Author(s)

Mohamed Shoukri^*, Futwan Al-Mohanna

Department of Cell Biology, National Biotechnology Center, Research Centre, King Faisal Specialist Hospital and Research Center, Riyadh, Saudi Arabia.

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.

Bayesian Inference, Posterior Distributions, Behrens-Fisher Problem, Posterior Moments, Edgeworth Expansion, Monte-Carlo Integration

Shoukri, M. and Al-Mohanna, F. (2018) Extending the Behrens-Fisher Problem to Testing Equality of Slopes in Linear Regression: The Bayesian Approach. Open Journal of Statistics, 8, 284-301. doi: 10.4236/ojs.2018.82018.