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September, 1985 Coherent Predictions are Strategic
David A. Lane, William D. Sudderth
Ann. Statist. 13(3): 1244-1248 (September, 1985). DOI: 10.1214/aos/1176349669

Abstract

Two random quantities $x$ and $y$, taking values in sets $X$ and $Y$, are to be observed sequentially. A predicter (bookie) posts odds on $(x, y)$ and on $y$ given $x$ according to functions $P$ and $q(x)$, respectively. The predicter is coherent (the bookie can avoid a sure loss) if and only if $P$ is a finitely additive probability distribution on $X \times Y$ and $q$ satisfies a general law of total probability: $P(A) = \int q(x)(Ax)P_0(dx)$ for $A \subset X \times Y, Ax = \{y: (x, y) \in A\}, P_0 = \text{marginal of} P \text{on} X.$

Citation

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David A. Lane. William D. Sudderth. "Coherent Predictions are Strategic." Ann. Statist. 13 (3) 1244 - 1248, September, 1985. https://doi.org/10.1214/aos/1176349669

Information

Published: September, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0585.62004
MathSciNet: MR803771
Digital Object Identifier: 10.1214/aos/1176349669

Subjects:
Primary: 62A15
Secondary: 60A05

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 3 • September, 1985
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