Abstract Bayesian Model Averaging (BMA) is a well-known statistical post-processing approach for probabilistically merging individual forecasts. In BMA, the posterior distribution of the predictand variable is determined by implementing the law of total probability. Therefore, possessing an ensemble of independent members (mutually exclusive) with the highest information content about observation variability (collectively exhaustive) is the main inherent assumption of the original BMA method. Mutually exclusive and collectively exhaustive are two contradictory criteria. Although constructing an ensemble of members that fully satisfied these two properties is practically impossible, providing a balance between them is a key requirement for enhancing the BMA performance. Through coupling BMA with Shannon entropy of information theory, this study proposes an entropy-based selection procedure to construct an ensemble of streamflow forecasts by better addressing the aforementioned contradictory criteria prior to performing the BMA. We investigate the effects of using ensembles with the aforementioned properties by comparing the results of original BMA with the proposed entropy-based BMA (En-BMA) for short- to medium-range daily streamflow forecasts in two different watersheds. The results indicate that the En-BMA leads to better results particularly for high flow predictions. Both probabilistic and deterministic high flow forecasts are more accurate and reliable when using the En-BMA approach. However, for the average flow forecasts, there are no clear differences in the general performance of both methods. The improvements observed are more pronounced for shorter lead-times and less pronounced, but still present, for longer lead times.

中文翻译：

---

介绍基于熵的贝叶斯模型平均用于流量预测

摘要 贝叶斯模型平均 (BMA) 是一种众所周知的统计后处理方法，用于概率合并单个预测。在 BMA 中，预测变量的后验分布是通过实施全概率定律来确定的。因此，拥有一个独立成员（互斥）的集合，其关于观测变异性的信息含量最高（集体详尽）是原始 BMA 方法的主要内在假设。相互排斥和共同详尽是两个相互矛盾的标准。尽管构建一个完全满足这两个属性的成员集合实际上是不可能的，但在它们之间提供平衡是提高 BMA 性能的关键要求。通过将 BMA 与信息论的香农熵耦合，本研究提出了一种基于熵的选择程序，通过在执行 BMA 之前更好地解决上述矛盾标准来构建流量预测集合。我们通过将原始 BMA 的结果与提出的基于熵的 BMA (En-BMA) 的结果进行比较，研究使用具有上述特性的集合对两个不同流域的中短期日流量预测的影响。结果表明，En-BMA 导致更好的结果，特别是对于高流量预测。使用 En-BMA 方法时，概率性和确定性高流量预测都更加准确和可靠。然而，对于平均流量预测，两种方法的总体性能没有明显差异。