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Bayesian model selection using encompassing priors

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  • Irene Klugkist
  • Bernet Kato
  • Herbert Hoijtink

Abstract

This paper deals with Bayesian selection of models that can be specified using inequality constraints among the model parameters. The concept of encompassing priors is introduced, that is, a prior distribution for an unconstrained model from which the prior distributions of the constrained models can be derived. It is shown that the Bayes factor for the encompassing and a constrained model has a very nice interpretation: it is the ratio of the proportion of the prior and posterior distribution of the encompassing model in agreement with the constrained model. It is also shown that, for a specific class of models, selection based on encompassing priors will render a virtually objective selection procedure. The paper concludes with three illustrative examples: an analysis of variance with ordered means; a contingency table analysis with ordered odds‐ratios; and a multilevel model with ordered slopes.

Suggested Citation

  • Irene Klugkist & Bernet Kato & Herbert Hoijtink, 2005. "Bayesian model selection using encompassing priors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 57-69, February.
    • Handle: RePEc:bla:stanee:v:59:y:2005:i:1:p:57-69
    DOI: 10.1111/j.1467-9574.2005.00279.x
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    Cited by:

    1. 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.
    2. Gordon Anderson, Alessio Farcomeni, Maria Grazia Pittau and Roberto Zelli, 2019. "Multidimensional Nation Wellbeing, More Equal yet More Polarized: An Analysis of the Progress of Human Development Since 1990," Journal of Economic Development, Chung-Ang Unviersity, Department of Economics, vol. 44(1), pages 1-22, March.
    3. Herbert Hoijtink & Irene Klugkist, 2007. "Comparison of Hypothesis Testing and Bayesian Model Selection," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(1), pages 73-91, February.
    4. Bartolucci, Francesco & Scaccia, Luisa & Farcomeni, Alessio, 2012. "Bayesian inference through encompassing priors and importance sampling for a class of marginal models for categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4067-4080.
    5. Wetzels, Ruud & Grasman, Raoul P.P.P. & Wagenmakers, Eric-Jan, 2010. "An encompassing prior generalization of the Savage-Dickey density ratio," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2094-2102, September.
    6. Wenqing Li & Ming-Hui Chen & Xiaojing Wang & Dipak K. Dey, 2018. "Bayesian Design of Non-inferiority Clinical Trials Via the Bayes Factor," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(2), pages 439-459, August.
    7. Oh, Man-Suk, 2014. "Bayesian comparison of models with inequality and equality constraints," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 176-182.
    8. Francesco Bartolucci & Alessio Farcomeni & Luisa Scaccia, 2017. "A Nonparametric Multidimensional Latent Class IRT Model in a Bayesian Framework," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 952-978, December.

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