• Communications for Statistical Applications and Methods
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• 제8권3호
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• pp.787-795
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• 2001

In this paper, Bayesian hypothesis testing procedures are proposed under the non-informative prior distributions, which can be thought as the Bayesian counterparts of the classical ones in the sense of using the concept of significance level. The performances of proposed procedures are compared with those of classical procedures through several examples.

• 응용통계연구
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• 제24권6호
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• pp.1149-1160
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• 2011

기존의 frequentist 추론에 비해 Bayesian 추론에서의 가설 검정 및 모형 선택 문제는 학자들 간에 일치된 견해를 보이지 못하고 있으며 아직도 논란이 되는 것들이 많다. Bayesian 추론에서 가설 검정 및 모형 선택의 기준으로 널리 쓰이는 Bayes factor는 이해하기 쉬우나 여러 경우에 구하기 어려운 단점이 존재한다. 그 외에 다른 기준으로 Spiegelhalter 등 (2002)가 제시한 DIC(Deviance Information Criterion)과 frequentist 추론에서의 P-value에 대비되는 Bayesian P-value가 있다. 본 논문에서는 Swiss banknote 자료를 Bayesian 로지스틱 회귀모형으로 분석하고 관련 기준들을 구하여 각 기준들이 일관성 있는 결론을 보이는지 확인하고자 한다.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 춘계 학술발표회 논문집
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• pp.67-72
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• 2002

A Bayesian testing procedure is proposed for assessment of bioequivalence in both mean and variance which ensures population bioequivalence under normality assumption. We derive the joint posterior distribution of the means and variances in a standard 2 ${\times}$ 2 crossover experimental design and propose a Bayesian testing procedure for bioequivalence based on a Markov chain Monte Carlo methods. The proposed method is applied to a real data set.

• Journal of the Korean Data and Information Science Society
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• 제18권3호
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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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• 제15권3호
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• pp.677-687
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• 2004

We consider the comparison of two one-parameter exponential distributions with the complete data as well as the type II censored data. We adapt Bayesian test procedure for nested hypothesis based on the Bayesian reference criterion. Specifically we derive the expression for the Bayesian reference criterion to solve our problem. Also we provide numerical examples using simulated data sets to illustrate our results.

• Communications for Statistical Applications and Methods
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• 제9권3호
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• pp.725-732
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• 2002

P-values are often perceived as measurements of degree of compatibility between the current data and the hypothesized model. In this paper, a new concept of Bayesian p-values is proposed and studied under the non-informative prior distributions, which can be thought as the Bayesian counterparts of the classical p-values in the sense of using the concept of significance level. The performances of the proposed Bayesian p-values are compared with those of the classical p-values through several examples.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1391-1396
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• 2008

In this paper, we consider two components system which the lifetimes have Marshall and Olkin's bivariate exponential model with bivariate type I censored data. We propose a Bayesian independent test procedure for above model using fractional Bayes factor method by O'Hagan based on improper prior distributions. And we compute the fractional Bayes factor and the posterior probabilities for the hypotheses, respectively. Also we select a hypothesis which has the largest posterior probability. Finally a numerical example is given to illustrate our Bayesian testing procedure.

• Journal of the Korean Data and Information Science Society
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• 제18권4호
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• pp.1191-1203
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• 2007

In this paper, we consider the hypothesis testing for the homogeneity of the shape parameters in the gamma distributions. The noninformative priors such as Jeffreys# prior or reference prior 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 objective Bayesian testing procedure for the homogeneity of the shape parameters 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 Data and Information Science Society
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• 제15권4호
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• pp.743-752
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• 2004

In this paper, we develop the Bayesian model selection procedure using the reference prior for comparing two nested model such as the independent and intraclass models using the distance or divergence between the two as the basis of comparison. A suitable criterion for this is the power divergence measure as introduced by Cressie and Read(1984). Such a measure includes the Kullback -Liebler divergence measures and the Hellinger divergence measure as special cases. For this problem, the power divergence measure turns out to be a function solely of $\rho$, the intraclass correlation coefficient. Also, this function is convex, and the minimum is attained at $\rho=0$. We use reference prior for $\rho$. Due to the duality between hypothesis tests and set estimation, the hypothesis testing problem can also be solved by solving a corresponding set estimation problem. The present paper develops Bayesian method based on the Kullback-Liebler and Hellinger divergence measures, rejecting $H_0:\rho=0$ when the specified divergence measure exceeds some number d. This number d is so chosen that the resulting credible interval for the divergence measure has specified coverage probability $1-{\alpha}$. The length of such an interval is compared with the equal two-tailed credible interval and the HPD credible interval for $\rho$ with the same coverage probability which can also be inverted into acceptance regions of $H_0:\rho=0$. Example is considered where the HPD interval based on the one-at- a-time reference prior turns out to be the shortest credible interval having the same coverage probability.