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June, 1991 Fully Coherent Inference
H. D. Brunk
Ann. Statist. 19(2): 830-849 (June, 1991). DOI: 10.1214/aos/1176348123


In a general setting in which prior distributions that may take on the value $\infty$ are admitted, an inference based on a posterior for a prior, $\mu$, that is "minimally compatible" with the inference is shown to have a strong property of expectation consistency, that implies a corresponding property of coherence: A nonnegative expected payoff function for a gambler's strategy is necessary 0 almost everywhere $(\mu)$. In the converse direction, under appropriate regularity conditions involving continuity of the sampling distribution and of the inference, a weaker version of coherence implies that the inference is based on a posterior distribution.


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H. D. Brunk. "Fully Coherent Inference." Ann. Statist. 19 (2) 830 - 849, June, 1991.


Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0737.62001
MathSciNet: MR1105847
Digital Object Identifier: 10.1214/aos/1176348123

Primary: 62A15
Secondary: 60A05

Keywords: Coherence , expectation consistent inference

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 2 • June, 1991
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