• Title/Summary/Keyword: fractional Bayes factor

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Bayesian Model Selection in Weibull Populations

  • Kang, Sang-Gil
    • Journal of the Korean Data and Information Science Society
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    • v.18 no.4
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    • pp.1123-1134
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    • 2007
  • This article addresses the problem of testing whether the shape parameters in k independent Weibull populations are equal. We propose a Bayesian model selection procedure for equality of the shape parameters. 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 model selection procedure based on the fractional Bayes factor and the intrinsic Bayes factor under the reference prior. Simulation study and a real example are provided.

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Bayesian Hypothesis Testing for the Difference of Quantiles in Exponential Models

  • Kang, Sang-Gil
    • Journal of the Korean Data and Information Science Society
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    • v.19 no.4
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    • pp.1379-1390
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    • 2008
  • This article deals with the problem of testing the difference of quantiles in exponential distributions. We propose Bayesian hypothesis testing procedures for the difference of two quantiles 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 matching prior. Simulation study and a real data example are provided.

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

  • 김경숙;손영숙
    • Journal of Korean Society for Quality Management
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    • v.30 no.2
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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.

Computing Fractional Bayes Factor Using the Generalized Savage-Dickey Density Ratio

  • Younshik Chung;Lee, Sangjeen
    • Journal of the Korean Statistical Society
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    • v.27 no.4
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    • pp.385-396
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    • 1998
  • A computing method of fractional Bayes factor (FBF) for a point null hypothesis is explained. We propose alternative form of FBF that is the product of density ratio and a quantity using the generalized Savage-Dickey density ratio method. When it is difficult to compute the alternative form of FBF analytically, each term of the proposed form can be estimated by MCMC method. Finally, two examples are given.

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Bayesian Multiple Comparison of Binomial Populations based on Fractional Bayes Factor

  • Kim, Dal-Ho;Kang, Sang-Gil;Lee, Woo-Dong
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.1
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    • pp.233-244
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    • 2006
  • In this paper, we develop the Bayesian multiple comparisons procedure for the binomial distribution. We suggest the Bayesian procedure based on fractional Bayes factor when noninformative priors are applied for the parameters. An example is illustrated for the proposed method. For this example, the suggested method is straightforward for specifying distributionally and to implement computationally, with output readily adapted for required comparison. Also, some simulation was performed.

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Bayesian Multiple Comparison of Bivariate Exponential Populations based on Fractional Bayes Factor

  • Cho, Jang-Sik;Cho, Kil-Ho;Choi, Seung-Bae
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.3
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    • pp.843-850
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    • 2006
  • In this paper, we consider the Bayesian multiple comparisons problem for K bivariate exponential populations to make inferences on the relationships among the parameters based on observations. And we suggest the Bayesian procedure based on fractional Bayes factor when noninformative priors are applied for the parameters. Also, we give a numerical examples to illustrate our procedure.

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Bayesian One-Sided Testing for the Ratio of Poisson Means

  • Kang, Sang-Gil;Kim, Dal-Ho;Lee, Woo-Dong
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.2
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    • pp.619-631
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    • 2006
  • When X and Y have independent Poisson distributions, we develop a Bayesian one-sided testing procedures for the ratio of two Poisson means. We propose the objective Bayesian one-sided testing procedures for the ratio of two Poisson means based on the fractional Bayes factor and the intrinsic Bayes factor. Some real examples are provided.

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Bayesian Test for the Equality of Gamma Means

  • Kang, Sang-Gil
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.4
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    • pp.1413-1425
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    • 2006
  • When X and Y have independent gamma distributions, we develop a Bayesian procedure for testing the equality of two gamma means. The reference prior is derived. Using the derived reference prior, we propose a Bayesian test procedure for the equality of two gamma means using fractional Bayes factor and intrinsic Bayes factor. Simulation study and a real data example are provided.

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Bayesian Test for the Difference of Exponential Guarantee Time Parameters

  • 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.1095-1106
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    • 2005
  • When X and Y have independent two parameter exponential distributions, we develop a Bayesian testing procedures for the equality of two location parameters. The reference prior in non-regular exponential model is derived. Under this reference prior, we propose a Bayesian test procedures for the equality of two location parameters using fractional Bayes factor and intrinsic Bayes factor. Simulation study and some real data examples are provided.

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Bayesian One-Sided Testing for the Ratio of Poisson Means

  • Kang, Sang-Gil;Kim, Dal-Ho;Lee, Woo-Dong
    • 한국데이터정보과학회:학술대회논문집
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    • 2006.04a
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    • pp.295-306
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    • 2006
  • When X and Y have independent Poisson distributions, we develop a Bayesian one-sided testing procedures for the ratio of two Poisson means. We propose the objective Bayesian one-sided testing procedures for the ratio of two Poisson means based on the fractional Bayes factor and the intrinsic Bayes factor. Some real examples are provided.

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