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Prior adjusted default Bayes factors for testing (in)equality constrained hypotheses

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  • Mulder, Joris

Abstract

A new method is proposed for testing multiple hypotheses with equality and inequality constraints on the parameters of interest. The method is based on the fractional Bayes factor with a modification that the updated prior is centered on the boundary of the constrained parameter space under investigation. The resulting prior adjusted default Bayes factors work as an “Ockham’s razor” when testing inequality constrained hypotheses, which is not the case for the fractional Bayes factor. Two different types of prior adjusted default Bayes factors are considered. In the first type, the updated prior is based on imaginary training data. Analytical and numerical examples show that this criterion converges fastest to a true inequality constrained hypothesis. In the second type, the updated prior is based on empirical training data. This second criterion only outperforms the fractional Bayes factor in the case of small samples.

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  • Mulder, Joris, 2014. "Prior adjusted default Bayes factors for testing (in)equality constrained hypotheses," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 448-463.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:448-463
    DOI: 10.1016/j.csda.2013.07.017
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    References listed on IDEAS

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    1. Overstall, Antony M. & Forster, Jonathan J., 2010. "Default Bayesian model determination methods for generalised linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3269-3288, December.
    2. A. O’Hagan, 1997. "Properties of intrinsic and fractional Bayes factors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 101-118, June.
    3. Mulder, Joris & Hoijtink, Herbert & Leeuw, Christiaan de, 2012. "BIEMS: A Fortran 90 Program for Calculating Bayes Factors for Inequality and Equality Constrained Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 46(i02).
    4. Klugkist, Irene & Hoijtink, Herbert, 2007. "The Bayes factor for inequality and about equality constrained models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6367-6379, August.
    5. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    7. Jose M. Perez, 2002. "Expected-posterior prior distributions for model selection," Biometrika, Biometrika Trust, vol. 89(3), pages 491-512, August.
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    Cited by:

    1. Mulder, Joris & Leenders, Roger Th.A.J., 2019. "Modeling the evolution of interaction behavior in social networks: A dynamic relational event approach for real-time analysis," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 73-85.
    2. Elías Moreno & Carmen Martínez, 2022. "Bayesian and frequentist evidence in one-sided hypothesis testing," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 278-297, March.
    3. Jean-Paul Fox & Joris Mulder & Sandip Sinharay, 2017. "Bayes Factor Covariance Testing in Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 979-1006, December.
    4. Florian Böing-Messing & Joris Mulder, 2018. "Automatic Bayes Factors for Testing Equality- and Inequality-Constrained Hypotheses on Variances," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 586-617, September.
    5. Guido Consonni & Roberta Paroli, 2017. "Objective Bayesian Comparison of Constrained Analysis of Variance Models," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 589-609, September.
    6. Roberta Paroli & Guido Consonni, 2020. "Objective Bayesian comparison of order-constrained models in contingency tables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 139-165, March.

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