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Nonparametric Bayesian test of homogeneity using a discretization approach
Journal of the Korean Data & Information Science Society 2018;29:303-11
Published online January 31, 2018
© 2018 Korean Data and Information Science Society.

MinSup Kim1 · Balgobin Nandram2 · Dal Ho Kim3

13Department of Statistics, Kyungpook National University
2Department of Mathematical Sciences, Worcester Polytechnic Institute
Correspondence to: Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea. E-mail:
Received October 24, 2017; Revised November 9, 2017; Accepted November 13, 2017.
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.
In this paper, we consider nonparametric Bayesian test of homogeneity using a hierarchical multinomial model with Dirichlet process priors in small area setup. If we discretize a continuous variable properly, the discretization approach could find some association between the groups and the variable even if the groups are homogeneous through k-sample tests involving one-way ANOVA. It could also be used to look at heterogeneity at specific levels of the variable of interest among groups. We use the clustering by the k-means and Dirichlet process to discretize the continuous variable. When we discretize the continuous variable, it can be treated as an analysis of the contingency table. Then the chi-squared test is the most common thought. If more slices are added, however, chi-squared test is less accurate. So we use the Bayes factor through the nonparmetric Bayesian model and apply it to the test of homogeneity.
Keywords : Bayesian nonparametrics, contingency table, Dirichlet process prior, discretization, homogeneity test, small areas.