• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.395-411
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• 2005

In this paper, we develop the Jeffreys' prior, reference prior and the the probability matching priors for the difference of intraclass correlation coefficients in familial data. e prove the sufficient condition for propriety of posterior distributions. Using marginal posterior distributions under those noninformative priors, we compare posterior quantiles and frequentist coverage probability.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.217-226
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• 2002

In this paper, we derive noninformative priors for the ratio of failure rates in exponential model. A class of priors is found by matching the coverage probabilities of one-sided Baysian credible interval with the corresponding frequentist coverage probabilities. And we prove that the noninformative prior matches the alternative coverage probabilities and is a HPD matching prior up to the second order. Finally, we provide simulated freqentist coverage probabilities under the derived noninformative prior for small samples.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.467-475
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• 2011

This paper develops the noninformative priors for the stress-strength reliability from one parameter generalized exponential distributions. When this reliability is a parameter of interest, we develop the first, second order matching priors, reference priors in its order of importance in parameters and Jeffreys' prior. We reveal that these probability matching priors are not the alternative coverage probability matching prior or a highest posterior density matching prior, a cumulative distribution function matching prior. In addition, we reveal that the one-at-a-time reference prior and Jeffreys' prior are actually a second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study and a provided example.

• 한국데이터정보과학회:학술대회논문집
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• 2005.10a
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• pp.71-84
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• 2005

The Fieller-Creasy problem involves statistical inference about the ratio of two independent normal means. It is difficult problem from either a frequentist or a likelihood perspective. As an alternatives, a Bayesian analysis with noninformative priors may provide a solution to this problem. In this paper, we extend the results of Yin and Ghosh (2001) to unbalanced sample case. We find various noninformative priors such as first and second order matching priors, reference and Jeffreys' priors. The posterior propriety under the proposed noninformative priors will be given. Using real data, we provide illustrative examples. Through simulation study, we compute the frequentist coverage probabilities for probability matching and reference priors. Some simulation results will be given.

• The Korean Journal of Applied Statistics
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• v.26 no.5
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• pp.737-746
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• 2013

The Bayesian method can be applied successfully to the estimation of the censored regression model introduced by Tobin (1958). The Bayes estimates show improvements over the maximum likelihood estimate; however, the performance of the Bayesian interval estimation is questionable. In Bayesian paradigm, the prior distribution usually reflects personal beliefs about the parameters. Such subjective priors will typically yield interval estimators with poor frequentist properties; however, an objective noninformative often yields a Bayesian procedure with good frequentist properties. We examine the performance of frequentist properties of noninformative priors for the Tobit regression model.

• Journal of the Korean Statistical Society
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• v.33 no.2
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• pp.203-218
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• 2004

In this paper, we develop the matching priors and the reference priors for linear combination of the means under the normal populations with equal variances. We prove that the matching priors are actually the second order matching priors and reveal that the second order matching priors match alternative coverage probabilities up to the second order (Mukerjee and Reid, 1999) and also, are HPD matching priors. It turns out that among all of the reference priors, one-at-a-time reference prior satisfies a second order matching criterion. Our simulation study indicates that one-at-a-time reference prior performs better than the other reference priors in terms of matching the target coverage probabilities in a frequentist sense. We compute Bayesian credible intervals for linear combination of the means based on the reference priors.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.1-9
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• 2003

In this article, we consider a Bayesian estimation method for the geometric mean of $textsc{k}$ exponential parameters, Using the Tibshirani's orthogonal parameterization, we suggest an invariant prior distribution of the $textsc{k}$ parameters. It is seen that the prior, probability matching prior, is better than the uniform prior in the sense of correct frequentist coverage probability of the posterior quantile. Then a weighted Monte Carlo method is developed to approximate the posterior distribution of the mean. The method is easily implemented and provides posterior mean and HPD(Highest Posterior Density) interval for the geometric mean. A simulation study is given to illustrates the efficiency of the method.

• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.429-440
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• 2008

In this paper, we develop the noninformative priors when the parameter of interest is the common coefficient of variation in two inverse Gaussian distributions. We want to develop the first and second order probability matching priors. But we prove that the second order probability matching prior does not exist. It turns out that the one-at-a-time and two group reference priors satisfy the first order matching criterion but Jeffreys' prior does not. The Bayesian credible intervals based on the one-at-a-time reference prior meet the frequentist target coverage probabilities much better than that of Jeffreys' prior. Some simulations are given.

• Proceedings of the Korean Association for Survey Research Conference
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• 2000.11a
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• pp.41-62
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• 2000

현실적으로 통계추론 방법의 적용시, 그 정당성이 보장되는 기본가정이외에도 추가적인 가정이 불가피하여, 본래의 정당성이 퇴색되는 경우가 흔히 발생한다. 따라서 이런 경우에는 통계추론의 평가가 필수적일 것이나, 많은 경우에 분석적 평가를 하기에는 너무 복잡하여, 특정상황을 상정한 모의분석 평가가 주류를 이루고 있다. 본 고에서는 보다 일반적 상황에서의 통계추론의 평가를 위해 브트스트랩방법과 같이 관찰값에 의존한 모의방법(observation-based simulation)을 이용한 평가방법을 제안한다. 우선 설득력 있는 평가요소로서 구간추정시 포함확률(coverage probability)와 같은 빈도성질(frequency property)를 선택하였다. 빈도성질은 고전적 통계추론은 물론 베이지안 통계추론을 대상으로도 의미있는 평가기준으로 판단되는 바, 이를 평가요소로서 선택하고, 이의 추정을 위한 방법과, 그 추정결과의 해석과 나아가 이를 기준으로 한 통계추론 결과의 조정 방법까지 일련의 절차에 대한 방법론을 제시하였다.

• Journal of the Korean Data and Information Science Society
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• v.26 no.1
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• pp.243-253
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• 2015

In this paper, we develop the noninformative priors for the common shape parameter of several inverse Gaussian distributions. Specially, we want to develop noninformative priors which satisfy certain objective criterion. The probability matching priors and reference priors of the common shape parameter will be developed. It turns out that the second order matching prior does not exist. The reference priors satisfy the first order matching criterion, but Jeffrey's prior is not the first order matching prior. We showed that the proposed reference prior matches the target coverage probabilities in a frequentist sense through simulation study, and an example based on real data is given.