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The Scientific World Journal
Volume 2014, Article ID 676545, 8 pages
Research Article

A Measure of Uncertainty regarding the Interval Constraint of Normal Mean Elicited by Two Stages of a Prior Hierarchy

Department of Statistics, Dongguk University, Seoul Campus, Pil-Dong 3Ga, Chung-Gu, Seoul 100-715, Republic of Korea

Received 3 March 2014; Revised 18 June 2014; Accepted 20 June 2014; Published 6 July 2014

Academic Editor: Montserrat Guillén

Copyright © 2014 Hea-Jung Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper considers a hierarchical screened Gaussian model (HSGM) for Bayesian inference of normal models when an interval constraint in the mean parameter space needs to be incorporated in the modeling but when such a restriction is uncertain. An objective measure of the uncertainty, regarding the interval constraint, accounted for by using the HSGM is proposed for the Bayesian inference. For this purpose, we drive a maximum entropy prior of the normal mean, eliciting the uncertainty regarding the interval constraint, and then obtain the uncertainty measure by considering the relationship between the maximum entropy prior and the marginal prior of the normal mean in HSGM. Bayesian estimation procedure of HSGM is developed and two numerical illustrations pertaining to the properties of the uncertainty measure are provided.