The Annals of Statistics

Lower Bounds on Bayes Factors for Multinomial Distributions, with Application to Chi-Squared Tests of Fit

Mohan Delampady and James O. Berger

Full-text: Open access

Abstract

Lower bounds on Bayes factors in favor of the null hypothesis in multinomial tests of point null hypotheses are developed. These are then applied to derive lower bounds on Bayes factors in both exact and asymptotic chi-squared testing situations. The general conclusion is that the lower bounds tend to be substantially larger than $P$-values, raising serious questions concerning the routine use of moderately small $P$-values (e.g., 0.05) to represent significant evidence against the null hypothesis.

Article information

Source
Ann. Statist., Volume 18, Number 3 (1990), 1295-1316.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347750

Digital Object Identifier
doi:10.1214/aos/1176347750

Mathematical Reviews number (MathSciNet)
MR1062709

Zentralblatt MATH identifier
0712.62027

JSTOR
links.jstor.org

Subjects
Primary: 62A15
Secondary: 62F15: Bayesian inference

Keywords
Conjugate densities unimodal spherically symmetric densities $P$-values point null hypotheses tests of fit

Citation

Delampady, Mohan; Berger, James O. Lower Bounds on Bayes Factors for Multinomial Distributions, with Application to Chi-Squared Tests of Fit. Ann. Statist. 18 (1990), no. 3, 1295--1316. doi:10.1214/aos/1176347750. https://projecteuclid.org/euclid.aos/1176347750


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