Bayesian Analysis of the Behrens-Fisher Problem under a Gamma Prior - Open Journal of Statistics

OJS > Vol.8 No.6, December 2018

Bayesian Analysis of the Behrens-Fisher Problem under a Gamma Prior ()

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DOI: 10.4236/ojs.2018.86060 580 Downloads 1,163 Views Citations

Author(s)

Nengak Emmanuel Goltong^*, Sani Ibrahim Doguwa

Affiliation(s)

Department of Statistics, Ahmadu Bello University, Zaria, Nigeria.

ABSTRACT

Yin [1] has developed a new Bayesian measure of evidence for testing a point null hypothesis which agrees with the frequentist p-value thereby, solving Lindley’s paradox. Yin and Li [2] extended the methodology of Yin [1] 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 [1] solves simultaneously, the Behrens-Fisher problem and Lindley’s paradox when a Gamma prior is assigned to the nuisance parameters.

KEYWORDS

Behrens-Fisher Problem, Lindley’s Paradox, Metropolis-Hastings Algorithm, Informative Priors

Share and Cite:

Goltong, N. and Doguwa, S. (2018) Bayesian Analysis of the Behrens-Fisher Problem under a Gamma Prior. Open Journal of Statistics, 8, 902-914. doi: 10.4236/ojs.2018.86060.

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