• Title, Summary, Keyword: Jeffreys' prior

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Noninformative Priors for the Ratio of the Lognormal Means with Equal Variances

  • Lee, Seung-A;Kim, Dal-Ho
    • Communications for Statistical Applications and Methods
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    • v.14 no.3
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    • pp.633-640
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    • 2007
  • We develop noninformative priors for the ratio of the lognormal means in equal variances case. The Jeffreys' prior and reference priors are derived. We find a first order matching prior and a second order matching prior. It turns out that Jeffreys' prior and all of the reference priors are first order matching priors and in particular, one-at-a-time reference prior is a second order matching prior. One-at-a-time reference prior meets very well the target coverage probabilities. We consider the bioequivalence problem. We calculate the posterior probabilities of the hypotheses and Bayes factors under Jeffreys' prior, reference prior and matching prior using a real-life example.

Noninformative priors for the common mean in log-normal distributions

  • Kang, Sang-Gil
    • Journal of the Korean Data and Information Science Society
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    • v.22 no.6
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    • pp.1241-1250
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    • 2011
  • In this paper, we develop noninformative priors for the log-normal distributions when the parameter of interest is the common mean. We developed Jeffreys' prior, th reference priors and the first order matching priors. It turns out that the reference prior and Jeffreys' prior do not satisfy a first order matching criterion, and Jeffreys' pri the reference prior and the first order matching prior are different. Some simulation study is performed and a real example is given.

Bayesian Analysis for the Difference of Exponential Means

  • Kang, Sang-Gil;Kim, Dal-Ho;Lee, Woo-Dong
    • 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.

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Noninformative priors for linear combinations of exponential means

  • Lee, Woo Dong;Kim, Dal Ho;Kang, Sang Gil
    • Journal of the Korean Data and Information Science Society
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    • v.27 no.2
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    • pp.565-575
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    • 2016
  • In this paper, we develop the noninformative priors for the linear combinations of means in the exponential distributions. We develop the matching priors and the reference priors. The matching priors, the reference prior and Jeffreys' prior for the linear combinations of means are developed. It turns out that the reference prior and Jeffreys' prior are not a matching prior. We show that the proposed matching prior matches the target coverage probabilities much more accurately than the reference prior and Jeffreys' prior in a frequentist sense through simulation study, and an example based on real data is given.

Reference Prior and Posterior in the AR(1) Model

  • Lee, Yoon-Jae
    • Journal of the Korean Data and Information Science Society
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    • v.16 no.1
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    • pp.71-78
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    • 2005
  • Recently an important issue in Bayesian methodology is determination of noninformative prior distributions, often required when there is no idea of prior information. In this thesis attention is focused on the development of noninformative priors for stationary AR(1) model. The noninformative priors primarily discussed are the Jeffreys prior, and the reference priors. The remarkable points in the result are that the Jeffreys prior coincides with the reference prior for the case that $\rho$ is the parameter of interest.

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Noninformative Priors for the Power Law Process

  • Kim, Dal-Ho;Kang, Sang-Gil;Lee, Woo-Dong
    • Journal of the Korean Statistical Society
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    • v.31 no.1
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    • pp.17-31
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    • 2002
  • This paper considers noninformative priors for the power law process under failure truncation. Jeffreys'priors as well as reference priors are found when one or both parameters are of interest. These priors are compared in the light of how accurately the coverage probabilities of Bayesian credible intervals match the corresponding frequentist coverage probabilities. It is found that the reference priors have a definite edge over Jeffreys'prior in this respect.

Bayesian Estimation for the Reliability of Stress-Strength Systems Using Noninformative Priors

  • Kim, Byung-Hwee
    • International Journal of Reliability and Applications
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    • v.2 no.2
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    • pp.117-130
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    • 2001
  • Consider the problem of estimating the system reliability using noninformative priors when both stress and strength follow generalized gamma distributions. We first treat the orthogonal reparametrization and then, using this reparametrization, derive Jeffreys'prior, reference prior, and matching priors. We next provide the suffcient condition for propriety of posterior distributions under those noninformative priors. Finally, we provide and compare estimated values of the system reliability based on the simulated values of the parameter of interest in some special cases.

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Noninformative Priors for Stress-Strength System in the Burr-Type X Model

  • Kim, Dal-Ho;Kang, Sang-Gil;Cho, Jang-Sik
    • Journal of the Korean Statistical Society
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    • v.29 no.1
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    • pp.17-27
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    • 2000
  • In this paper, we develop noninformative priors that are used for estimating the reliability of stress-strength system under the Burr-type X model. A class of priors is found by matching the coverage probabilities of one-sided Bayesian credible interval with the corresponding frequentist coverage probabilities. It turns out that the reference prior as well as the Jeffreys prior are the second order matching prior. The propriety of posterior under the noninformative priors is proved. The frequentist coverage probabilities are investigated for samll samples via simulation study.

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OBJECTIVE BAYESIAN APPROACH TO STEP STRESS ACCELERATED LIFE TESTS

  • Kim Dal-Ho;Lee Woo-Dong;Kang Sang-Gil
    • 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.

Bayesian Inference for Stress-Strength Systems

  • Chang, In-Hong;Kim, Byung-Hwee
    • 한국데이터정보과학회:학술대회논문집
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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.

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