TITLE:
Bayesian Analysis of the Behrens-Fisher Problem under a Gamma Prior
AUTHORS:
Nengak Emmanuel Goltong, Sani Ibrahim Doguwa
KEYWORDS:
Behrens-Fisher Problem, Lindley’s Paradox, Metropolis-Hastings Algorithm, Informative Priors
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.6,
December
4,
2018
ABSTRACT: Yin [1] has developed a new Bayesian measure of evidence
for testing a point null hypothesis which agrees with the frequentist p-value
thereby, solving Lindley’s paradox. Yin and Li [2] extended the methodology of Yin [1] to the case of the Behrens-Fisher problem by assigning Jeffreys’
independent prior to the nuisance parameters. In this paper, we were able to
show both analytically and through the results from simulation studies that the
methodology of Yin[1] solves
simultaneously, the Behrens-Fisher problem and Lindley’s paradox when a Gamma
prior is assigned to the nuisance parameters.