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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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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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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