The Annals of Statistics

W. E. Johnson's "Sufficientness" Postulate

Sandy L. Zabell

Full-text: Open access

Abstract

How do Bayesians justify using conjugate priors on grounds other than mathematical convenience? In the 1920's the Cambridge philosopher William Ernest Johnson in effect characterized symmetric Dirichlet priors for multinomial sampling in terms of a natural and easily assessed subjective condition. Johnson's proof can be generalized to include asymmetric Dirichlet priors and those finitely exchangeable sequences with linear posterior expectation of success. Some interesting open problems that Johnson's result raises, and its historical and philosophical background, are also discussed.

Article information

Source
Ann. Statist., Volume 10, Number 4 (1982), 1090-1099.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345975

Digital Object Identifier
doi:10.1214/aos/1176345975

Mathematical Reviews number (MathSciNet)
MR673645

Zentralblatt MATH identifier
0512.62007

JSTOR
links.jstor.org

Subjects
Primary: 62A15
Secondary: 01A60: 20th century

Keywords
62-03 W. E. Johnson sufficientness postulate exchangeability Dirichlet prior Rudolph Carnap

Citation

Zabell, Sandy L. W. E. Johnson's "Sufficientness" Postulate. Ann. Statist. 10 (1982), no. 4, 1090--1099. doi:10.1214/aos/1176345975. https://projecteuclid.org/euclid.aos/1176345975


Export citation