• Title, Summary, Keyword: probability 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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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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On the Development of Probability Matching Priors for Non-regular Pareto Distribution

  • Lee, Woo Dong;Kang, Sang Gil;Cho, Jang Sik
    • Communications for Statistical Applications and Methods
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    • v.10 no.2
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    • pp.333-339
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    • 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.

NONINFORMATIVE PRIORS FOR PARETO DISTRIBUTION : REGULAR CASE

  • Kim, Dal-Ho;Lee, Woo-Dong;Kang, Sang-Gil
    • 한국데이터정보과학회:학술대회논문집
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    • pp.27-37
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    • 2003
  • In this paper, we develop noninformative priors for two parameter Pareto distribution. Specially, we derive Jeffrey's prior, probability matching prior and reference prior for the parameter of interest. In our case, the probability matching prior is only a first order and there does not exist a second order matching prior. Some simulation reveals that the matching prior performs better to achieve the coverage probability. And a real example will be given.

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Reference Priors in a Two-Way Mixed-Effects Analysis of Variance Model

  • Chang, In-Hong;Kim, Byung-Hwee
    • 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.

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Noninformative Priors for the Difference of Two Quantiles in Exponential Models

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

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.

DEVELOPING NONINFORMATIVE PRIORS FOR THE FAMILIAL DATA

  • Heo, Jung-Eun;Kim, Yeong-Hwa
    • 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.

Noninformative Priors for the Coefficient of Variation in Two Inverse Gaussian Distributions

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

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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