TITLE:
On Analysis of the Behrens-Fisher Problem Based on Bayesian Evidence
AUTHORS:
Nengak Emmanuel Goltong, Sani Ibrahim Doguwa
KEYWORDS:
Behrens-Fisher Problem, Lindley's Paradox, Metropolis-Hastings Algorithm, Pareto Prior, t Distribution
JOURNAL NAME:
Open Journal of Statistics,
Vol.9 No.1,
January
21,
2019
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 di erence 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 Goltongand Doguwa (2018, Open Journal of Statistics, 8: 902-914).Using the Pareto prior as an example, we have shown by the use ofsimulation results that the new Bayesian measure of evidence solvesLindley's paradox.