• Title, Summary, Keyword: matching prior

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Noninformative priors for Pareto distribution

  • Kim, Dal-Ho;Kang, Sang-Gil;Lee, Woo-Dong
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.6
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    • pp.1213-1223
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    • 2009
  • In this paper, we develop noninformative priors for two parameter Pareto distribution. Specially, we derive Jereys' prior, probability matching prior and reference prior for the parameter of interest. In our case, the probability matching prior is only a first order matching prior and there does not exist a second order matching prior. Some simulation reveals that the matching prior performs better to achieve the coverage probability. A real example is also considered.

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Noninformative priors for the scale parameter in the generalized Pareto distribution

  • Kang, Sang Gil
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.6
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    • pp.1521-1529
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    • 2013
  • In this paper, we develop noninformative priors for the generalized Pareto distribution when the scale parameter is of interest. We developed the rst order and the second order matching priors. We revealed that the second order matching prior does not exist. It turns out that the reference prior and Jeffrey's prior do not satisfy a first order matching criterion, and Jeffreys' prior, the reference prior and the matching prior are different. Some simulation study is performed and a real example is given.

Noninformative Priors for the Stress-Strength Reliability in the Generalized Exponential Distributions

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

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 Ratio of the Scale Parameters in the Inverted Exponential Distributions

  • Kang, Sang Gil;Kim, Dal Ho;Lee, Woo Dong
    • Communications for Statistical Applications and Methods
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    • v.20 no.5
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    • pp.387-394
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    • 2013
  • In this paper, we develop the noninformative priors for the ratio of the scale parameters in the inverted exponential distributions. The first and second order matching priors, the reference prior and Jeffreys prior are developed. It turns out that the second order matching prior matches the alternative coverage probabilities, is a cumulative distribution function matching prior and is a highest posterior density matching prior. In addition, the reference prior and Jeffreys' prior are the second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study as well as provide an example based on real data is given.

Noninformative Priors for the Common Scale Parameter in the Inverse Gaussian Distributions

  • Kang, Sang-Gil
    • Journal of the Korean Data and Information Science Society
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    • v.15 no.4
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    • pp.981-992
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    • 2004
  • In this paper, we develop the noninformative priors for the common scale parameter in the inverse gaussian distributions. We developed the first and second order matching priors. Next we revealed that the second order matching prior satisfies a HPD matching criterion. Also we showed that the second order matching prior matches alternative coverage probabilities up to the second order. It turns out that the one-at-a-time reference prior satisfies a second order matching criterion. Some simulation study is performed.

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Bayesian Analysis for the Ratio of Variance Components

  • Kang, Sang-Gil
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.2
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    • pp.559-568
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    • 2006
  • In this paper, we develop the noninformative priors for the linear mixed models when the parameter of interest is the ratio of variance components. We developed the first and second order matching priors. We reveal that the one-at-a-time reference prior satisfies the second order matching criterion. It turns out that the two group reference prior satisfies a first order matching criterion, but Jeffreys' prior is not first order matching prior. Some simulation study is performed.

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Development of Noninformative Priors in the Burr Model

  • Cho, Jang-Sik;Kang, Sang-Gil;Baek, Sung-Uk
    • Journal of the Korean Data and Information Science Society
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    • v.14 no.1
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    • pp.83-92
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    • 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.

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Noninformative priors for the log-logistic distribution

  • Kang, Sang Gil;Kim, Dal Ho;Lee, Woo Dong
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.1
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    • pp.227-235
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    • 2014
  • In this paper, we develop the noninformative priors for the scale parameter and the shape parameter in the log-logistic distribution. We developed the first and second order matching priors. It turns out that the second order matching prior matches the alternative coverage probabilities, and is a highest posterior density matching prior. Also we revealed that the derived reference prior is the second order matching prior for both parameters, but Jerffrey's prior is not a second 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.

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.