• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.835-844
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• 2002

For the one-way random model when the ratio of the variance components is of interest, Bayesian analysis is often appropriate. In this paper, we develop the noninformative priors for the ratio of the variance components under the balanced one-way random effect model. We reveal that the second order matching prior matches alternative coverage probabilities up to the second order (Mukerjee and Reid, 1999) and is a HPD(Highest Posterior Density) matching prior. It turns out that among all of the reference priors, the only one reference prior (one-at-a-time reference prior) satisfies a second order matching criterion. Finally we show that one-at-a-time reference prior produces confidence sets with expected length shorter than the other reference priors and Cox and Reid (1987) adjustment.

• Journal of the Korean Statistical Society
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• v.35 no.3
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• pp.225-238
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• 2006

This paper considers noninformative priors for the scale parameter of exponential distribution when the data are collected in step stress accelerated life tests. We find the Jeffreys' and reference priors for this model and show that the reference prior satisfies first order matching criterion. Also, we show that there exists no second order matching prior in this problem. Some simulation results are given and we perform Bayesian analysis for proposed priors using some data.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.431-442
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• 2007

In this paper, we develop the noninformative priors when the parameter of interest is the difference between quantiles of two exponential 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 Jeffreys' prior does not satisfy the first order matching criterion. The Bayesian credible intervals based on the first order probability matching prior meet the frequentist target coverage probabilities much better than the frequentist intervals of Jeffreys' prior. Some simulation and real example will be given.

• Communications for Statistical Applications and Methods
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• v.18 no.2
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• pp.189-199
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• 2011

In this paper, we develop the noninformative priors for the common intraclass correlation coefficient when independent samples drawn from multivariate normal populations. We derive the first and second order matching priors. We reveal that the second order matching prior dose not match alternative coverage probabilities up to the second order and is not a HPD matching prior. 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.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.317-328
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• 2002

We first derive group ordering reference priors in a two-way mixed-effects analysis of variance (ANOVA) model. We show that posterior distributions are proper and provide marginal posterior distributions under reference priors. We also examine whether the reference priors satisfy the probability matching criterion. Finally, the reference prior satisfying the probability matching criterion is shown to be good in the sense of frequentist coverage probability of the posterior quantile.

• 한국데이터정보과학회:학술대회논문집
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• 2005.10a
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• pp.27-34
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• 2005

We consider the problem of estimating the system reliability noninformative priors when both stress and strength follow generalized gamma distributions. We first derive Jeffreys' prior, group ordering reference priors, and matching priors. We investigate the propriety of posterior distributions and provide marginal posterior distributions under those noninformative priors. We also examine whether the reference priors satisfy the probability matching criterion.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.77-91
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• 2007

This paper considers development of noninformative priors for the familial data when the families have equal number of offspring. Several noninformative priors including the widely used Jeffreys' prior as well as the different reference priors are derived. Also, a simultaneously-marginally-probability-matching prior is considered and probability matching priors are derived when the parameter of interest is inter- or intra-class correlation coefficient. The simulation study implemented by Gibbs sampler shows that two-group reference prior is slightly edge over the others in terms of coverage probability.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1067-1078
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• 2005

In this paper, we develop the noninformative priors for the exponential models when the parameter of interest is the difference of two means. We develop the first and second order matching priors. We reveal that the second order matching priors do not exist. It turns out that Jeffreys' prior does not satisfy the first order matching criterion. The Bayesian credible intervals based on the first order matching meet the frequentist target coverage probabilities much better than the frequentist intervals of Jeffreys' prior.

• Journal of the Korean Statistical Society
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• v.27 no.4
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• pp.421-433
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• 1998

In this paper, matching priors for P(X < Y) are investigated when both distributions are exponential distributions. Two recent approaches for finding noninformative priors are introduced. The first one is the verger and Bernardo's forward and backward reference priors that maximizes the expected Kullback-Liebler Divergence between posterior and prior density. The second one is the matching prior identified by matching the one sided posterior credible interval with the frequentist's desired confidence level. The general forms of the second- order matching prior are presented so that the one sided posterior credible intervals agree with the frequentist's desired confidence levels up to O(n$^{-1}$ ). The frequentist coverage probabilities of confidence sets based on several noninformative priors are compared for small sample sizes via the Monte-Carlo simulation.