• Communications for Statistical Applications and Methods
• /
• v.9 no.2
• /
• pp.401-410
• /
• 2002

This paper revisits parallel-line bioassay problem, from a Bayesian point of view using noninformative priors such as Jeffreys' prior, reference priors, and probability matching priors. After finding the orthogonal transformation, the class of first order and second order probability matching priors are derived. Jeffreys' prior and reference priors are derived also. Numerical examples are given to show the effectiveness of noninformative priors.

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

• Communications for Statistical Applications and Methods
• /
• v.10 no.2
• /
• pp.333-339
• /
• 2003

In this paper, we develop the probability matching priors for the parameters of non-regular Pareto distribution. We prove the propriety of joint posterior distribution induced by probability matching priors. Through the simulation study, we show that the proposed probability matching Prior matches the coverage probabilities in a frequentist sense. A real data example is given.

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

• Proceedings of the Korean Statistical Society Conference
• /
• 2003.10a
• /
• pp.15-19
• /
• 2003

In this paper, we develop the Jeffreys' prior, reference priors and the probability matching priors for the intraclass correlation coefficient of a symmetric normal distribution. We next verify propriety of posterior distributions under those noninformative priors. We examine whether reference priors satisfy the probability matching criterion.

• 한국데이터정보과학회:학술대회논문집
• /
• 2005.10a
• /
• pp.27-34
• /
• 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
• /
• v.33 no.2
• /
• pp.203-218
• /
• 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.

• Journal of the Korean Data and Information Science Society
• /
• v.14 no.1
• /
• pp.83-92
• /
• 2003

In this paper, we derive noninformative priors for the ratio of parameters in the Burr model. We obtain Jeffreys' prior, reference prior and second order probability matching prior. Also we prove that the noninformative prior matches the alternative coverage probabilities and a HPD matching prior up to the second order, respectively. Finally, we provide simulated frequentist coverage probabilities under the derived noninformative priors for small and moderate size of samples.

• Journal of the Korean Data and Information Science Society
• /
• v.24 no.3
• /
• pp.643-650
• /
• 2013

We develop noninformative priors for a ratio of parameters of two Maxwell distributions which is used to check the equality of two Maxwell distributions. Specially, we focus on developing probability matching priors and Je reys' prior for objectiv Bayesian inferences. The probability matching priors, under which the probability of the Bayesian credible interval matches the frequentist probability asymptotically, are developed. The posterior propriety under the developed priors will be shown. Some simulations are performed for identifying the usefulness of proposed priors in objective Bayesian inference.

• Proceedings of the Korean Reliability Society Conference
• /
• 2000.11a
• /
• pp.411-411
• /
• 2000

Consider the problem of estimating the reliability of a multicomponent stress-strength system which functions if at least r of the k identical components simultaneously function. All stresses and strengths are assumed to be independent random variables with two parameter Weibull distributions. First, we derive reference priors and probability matching priors which are noninformative priors. We next investigate sufficient conditions for propriety of posteriors under reference priors and probability matching priors. Finally, we provide, using these priors, some numerical results for Bayes estimates of the reliability by applying Gibbs sampling technique.