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Bayesian Goodness of Fit Testing with Mixtures of Triangular Distributions

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  • ROSS McVINISH
  • JUDITH ROUSSEAU
  • KERRIE MENGERSEN

Abstract

. We consider the consistency of the Bayes factor in goodness of fit testing for a parametric family of densities against a non‐parametric alternative. Sufficient conditions for consistency of the Bayes factor are determined and demonstrated with priors using certain mixtures of triangular densities.

Suggested Citation

  • ROSS McVINISH & JUDITH ROUSSEAU & KERRIE MENGERSEN, 2009. "Bayesian Goodness of Fit Testing with Mixtures of Triangular Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 337-354, June.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:2:p:337-354
    DOI: 10.1111/j.1467-9469.2008.00620.x
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    References listed on IDEAS

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    1. F. Perron & K. Mengersen, 2001. "Bayesian Nonparametric Modeling Using Mixtures of Triangular Distributions," Biometrics, The International Biometric Society, vol. 57(2), pages 518-528, June.
    2. Miguel Arcones, 2002. "Moderate deviations for M-estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 465-500, December.
    3. Sonia Petrone & Larry Wasserman, 2002. "Consistency of Bernstein polynomial posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 79-100, January.
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    Cited by:

    1. Gwangsu Kim & Yongdai Kim & Taeryon Choi, 2017. "Bayesian Analysis of the Proportional Hazards Model with Time-Varying Coefficients," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 524-544, June.
    2. Luai Al-Labadi, 2021. "The two-sample problem via relative belief ratio," Computational Statistics, Springer, vol. 36(3), pages 1791-1808, September.
    3. Surya T. Tokdar & Ryan Martin, 2021. "Bayesian Test of Normality Versus a Dirichlet Process Mixture Alternative," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 66-96, May.
    4. Barrientos, Andrés F. & Canale, Antonio, 2021. "A Bayesian goodness-of-fit test for regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    5. Vaidehi Dixit & Ryan Martin, 2022. "Estimating a Mixing Distribution on the Sphere Using Predictive Recursion," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 596-626, November.
    6. repec:dau:papers:123456789/13438 is not listed on IDEAS
    7. Angela Schörgendorfer & Adam J. Branscum & Timothy E. Hanson, 2013. "A Bayesian Goodness of Fit Test and Semiparametric Generalization of Logistic Regression with Measurement Data," Biometrics, The International Biometric Society, vol. 69(2), pages 508-519, June.

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