Constraints versus Priors
Constraints versus Priors
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DOI：
10.1137/130920721
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发表时间：
2015-07
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影响因子：
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通讯作者：
P. Stark
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文献类型：
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作者：
P. Stark
贝叶斯和频率论在量化不确定性方面存在深刻而重要的哲学差异。然而，一些从业者主要根据方便性在这些方法之间进行选择。例如，结合参数约束的能力有时被引用为使用贝叶斯方法的原因。这反映了两个误解：第一，频率论方法确实可以包含对参数值的约束。其次，它忽略了分析结果意味着什么这一关键问题。贝叶斯和频率论的不确定性度量有着相似的名字，但含义却大不相同。例如，贝叶斯不确定性通常涉及关于参数的后验分布的期望，保持数据固定;频率论不确定性通常涉及关于数据分布的期望，保持参数固定。贝叶斯方法，包括方法纳入参数约束，要求…
There are deep and important philosophical differences between Bayesian and frequentist approaches to quantifying uncertainty. However, some practitioners choose between these approaches primarily on the basis of convenience. For instance, the ability to incorporate parameter constraints is sometimes cited as a reason to use Bayesian methods. This reflects two misunderstandings: First, frequentist methods can indeed incorporate constraints on parameter values. Second, it ignores the crucial question of what the result of the analysis will mean. Bayesian and frequentist measures of uncertainty have similar sounding names but quite different meanings. For instance, Bayesian uncertainties typically involve expectations with respect to the posterior distribution of the parameter, holding the data fixed; frequentist uncertainties typically involve expectations with respect to the distribution of the data, holding the parameter fixed. Bayesian methods, including methods incorporating parameter constraints, requ...