• Title/Summary/Keyword: reference priors

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Default Bayesian hypothesis testing for the scale parameters in the half logistic distributions

  • 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.2
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    • pp.465-472
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    • 2014
  • This article deals with the problem of testing the equality of the scale parameters in the half logistic distributions. We propose Bayesian hypothesis testing procedures for the equality of the scale parameters under the noninformative priors. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be dened up to a multiplicative constant. Thus 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.

Default Bayesian testing for the scale parameters in two parameter exponential distributions

  • Kang, Sang Gil;Kim, Dal Ho;Lee, Woo Dong
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.4
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    • pp.949-957
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    • 2013
  • In this paper, we consider the problem of testing the equality of the scale parameters in two parameter exponential distributions. We propose Bayesian testing procedures for the equality of the scale parameters under the noninformative priors. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Thus, 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.

Testing Two Exponential Means Based on the Bayesian Reference Criterion

  • Kim, Dal-Ho;Chung, Dae-Sik
    • Journal of the Korean Data and Information Science Society
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    • v.15 no.3
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    • pp.677-687
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    • 2004
  • We consider the comparison of two one-parameter exponential distributions with the complete data as well as the type II censored data. We adapt Bayesian test procedure for nested hypothesis based on the Bayesian reference criterion. Specifically we derive the expression for the Bayesian reference criterion to solve our problem. Also we provide numerical examples using simulated data sets to illustrate our results.

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ARMA Model Identification Using the Bayes Factor

  • Son, Young-Sook
    • Journal of the Korean Statistical Society
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    • v.28 no.4
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    • pp.503-513
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    • 1999
  • The Bayes factor for the identification of stationary ARM(p,q) models is exactly computed using the Monte Carlo method. As priors are used the uniform prior for (\ulcorner,\ulcorner) in its stationarity-invertibility region, the Jefferys prior and the reference prior that are noninformative improper for ($\mu$,$\sigma$\ulcorner).

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Bayesian Test for the Intraclass Correlation Coefficient in the One-Way Random Effect Model

  • Kang, Sang-Gil;Lee, Hee-Choon
    • Journal of the Korean Data and Information Science Society
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    • v.15 no.3
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    • pp.645-654
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    • 2004
  • In this paper, we develop the Bayesian test procedure for the intraclass correlation coefficient in the unbalanced one-way random effect model based on the reference priors. That is, the objective is to compare two nested model such as the independent and intraclass models using the factional Bayes factor. Thus the model comparison problem in this case amounts to testing the hypotheses $H_1:\rho=0$ versus $H_2:{\rho}{\neq}0$. Some real data examples are provided.

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Noninformative Priors for the Ratio of Parameters in Inverse Gaussian Distribution (INVERSE GAUSSIAN분포의 모수비에 대한 무정보적 사전분포에 대한 연구)

  • 강상길;김달호;이우동
    • The Korean Journal of Applied Statistics
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    • v.17 no.1
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    • pp.49-60
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    • 2004
  • In this paper, when the observations are distributed as inverse gaussian, we developed the noninformative priors for ratio of the parameters of inverse gaussian distribution. We developed the first order matching prior and proved that the second order matching prior does not exist. It turns out that one-at-a-time reference prior satisfies a first order matching criterion. Some simulation study is performed.

Bayesian Hypothesis Testing for Homogeneity of the Shape Parameters in the Gamma Populations

  • Kang, Sang-Gil;Kim, Dal-Ho;Lee, Woo-Dong
    • Journal of the Korean Data and Information Science Society
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    • v.18 no.4
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    • pp.1191-1203
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    • 2007
  • In this paper, we consider the hypothesis testing for the homogeneity of the shape parameters in the gamma distributions. The noninformative priors such as Jeffreys# prior or reference prior 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 objective Bayesian testing procedure for the homogeneity of the shape parameters based on the fractional Bayes factor and the intrinsic Bayes factor under the reference prior. Simulation study and a real data example are provided.

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Default Bayesian testing for normal mean with known coefficient of variation

  • Kang, Sang-Gil;Kim, Dal-Ho;Le, Woo-Dong
    • Journal of the Korean Data and Information Science Society
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    • v.21 no.2
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    • pp.297-308
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    • 2010
  • This article deals with the problem of testing mean when the coefficient of variation in normal distribution is known. We propose Bayesian hypothesis testing procedures for the normal mean 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 objective Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factor under the reference prior. Specially, we develop intrinsic priors which give asymptotically same Bayes factor with the intrinsic Bayes factor under the reference prior. Simulation study and a real data example are provided.

Bayesian Testing for the Equality of Two Inverse Gaussian Populations with the Fractional Bayes Factor

  • Ko, Jeong-Hwan
    • Journal of the Korean Data and Information Science Society
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    • v.16 no.3
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    • pp.539-547
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    • 2005
  • We propose the Bayesian testing for the equality of two independent Inverse Gaussian population means using the fractional Bayesian factors suggested by O' Hagan(1995). As prior distribution for the parameters, we assumed the noninformative priors. In order to investigate the usefulness of the proposed Bayesian testing procedures, the behaviors of the proposed results are examined via real data analysis.

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Bayesian Hypothesis Testing for Two Lognormal Variances with the Bayes Factors

  • Moon, Gyoung-Ae
    • Journal of the Korean Data and Information Science Society
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    • v.16 no.4
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    • pp.1119-1128
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    • 2005
  • The Bayes factors with improper noninformative priors are defined only up to arbitrary constants. So it is known that Bayes factors are not well defined due to this arbitrariness in Bayesian hypothesis testing and model selections. The intrinsic Bayes factor and the fractional Bayes factor have been used to overcome this problem. In this paper, we suggest a Bayesian hypothesis testing based on the intrinsic Bayes factor and the fractional Bayes factor for the comparison of two lognormal variances. Using the proposed two Bayes factors, we demonstrate our results with some examples.

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