Fully Coherent Inference
The Annals of Statistics · 1991 · Volume 19 · Issue 2
Abstract
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.
Keywords
60A05, 62A15, Coherence, expectation consistent inference
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