• Journal of the Korean Data and Information Science Society
• /
• v.18 no.4
• /
• pp.1123-1134
• /
• 2007

This article addresses the problem of testing whether the shape parameters in k independent Weibull populations are equal. We propose a Bayesian model selection procedure for equality of the shape parameters. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the objective Bayesian model selection procedure based on the fractional Bayes factor and the intrinsic Bayes factor under the reference prior. Simulation study and a real example are provided.

• Journal of the Korean Statistical Society
• /
• v.29 no.4
• /
• pp.395-405
• /
• 2000

This article addresses the Bayesian hypothesis testing for the comparison of two exponential mans. Conventional Bayes factors with improper non-informative priors are into well defined. The fractional Byes factor(FBF) of O'Hagan(1995) is used to overcome such as difficulty. we derive proper intrinsic priors, whose Bayes factors are asymptotically equivalent to the corresponding FBFs. We demonstrate our results with three examples.

• Journal of the Korean Statistical Society
• /
• v.29 no.4
• /
• pp.443-454
• /
• 2000

In Bayesian model selection or testing problems of different dimensions, the conventional Bayes factors with improper noninformative priors are not well defined. The intrinsic Bayes factor and the fractional Bayes factor are used to overcome such problems by using a data-splitting idea and fraction, respectively. This article addresses a Bayesian testing for the comparison of two normal means with unknown variance. We derive proper intrinsic priors, whose Bayes factors are asymptotically equivalent to the corresponding fractional Bayes factor. We demonstrate our results with two examples.

• Journal of the Korean Data and Information Science Society
• /
• v.22 no.5
• /
• pp.1007-1016
• /
• 2011

This article deals with the problem of testing for the correlation coefficient in the bivariate normal distribution. We propose Bayesian hypothesis testing procedures for the bivariate normal correlation coefficient under the noninformative prior. The noninformative priors are usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. A simulation study and an example are provided.

• Journal of the Korean Data and Information Science Society
• /
• v.25 no.2
• /
• pp.465-472
• /
• 2014

This article deals with the problem of testing the equality of the scale parameters in the half logistic distributions. We propose Bayesian hypothesis testing procedures for the equality of the scale parameters under the noninformative priors. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be dened up to a multiplicative constant. Thus we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• Journal of the Korean Data and Information Science Society
• /
• v.24 no.4
• /
• pp.949-957
• /
• 2013

In this paper, we consider the problem of testing the equality of the scale parameters in two parameter exponential distributions. We propose Bayesian testing procedures for the equality of the scale parameters under the noninformative priors. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Thus, we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• Communications for Statistical Applications and Methods
• /
• v.8 no.1
• /
• pp.97-107
• /
• 2001

A simultaneous test criterion for multiple hypotheses concerning comparison of two multivariate normal populations is considered by using the so called Bayes factor method. Fully parametric frequentist approach for the test is not available and thus Bayesian criterion is pursued using a Bayes factor that eliminates its arbitrariness problem induced by improper priors. Specifically, the fractional Bayes factor (FBF) by O'Hagan (1995) is used to derive the criterion. Necessary theories involved in the derivation an computation of the criterion are provided. Finally, an illustrative simulation study is given to show the properties of the criterion.

• The Korean Journal of Applied Statistics
• /
• v.16 no.2
• /
• pp.335-349
• /
• 2003

In this paper, we use Bayesian method for model selection of poisson vs. negative binomial distribution, and normal, double exponential vs. cauchy distribution. The fractional Bayes factor of O'Hagan (1995) was applied to Bayesian model selection under the assumption of noninformative improper priors for all parameters in the models. Through the analyses of real data and simulation data, we examine the usefulness of the fractional Bayes factor in comparison with intrinsic Bayes factors of Berger and Pericchi (1996, 1998).

• Journal of the Korean Data and Information Science Society
• /
• v.18 no.3
• /
• pp.833-845
• /
• 2007

When X and Y have independent exponential distributions, we develop a Bayesian testing procedure for the ratio of two quantiles under reference prior. The noninformative prior such as reference prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we develop a Bayesian testing procedure based on fractional Bayes factor and intrinsic Bayes factor. We show that the posterior density under the reference prior is proper and propose the Bayesian testing procedure for the ratio of two quantiles using fractional Bayes factor and intrinsic Bayes factor. Simulation study and a real data example are provided.

• Journal of the Korean Data and Information Science Society
• /
• v.16 no.4
• /
• pp.1119-1128
• /
• 2005

The Bayes factors with improper noninformative priors are defined only up to arbitrary constants. So it is known that Bayes factors are not well defined due to this arbitrariness in Bayesian hypothesis testing and model selections. The intrinsic Bayes factor and the fractional Bayes factor have been used to overcome this problem. In this paper, we suggest a Bayesian hypothesis testing based on the intrinsic Bayes factor and the fractional Bayes factor for the comparison of two lognormal variances. Using the proposed two Bayes factors, we demonstrate our results with some examples.