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The behrens‐fisher problem revisited: A bayes‐frequentist synthesis
Author(s) -
Ghosh Malay,
Kim YeongHwa
Publication year - 2001
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3316047
Subject(s) - frequentist inference , credible interval , mathematics , coverage probability , confidence interval , statistics , interval (graph theory) , bayes' theorem , frequentist probability , binomial proportion confidence interval , interval estimation , statistical inference , inference , fisher information , bayesian probability , confidence distribution , econometrics , bayesian inference , computer science , combinatorics , artificial intelligence , negative binomial distribution , poisson distribution
The Behrens‐Fisher problem concerns the inference for the difference between the means of two normal populations whose ratio of variances is unknown. In this situation, Fisher's fiducial interval differs markedly from the Neyman‐Pearson confidence interval. A prior proposed by Jeffreys leads to a credible interval that is equivalent to Fisher's solution but it carries a different interpretation. The authors propose an alternative prior leading to a credible interval whose asymptotic coverage probability matches the frequentist coverage probability more accurately than the interval of Jeffreys. Their simulation results indicate excellent matching even in small samples.