records of a coastal plain watershed in the southeast United States. Various specifications for Zellner's g prior including Hyper, Fixed, and Empirical Bayes Local (EBL) g priors were also employed to account for the sensitivity of BMA and derive the conditional pdf of each constituent ensemble member. These priors were examined using the simulation results of conceptual and semidistributed rainfall‐runoff models. The hydrologic simulations were first coupled with a new sensitivity analysis model and a parameter uncertainty algorithm to assess the sensitivity and uncertainty associated with each model. BMA was then used to subsequently combine the simulations of the posterior pdf of each constituent hydrological model. Analysis suggests that a BMA based on combined fixed and flexible priors provides a coherent mechanism and promising results for calculating a weighted posterior probability compared to individual model calibration. Furthermore, the probability of Uniform and Informative Prior Inclusion priors received significantly lower predictive error, whereas more uncertainty resulted from a fixed g prior (i.e., EBL).

中文翻译：

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贝叶斯模型在固定和灵活先验条件下的平均：降雨径流模型的理论，概念和校准实验

本文首次介绍了具有多个先验结构的贝叶斯模型平均（BMA）概念，用于降雨径流建模应用。Raftery等人提出的原始BMA模型。（2005，https：//doi.org.10.1175/MWR2906.1）假定先验概率密度函数（pdf）由Gamma和高斯分布的混合充分描述。在这里，我们讨论使用具有固定和灵活的先验分布的BMA的优势。统一，二项式，二项式-贝塔，基准和全球经验贝叶斯先验以及信息先验包含和联合先验概率被用于校准美国东南沿海平原流域的每日流量记录。Zellner's g的各种规格先验，包括本地超级，固定和经验贝叶斯（EBL）g先验也被用来解释BMA的敏感性，并得出每个组成整体成员的条件pdf。使用概念性和半分布式降雨径流模型的模拟结果检查了这些先验。首先将水文模拟与新的敏感性分析模型和参数不确定性算法相结合，以评估与每个模型相关的敏感性和不确定性。然后使用BMA随后结合每个组成水文模型的后pdf的模拟。分析表明，基于固定和灵活先验组合的BMA与单个模型校准相比，为计算加权后验概率提供了一种连贯的机制和有希望的结果。此外，g优先（即EBL）。