Measuring statistical evidence using relative belief.
Measuring statistical evidence using relative belief.
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DOI：
10.1016/j.csbj.2015.12.001
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发表时间：
2016
影响因子：
6
通讯作者：
Evans M
中科院分区：
文献类型：
--
作者：
Evans M
统计推断理论的一个基本问题是，人们应该如何衡量统计证据。当然，“统计证据”这一词，或者仅仅是“证据”，在统计语境中经常被使用。然而，公平地说，对这一概念的准确描述有些难以捉摸。我们这里的目标是为任何特定的统计问题提供一个如何衡量统计证据的定义。由于证据是导致信念改变的原因，因此建议通过信念从先验到后验的变化量来衡量证据。因此，我们的定义涉及先前的信念，这就提出了统计分析中主观性与客观性的问题。这是通过一个原则来处理的，该原则要求统计分析的任何成分都是可证伪的。这些顾虑导致检查先验数据冲突并测量先验数据中的先验偏差。
A fundamental concern of a theory of statistical inference is how one should measure statistical evidence. Certainly the words “statistical evidence,” or perhaps just “evidence,” are much used in statistical contexts. It is fair to say, however, that the precise characterization of this concept is somewhat elusive. Our goal here is to provide a definition of how to measure statistical evidence for any particular statistical problem. Since evidence is what causes beliefs to change, it is proposed to measure evidence by the amount beliefs change from a priori to a posteriori. As such, our definition involves prior beliefs and this raises issues of subjectivity versus objectivity in statistical analyses. This is dealt with through a principle requiring the falsifiability of any ingredients to a statistical analysis. These concerns lead to checking for prior-data conflict and measuring the a priori bias in a prior.