Invariance of posterior distributions under reparametrization
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- 作者：Morris L. Eaton (12) eaton@stat.umn.edu
William D. Sudderth (1) bill@stat.umn.edu - 关键词：and phrases Jeffreys priors ; invariance under reparametrization ; group invariant models and Jeffreys invariance ; coordinate system choices and prior distributions
- 刊名：Sankhya A
- 出版时间：February 2010
- 出版年：2010
- 期刊代码：163_0976-8378
- 类别：mat
- 卷：72
- 期：1
- 页码：101-118
- 数据来源：sp
摘要
In 1946, Sir Harold Jeffreys introduced a prior distribution whose density is the square root of the determinant of Fisher information. The motivation for suggesting this prior distribution is that the method results in a posterior that is invariant under reparametrization. For invariant statistical models when there is a transitive group action on the parameter space, it is shown that all relatively invariant priors have this “Jeffreys Invariance” property. However, this invariance may not prevail when using a subtle modification suggested by an alternative argument.