• 제목/요약/키워드: Default Bayes factors

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Default Bayes Factors for Testing the Equality of Poisson Population Means

  • Son, Young Sook;Kim, Seong W.
    • Communications for Statistical Applications and Methods
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    • 제7권2호
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    • pp.549-562
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    • 2000
  • Default Bayes factors are computed to test the equality of one Poisson population mean and the equality of two independent Possion population means. As default priors are assumed Jeffreys priors, noninformative improper priors, and default Bayes factors such as three intrinsic Bayes factors of Berger and Pericchi(1996, 1998), the arithmetic, the median, and the geometric intrinsic Bayes factor, and the factional Bayes factor of O'Hagan(1995) are computed. The testing results by each default Bayes factor are compared with those by the classical method in the simulation study.

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디폴트 베이즈인자를 이용한 포아송 평균모수에 대한 다중검정 (A Multiple Test of a Poisson Mean Parameter Using Default Bayes Factors)

  • 김경숙;손영숙
    • 품질경영학회지
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    • 제30권2호
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    • pp.118-129
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    • 2002
  • A multiple test of a mean parameter, λ, in the Poisson model is considered using the Bayes factor. Under noninformative improper priors, the intrinsic Bayes factor(IBF) of Berger and Pericchi(1996) and the fractional Bayes factor(FBF) of O'Hagan(1995) called as the default or automatic Bayes factors are used to select one among three models, M$_1$: λ< $λ_0, M$_2$: λ= $λ_0, M$_3$: λ> $λ_0. Posterior probability of each competitive model is computed using the default Bayes factors. Finally, theoretical results are applied to simulated data and real data.

Intrinsic Priors for Testing Two Normal Means with the Default Bayes Factors

  • Jongsig Bae;Kim, Hyunsoo;Kim, Seong W.
    • Journal of the Korean Statistical Society
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    • 제29권4호
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    • pp.443-454
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    • 2000
  • In Bayesian model selection or testing problems of different dimensions, the conventional Bayes factors with improper noninformative priors are not well defined. The intrinsic Bayes factor and the fractional Bayes factor are used to overcome such problems by using a data-splitting idea and fraction, respectively. This article addresses a Bayesian testing for the comparison of two normal means with unknown variance. We derive proper intrinsic priors, whose Bayes factors are asymptotically equivalent to the corresponding fractional Bayes factor. We demonstrate our results with two examples.

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DEFAULT BAYESIAN INFERENCE OF REGRESSION MODELS WITH ARMA ERRORS UNDER EXACT FULL LIKELIHOODS

  • Son, Young-Sook
    • Journal of the Korean Statistical Society
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    • 제33권2호
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    • pp.169-189
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    • 2004
  • Under the assumption of default priors, such as noninformative priors, Bayesian model determination and parameter estimation of regression models with stationary and invertible ARMA errors are developed under exact full likelihoods. The default Bayes factors, the fractional Bayes factor (FBF) of O'Hagan (1995) and the arithmetic intrinsic Bayes factors (AIBF) of Berger and Pericchi (1996a), are used as tools for the selection of the Bayesian model. Bayesian estimates are obtained by running the Metropolis-Hastings subchain in the Gibbs sampler. Finally, the results of numerical studies, designed to check the performance of the theoretical results discussed here, are presented.

Default Bayesian Method for Detecting the Changes in Sequences of Independent Exponential and Poisson Random Variates

  • Jeong, Su-Youn;Son, Young-Sook
    • Communications for Statistical Applications and Methods
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    • 제9권1호
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    • pp.129-139
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    • 2002
  • Default Bayesian method for detecting the changes in sequences of independent exponential random variates and independent Poisson random variates is considered. Noninformative priors are assumed for all the parameters in both of change models. Default Bayes factors, AIBF, MIBF, FBF, to check whether there is any change or not on each sequence and the posterior probability densities of change at each time point are derived. Theoretical results discussed in this paper are applied to some numerical data.

Default Bayesian one sided testing for the shape parameter in the log-logistic distribution

  • Kang, Sang Gil
    • Journal of the Korean Data and Information Science Society
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    • 제26권6호
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    • pp.1583-1592
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    • 2015
  • This paper deals with the problem of testing on the shape parameter in the log-logistic distribution. We propose default Bayesian testing procedures for the shape parameter under the reference priors. The reference prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. We can solve the this problem by the intrinsic Bayes factor and the fractional Bayes factor. Therefore we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

Default Bayesian testing equality of scale parameters in several inverse Gaussian distributions

  • Kang, Sang Gil;Kim, Dal Ho;Lee, Woo Dong
    • Journal of the Korean Data and Information Science Society
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    • 제26권3호
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    • pp.739-748
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    • 2015
  • This paper deals with the problem of testing about the equality of the scale parameters in several inverse Gaussian distributions. We propose default Bayesian testing procedures for the equality of the shape parameters under the reference priors. The reference prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Therefore we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

Instrinsic Priors for Testing Two Exponential Means with the Fractional Bayes Factor

  • Kim, Seong W.;Kim, Hyunsoo
    • Journal of the Korean Statistical Society
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    • 제29권4호
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    • pp.395-405
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    • 2000
  • This article addresses the Bayesian hypothesis testing for the comparison of two exponential mans. Conventional Bayes factors with improper non-informative priors are into well defined. The fractional Byes factor(FBF) of O'Hagan(1995) is used to overcome such as difficulty. we derive proper intrinsic priors, whose Bayes factors are asymptotically equivalent to the corresponding FBFs. We demonstrate our results with three examples.

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Default Bayesian testing for the bivariate normal correlation coefficient

  • Kang, Sang-Gil;Kim, Dal-Ho;Lee, Woo-Dong
    • Journal of the Korean Data and Information Science Society
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    • 제22권5호
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    • pp.1007-1016
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    • 2011
  • This article deals with the problem of testing for the correlation coefficient in the bivariate normal distribution. We propose Bayesian hypothesis testing procedures for the bivariate normal correlation coefficient under the noninformative prior. The noninformative priors are usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. A simulation study and an example are provided.

Default Bayesian testing for the equality of the scale parameters of several inverted exponential distributions

  • Kang, Sang Gil;Kim, Dal Ho;Lee, Woo Dong
    • Journal of the Korean Data and Information Science Society
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    • 제25권4호
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    • pp.961-970
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    • 2014
  • This article deals with the problem of testing the equality of the scale parameters of several inverted exponential distributions. We propose Bayesian hypothesis testing procedures for the equality of the scale parameters under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.