On Analysis of the Behrens-Fisher Problem Based on Bayesian Evidence - Open Journal of Statistics

OJS > Vol.9 No.1, February 2019

On Analysis of the Behrens-Fisher Problem Based on Bayesian Evidence ()

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DOI: 10.4236/ojs.2019.91001 758 Downloads 1,334 Views Citations

Author(s)

Nengak Emmanuel Goltong^*, Sani Ibrahim Doguwa

Affiliation(s)

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

ABSTRACT

In this paper we have demonstrated the ability of the new Bayesian measure of evidence of Yin (2012, Computational Statistics, 27: 237-249) to solve both the Behrens-Fisher problem and Lindley's paradox. We have provided a general proof that for any prior which yields a linear combination of two independent t random variables as posterior distribution of the dierence of means, the new Bayesian measure of evidence given that prior will solve Lindleys' paradox thereby serving as a general proof for the works of Yin and Li (2014, Journal of Applied Mathematics, 2014(978691)) and Goltong and Doguwa (2018, Open Journal of Statistics, 8: 902-914). Using the Pareto prior as an example, we have shown by the use of simulation results that the new Bayesian measure of evidence solves Lindley's paradox.

KEYWORDS

Behrens-Fisher Problem, Lindley's Paradox, Metropolis-Hastings Algorithm, Pareto Prior, t Distribution

Share and Cite:

Goltong, N. and Doguwa, S. (2019) On Analysis of the Behrens-Fisher Problem Based on Bayesian Evidence. Open Journal of Statistics, 9, 1-14. doi: 10.4236/ojs.2019.91001.

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