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A unified Bayesian inference on treatment means with order constraints

Title
A unified Bayesian inference on treatment means with order constraints
Authors
Oh M.-S.Shin D.W.
Ewha Authors
오만숙신동완
SCOPUS Author ID
오만숙scopus; 신동완scopus
Issue Date
2011
Journal Title
Computational Statistics and Data Analysis
ISSN
0167-9473JCR Link
Citation
vol. 55, no. 1, pp. 924 - 934
Indexed
SCIE; SCOPUS WOS scopus
Abstract
In some applications involving comparison of treatment means, it is known a priori that population means are ordered in a certain way. In such situations, imposing constraints on the treatment means can greatly increase the effectiveness of statistical procedures. This paper proposes a unified Bayesian method which performs a simultaneous comparison of treatment means and parameter estimation in ANOVA models with order constraints on the means. A continuous prior restricted to order constraints is employed, and posterior samples of parameters are generated using a Markov chain Monte Carlo method. Posterior probabilities of all possible hypotheses on the equality/inequality of treatment means are obtained using Savage-Dickey density ratios, for which we propose a simple and computationally efficient estimation method. Posterior densities and HPD intervals of parameters of interest are estimated with almost no extra cost, given some by-products from the test procedure. Simulation study results show that the proposed method outperforms the test without constraints and that the method is powerful in detecting the true hypothesis. The method is applied to the ramus bone sizes of 20 boys, which were measured at four time points. The proposed Bayesian test reveals that there are two growth spurts in the ramus bone size during the observed period, which could not be detected by pairwise comparisons of the means. © 2010 Elsevier B.V. All rights reserved.
DOI
10.1016/j.csda.2010.07.026
Appears in Collections:
자연과학대학 > 통계학전공 > Journal papers
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