A model of prior ignorance for inferences in the one-parameter exponential family
- 作者：Alessio Benavoli ; alessio@idsia.ch ; Marco Zaffalon zaffalon@idsia.ch
- 关键词：Prior ignorance ; Exponential families ; Lower and upper expectations
- 刊名：Journal of Statistical Planning and Inference
- 出版年：2012
- 期刊代码：36_03783758
- 类别：mt
- 出版时间：July, 2012
- 卷：142
- 期：7
- 页码：1960-1979
- 文件大小：445 K
摘要
This paper proposes a model of prior ignorance about a scalar variable based on a set of distributions . In particular, a set of minimal properties that a set of distributions should satisfy to be a model of prior ignorance without producing vacuous inferences is defined. In the case the likelihood model corresponds to a one-parameter exponential family of distributions, it is shown that the above minimal properties are equivalent to a special choice of the domains for the parameters of the conjugate exponential prior. This makes it possible to define the largest (that is, the least-committal) set of conjugate priors that satisfies the above properties. The obtained set is a model of prior ignorance with respect to the functions (queries) that are commonly used for statistical inferences; it is easy to elicit and, because of conjugacy, tractable; it encompasses frequentist and the so-called objective Bayesian inferences with improper priors. An application of the model to a problem of inference with count data is presented.