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November, 1978 Diffuse Models for Sampling and Predictive Inference
David A. Lane, William D. Sudderth
Ann. Statist. 6(6): 1318-1336 (November, 1978). DOI: 10.1214/aos/1176344377


As a natural, intuitive model for inferences about certain characteristics of finite populations, Bruce Hill has proposed a sequence of exchangeable variables $X_1, \cdots, X_{n + 1}$ which have distinct values with probability one and have the property that, conditional on $X_1, \cdots, X_n$, the next observation $X_{n + 1}$ is equally likely to fall in any of the $n + 1$ intervals determined by $X_1, \cdots, X_n$. Harold Jeffreys had previously assumed such a model (in the case $n = 2$) for normal measurements with unknown mean and variance. Hill has shown that, for $n \geqslant 1$, there exist no countably additive distributions with the prescribed properties. It is shown here that finitely additive distributions with these properties do exist for all $n$ and have a number of interesting properties.


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David A. Lane. William D. Sudderth. "Diffuse Models for Sampling and Predictive Inference." Ann. Statist. 6 (6) 1318 - 1336, November, 1978.


Published: November, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0398.62003
MathSciNet: MR523766
Digital Object Identifier: 10.1214/aos/1176344377

Primary: 62A15
Secondary: 28A35

Keywords: diffuse priors , exchangeable variables , Ferguson priors , finite additivity , Game theory , Polya urns , product measures , sampling models , strategic measures

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 6 • November, 1978
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