Mohamed Shoukri, Futwan Al-Mohanna
||Open Journal of Statistics, 2018, Vol.08 (02), pp.284-301
||Scientific Research Publishing Journal
Testing the equality of means of two normally distributed randomvariables when their variances are unequal is known in the statisticalliterature as the “Behrens-Fisher problem”. It is well-known that the posteriordistributions of the parameters of interest are the primitive of Bayesianstatistical inference. For routine implementation of statistical proceduresbased on posterior distributions, simple and efficient approaches are required.Since the computation of the exact posterior distribution of the Behrens-Fisherproblem is obtained using numerical integration, several approximations arediscussed and compared. Tests and Bayesian Highest-Posterior Density (H.P.D)intervals based upon these approximations are discussed. We extend the proposedapproximations to test of parallelism in simple... linear regression models.