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Bayesian inference for nonlinear functions of means in normal distributions
Journal of the Korean Data & Information Science Society 2019;30:491-502
Published online March 31, 2019;
© 2019 Korean Data and Information Science Society.

Woo Dong Lee1  Dal Ho Kim2  Sang Gil Kang3 1

1Pre-major of Cosmetics and Pharmaceutics, Daegu Haany University, 2Department of Statistics, Kyungpook National University, 3Department of Computer and Data Information, Sangji University
Correspondence to: Professor, Department of Computer and Data Information, Sangji University, Wonju 26339, Korea. E-mail:
Received February 13, 2019; Revised February 22, 2019; Accepted February 28, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the objective Bayesian inference for the product of different powers of two means in the normal distributions. In order to perform the objective Bayesian inference, the noninformative priors are essential. In this paper, we develop the match- ing prior as the noninformative priors for the product of different powers of two means in the normal distributions. We develop the first order matching priors using the or- thogonal parameterization. Then we reveal that Jeffreys' prior and the matching prior have the different forms. Also we prove the propriety of posteriors under general priors based on the developed priors. We investigate that the matching prior provides better performance than Jeffreys' prior in view points of coverage probability from numerical studies.
Keywords : Matching prior, normal distribution, product of powers of two means.