Bayesian Analysis of Hypothesis Testing Problems for General Population: A Kullback–Leibler Alternative

Authors

Naveen K. Bansal, Marquette UniversityFollow
Gholamhossein Hamedani, Marquette UniversityFollow
Ru Sheng, Marquette UniversityFollow

Document Type

Article

Language

eng

Format of Original

8 p.

Publication Date

7-2012

Publisher

Elsevier

Source Publication

Journal of Statistical Planning and Inference

Source ISSN

0378-3758

Original Item ID

doi: 10.1016/j.jspi.2012.02.017

Abstract

We consider a hypothesis problem with directional alternatives. We approach the problem from a Bayesian decision theoretic point of view and consider a situation when one side of the alternatives is more important or more probable than the other. We develop a general Bayesian framework by specifying a mixture prior structure and a loss function related to the Kullback–Leibler divergence. This Bayesian decision method is applied to Normal and Poisson populations. Simulations are performed to compare the performance of the proposed method with that of a method based on a classical z-test and a Bayesian method based on the “0–1” loss.

Comments

Accepted version. Journal of Statistical Planning and Inference, Vol. 142, No. 7 (July, 2012): 1991-1998. DOI. © 2012 Elsevier. Used with permission.

Recommended Citation

Bansal, Naveen K.; Hamedani, Gholamhossein; and Sheng, Ru, "Bayesian Analysis of Hypothesis Testing Problems for General Population: A Kullback–Leibler Alternative" (2012). Mathematics, Statistics and Computer Science Faculty Research and Publications. 94.
https://epublications.marquette.edu/mscs_fac/94