TITLE:
Extending the Behrens-Fisher Problem to Testing Equality of Slopes in Linear Regression: The Bayesian Approach
AUTHORS:
Mohamed Shoukri, Futwan Al-Mohanna
KEYWORDS:
Bayesian Inference, Posterior Distributions, Behrens-Fisher Problem, Posterior Moments, Edgeworth Expansion, Monte-Carlo Integration
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.2,
April
13,
2018
ABSTRACT: Testing the equality of means of two normally distributed random
variables when their variances are unequal is known in the statistical
literature as the “Behrens-Fisher problem”. It is well-known that the posterior
distributions of the parameters of interest are the primitive of Bayesian
statistical inference. For routine implementation of statistical procedures
based on posterior distributions, simple and efficient approaches are required.
Since the computation of the exact posterior distribution of the Behrens-Fisher
problem is obtained using numerical integration, several approximations are
discussed and compared. Tests and Bayesian Highest-Posterior Density (H.P.D)
intervals based upon these approximations are discussed. We extend the proposed
approximations to test of parallelism in simple linear regression models.