• Journal of the Korean Statistical Society
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• v.29 no.2
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• pp.155-168
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• 2000

Regarding to multiple comparison problem (MCP) of k normal population variances, we suggest a Bayesian method for calculating posterior probabilities for various hypotheses of equality among population variances. This leads to a simple method for obtaining pairwise comparisons of variances in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships among the variances. The method is derived from the fact that certain features of the hierarchical nonparametric family of Dirichlet process priors, in general, make it amenable to solving the MCP and estimating the posterior probabilities by means of posterior simulation, the Gibbs sampling. Two examples are illustrated for the method. For these examples, the method is straightforward for specifying distributionally and to implement computationally, with output readily adapted for required comparison.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1129-1140
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• 2005

A nonparametric Bayesian method for calculating posterior probabilities of the multiple comparison problem on the parameters of several Geometric populations is presented. Bayesian multiple comparisons under two different prior/ likelihood combinations was studied by Gopalan and Berry(1998) using Dirichlet process priors. In this paper, we followed the same approach to calculate posterior probabilities for various hypotheses in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships on the parameters of several geometric populations. This also leads to a simple method for obtaining pairwise comparisons of probability of successes. Gibbs sampling technique was used to evaluate the posterior probabilities of all possible hypotheses that are analytically intractable. A numerical example is given to illustrate the procedure.

• 한국데이터정보과학회:학술대회논문집
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• 2006.11a
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• pp.71-80
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• 2006

A nonparametric Bayesian multiple comparisons problem (MCP) for dependence parameters in I bivariate exponential populations is studied here. A simple method for pairwise comparisons of these parameters is also suggested. Here we extend the methodology studied by Gopalan and Berry (1998) using Dirichlet process priors. The family of Dirichlet process priors is applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through Markov Chain Monte Carlo method, namely, Gibbs sampling, due to the intractability of analytic evaluation. The whole process of MCP for the dependent parameters of bivariate exponential populations is illustrated through a numerical example.