## The Annals of Statistics

### On the existence of inferences which are consistent with a given model

#### Abstract

4 If ${p_{\theta}$ is a $\sigma$-additive statistical model and $\pi$ a finitely additive prior, then any statistic T is sufficient, with respect to a suitable inference consistent with ${p_{\theta}$ and $\pi$, provided only that $p_{\theta}(T = t) = 0$ for all $\theta$ and t. Here, sufficiency is to be intended in the Bayesian sense, and consistency in the sense of Lane and Sudderth. As a corollary, if ${p_{\theta}$ is $\sigma$-additive and diffuse, then, whatever the prior $\pi$, there is an inference which is consistent with ${p_{\theta}$ and $\pi$. Two versions of the main result are also obtained for predictive problems.

#### Article information

Source
Ann. Statist., Volume 24, Number 3 (1996), 1235-1249.

Dates
First available in Project Euclid: 20 September 2002

https://projecteuclid.org/euclid.aos/1032526966

Digital Object Identifier
doi:10.1214/aos/1032526966

Mathematical Reviews number (MathSciNet)
MR1401847

Zentralblatt MATH identifier
0866.62001

Subjects
Primary: 62A15
Secondary: 60A05: Axioms; other general questions

#### Citation

Berti, Patrizia; Rigo, Pietro. On the existence of inferences which are consistent with a given model. Ann. Statist. 24 (1996), no. 3, 1235--1249. doi:10.1214/aos/1032526966. https://projecteuclid.org/euclid.aos/1032526966

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