The Role of Prior Probabilities on Parameter Estimation in Hydrological Models
The Role of Prior Probabilities on Parameter Estimation in Hydrological Models
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DOI：
10.1029/2021wr031291
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发表时间：
2022-04
影响因子：
5.4
通讯作者：
A. Gupta;R. Govindaraju;R. Morbidelli;C. Corradini
中科院分区：
文献类型：
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作者：
A. Gupta;R. Govindaraju;R. Morbidelli;C. Corradini
贝叶斯定理为在存在测量误差和结构误差的情况下结合先验信息和样本信息进行参数估计提供了一个形式框架。然而，先验知识可能并不总是可用的，或者可能过于含糊而无法纳入先前的分发。在这种情况下，必须选择参考先验进行客观分析。通常，在可能的参数范围内选择均匀的密度作为参考先验。然而，统一先验作为参考先验的有效性很少受到质疑。在这项研究中，采用信息论的方法来获得参考先验，并将其结果与使用一致先验所获得的结果进行了比较。文中给出了估算饱和导水率的实例。用信息论方法得到的导水率的先验是变换不变的，而且通常是不均匀的。当样本信息较小时，信息论和均匀先验之间的选择会影响渗透系数的后验分布。还通过PDG-GIUH水文模型演示了参考先验的使用，并讨论了计算可处理性的问题。
Bayes theorem provides a formal framework for combining prior and sample information for parameter estimation in the presence of measurement and structural errors. Prior knowledge, however, may not always be available or may be too vague to incorporate into a prior distribution. In such cases, a reference prior must be chosen for an objective analysis. Typically, a uniform density over the possible ranges of parameters is chosen as the reference prior. However, the validity of a uniform prior as a reference prior is seldom questioned. In this study, an information‐theoretic approach is pursued to derive reference priors, and the results are compared to those obtained by using a uniform prior. Examples of estimating saturated hydraulic conductivity are presented. Priors over hydraulic conductivity obtained by using the information‐theoretic approach are transformation‐invariant and typically nonuniform. The choice between information‐theoretic and uniform prior influences the posterior distribution of hydraulic conductivity, when sample information is small. The use of reference prior is also demonstrated through the PDG‐GIUH hydrologic model, and issues of computational tractability are addressed.