论决策理论在不确定性分析中的作用
On the Role of Decision Theory in Uncertainty Analysis
摘要：
极大似然估计（MLE）和启发式预测估计（HPE）是工业不确定性分析中应用最广泛的两种方法。我们从决策理论的角度来回顾它们，使用贝叶斯推断作为比较的金标准。MLE的主要缺点是它可能无法正确地解释生成数据的物理过程的不确定性，特别是当只有少量数据可用时。HPE提供了一种改进，因为它考虑到了这种不确定性。然而，我们表明，这种方法实际上是等价于贝叶斯估计的一个特定的成本函数，这是没有明确选择的决策者。从决策的角度来看，这可能会产生次优的结果。这些结果恳求系统使用贝叶斯估计仔细定义的成本函数的基础上。
英文摘要：
Maximum likelihood estimation (MLE) and heuristic predictive estimation (HPE) are two widely used approaches in industrial uncertainty analysis. We review them from the point of view of decision theory, using Bayesian inference as a gold standard for comparison. The main drawback of MLE is that it may fail to properly account for the uncertainty on the physical process generating the data, especially when only a small amount of data are available. HPE offers an improvement in that it takes this uncertainty into account. However, we show that this approach is actually equivalent to Bayes estimation for a particular cost function that is not explicitly chosen by the decision maker. This may produce results that are suboptimal from a decisional perspective. These results plead for a systematic use of Bayes estimators based on carefully defined cost functions.
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