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.
Cite this paper
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