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Cuzick, J., Dowsett, M., Pineda, S., Wale, C., Salter, J., Quinn, E., et al. (2011) Prognostic Value of a Combined Estrogen Receptor, Progesterone Receptor, Ki-67, and Human Epidermal Growth Factor Receptor 2 Immuno-Histochemical Score and Comparison with the Genomic Health Recurrence Score in Early Breast Cancer. Journal of Clinical Oncology, 29, 4273-4278.

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• 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.