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

• Journal of the Korean Data and Information Science Society
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• v.21 no.1
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• pp.163-172
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• 2010

In this paper, we deal with the problem for testing homogeneity of coecients of variation in several normal distributions. We propose Bayesian hypothesis testing procedures based on the Bayes factor under noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be dened up to a multiplicative constant. So we propose the objective Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factor under the reference prior. Simulation study and a real data example are provided.

• Journal of the Korean Statistical Society
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• v.29 no.4
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• pp.443-454
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• 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 Korean Society for Quality Management
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• v.30 no.2
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• pp.118-129
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• 2002

A multiple test of a mean parameter, λ, in the Poisson model is considered using the Bayes factor. Under noninformative improper priors, the intrinsic Bayes factor(IBF) of Berger and Pericchi(1996) and the fractional Bayes factor(FBF) of O'Hagan(1995) called as the default or automatic Bayes factors are used to select one among three models, M$_1$: λ< $λ_0, M$_2$: λ= $λ_0, M$_3$: λ> $λ_0. Posterior probability of each competitive model is computed using the default Bayes factors. Finally, theoretical results are applied to simulated data and real data.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.549-562
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• 2000

Default Bayes factors are computed to test the equality of one Poisson population mean and the equality of two independent Possion population means. As default priors are assumed Jeffreys priors, noninformative improper priors, and default Bayes factors such as three intrinsic Bayes factors of Berger and Pericchi(1996, 1998), the arithmetic, the median, and the geometric intrinsic Bayes factor, and the factional Bayes factor of O'Hagan(1995) are computed. The testing results by each default Bayes factor are compared with those by the classical method in the simulation study.

• 한국데이터정보과학회:학술대회논문집
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• 2003.10a
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• pp.39-47
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• 2003

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 by Berger and Pericchi (1996) and the fractional Bayes factor by O'Hagan (1995) have been used to overcome this problems. This paper suggests intrinsic priors for testing the equality of two lognormal means, whose Bayes factors are asymptotically equivalent to the corresponding fractional Bayes factors. Using proposed intrinsic priors, we demonstrate our results with a simulated dataset.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.661-671
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• 2003

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 by Berger and Pericchi (1996) and the fractional Bayes factor by O'Hagan (1995) have been used to overcome this problems. This paper suggests intrinsic priors for testing the equality of two lognormal means, whose Bayes factors are asymptotically equivalent to the corresponding fractional Bayes factors. Using proposed intrinsic priors, we demonstrate our results with real example and a simulated dataset.

• Journal of the Korean Data and Information Science Society
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• v.21 no.2
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• pp.297-308
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• 2010

This article deals with the problem of testing mean when the coefficient of variation in normal distribution is known. We propose Bayesian hypothesis testing procedures for the normal mean under the noninformative prior. 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 hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factor under the reference prior. Specially, we develop intrinsic priors which give asymptotically same Bayes factor with the intrinsic Bayes factor under the reference prior. Simulation study and a real data example are provided.

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.833-845
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• 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
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• v.18 no.4
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• pp.1123-1134
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• 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.