%0 Journal Article
%T Bayesian Analysis of the Behrens-Fisher Problem under a Gamma Prior
%A Nengak Emmanuel Goltong
%A Sani Ibrahim Doguwa
%J Open Journal of Statistics
%P 902-914
%@ 2161-7198
%D 2018
%I Scientific Research Publishing
%R 10.4236/ojs.2018.86060
%X Yin<span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"> [1]</span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"> has developed a new Bayesian measure</span></span></span><span><span><span style=\"font-family:;\" \"=\"\"> </span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">of evidence
for testing a point null hypothesis which agrees with the frequentist p-value
thereby, solving Lindley¡¯s paradox. Yin and Li</span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"> [2]</span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"> extended the methodology of Yin</span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"> [1]</span></span></span><span><span><span style=\"font-family:;\" \"=\"\"><span style=\"font-family:Verdana;\"> 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</span><span style=\"color:#943634;\">&nbsp;</span></span></span></span><span><span><span style=\"font-family:Verdana;\">[1]</span><span></span></span></span><span><span></span></span><span></span><span><span></span></span><span><span><span style=\"font-family:;\" \"=\"\"> </span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">solves
simultaneously, the Behrens-Fisher problem and Lindley¡¯s paradox when a Gamma
prior is assigned to the nuisance parameters.</span></span></span>
%K Behrens-Fisher Problem
%K Lindley¡¯s Paradox
%K Metropolis-Hastings Algorithm
%K Informative Priors
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=88956