• Title/Summary/Keyword: Imaginary training sample method

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A Bayesian Test Criterion for the Multivariate Behrens-Fisher Problem

  • Kim, Hea-Jung
    • Journal of the Korean Statistical Society
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    • v.28 no.1
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    • pp.107-124
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    • 1999
  • An approximate Bayes criterion for multivariate Behrens-Fisher problem is proposed and examined. Development of the criterion involves derivation of approximate Bayes factor using the imaginary training sample approach introduced by Speigelhalter and Smith (1982). The criterion is designed to develop a Bayesian test, so that it provides an alternative test to other tests based upon asymptotic sampling theory (such as the tests suggested by Bennett(1951), James(1954) and Yao(1965). For the derived criterion, numerical studies demonstrate routine application and give comparisons with the classical tests.

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A Bayes Criterion for Testing Homogeneity of Two Multivariate Normal Covariances

  • Kim, Hea-Jung
    • Journal of the Korean Statistical Society
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    • v.27 no.1
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    • pp.11-23
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    • 1998
  • A Bayes criterion for testing the equality of covariance matrices of two multivariate normal distributions is proposed and studied. Development of the criterion invloves calculation of Bayes factor using the imaginary sample method introduced by Spiegelhalter and Smith (1982). The criterion is designed to develop a Bayesian test criterion, so that it provides an alternative test criterion to those based upon asymptotic sampling theory (such as Box's M test criterion). For the constructed criterion, numerical studies demonstrate routine application and give comparisons with the traditional test criteria.

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A Bayes Criterion for Selecting Variables in MDA (MDA에서 판별변수 선택을 위한 베이즈 기준)

  • 김혜중;유희경
    • The Korean Journal of Applied Statistics
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    • v.11 no.2
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    • pp.435-449
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    • 1998
  • In this article we have introduced a Bayes criterion for the variable selection in multiple discriminant analysis (MDA). The criterion is a default Bayes factor for the comparision of homo/heteroscadasticity of the multivariate normal means. The default Bayes factor is obtained from a development of the imaginary training sample method introduced by Spiegelhalter and Smith (1982). Based an the criterion, we also provided a test for additional discrimination in MDA. The advantage of the criterion is that it is not only applicable for the optimal subset selection method but for the stepwise method. More over, the criterion can be reduced to that for two-group discriminant analysis. Thus the criterion can be regarded as an unified alternative to variable selection criteria suggested by various sampling theory approaches. To illustrate the performance of the criterion, a numerical study has bean done via Monte Carlo experiment.

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A Bayesian Diagnostic for Influential Observations in LDA

  • Lim, Jae-Hak;Lee, Chong-Hyung;Cho, Byung-Yup
    • Journal of Korean Society for Quality Management
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    • v.28 no.1
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    • pp.119-131
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    • 2000
  • This paper suggests a new diagnostic measure for detecting influential observations in linear discriminant analysis (LDA). It is developed from a Bayesian point of view using a default Bayes factor obtained from the imaginary training sample methodology. The Bayes factor is taken as a criterion for testing homogeneity of covariance matrices in LDA model. It is noted that the effect of an observation over the criterion is fully explained by the diagnostic measure. We suggest a graphical method that can be taken as a tool for interpreting the diagnostic measure and detecting influential observations. Performance of the measure is examined through an illustrative example.

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