Objective Bayes Factors for Informative Hypotheses: “Completing” the Informative Hypothesis and “Splitting” the Bayes Factors

  • Luis Raúl Pericchi GuerraEmail author
  • Guimei Liu
  • David Torres Núñez
Part of the Statistics for Social and Behavioral Sciences book series (SSBS)


Informative hypotheses are particular hypotheses about the vector of means μ in the classical normal ANOVA model


Training Sample Markov Chain Monte Carlo Prior Probability Markov Chain Monte Carlo Method Posterior Model Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions. Applied Mathematics Series, Vol. 55. Washington, DC, National Bureau of Standards (1970)Google Scholar
  2. [2]
    Akaike, H.: Information theory and the extension of the maximum likelihood principle. In Second International Symposium on Information Theory. Petrov, B.N., Csaki, F. (eds). Budapest, Akademia Kiado (1973) pp. 267-281Google Scholar
  3. [3]
    Berger, J., Mortera, J.: Default Bayes factors for one-sided hypothesis testing. Journal of the American Statistical Association, 31, 542–554 (1999)CrossRefMathSciNetGoogle Scholar
  4. [4]
    Berger, J., Pericchi, L.: The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association, 91, 109–122 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Berger, J., Pericchi, L.: The intrinsic Bayes factor for linear models. In Bernardo, J.M. et al. (eds) Bayesian Statistics 5. London, Oxford University Press (1996) 23–42,Google Scholar
  6. [6]
    Berger, J., Pericchi, L.: On the justification of default and intrinsic Bayes factors. In Lee, J.C. et al. (eds) Modeling and Prediction. Berlin, Springer (1997) 276–293Google Scholar
  7. [7]
    Berger, J., Pericchi, R.: Objective Bayesian methods for model selection: Introduction and comparison. In: Lahiri, P. (ed) Model Selection. Beachwood, OH, Institute of Mathematical Statistics Lecture Notes Monograph Series 38, 135–207 (2001)Google Scholar
  8. [8]
    Berger, J., Pericchi, L.: Training samples in objective Bayesian model selection. Annals of Statistics, 32, 841–869 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Berger, J., Pericchi, L., Varshavsky, J.: Bayes factors and marginal distributions in invariant situations. Sankhya, Series A, 60, 135–321 (1998)MathSciNetGoogle Scholar
  10. [10]
    De Santis, F., Spezzaferri, F.: Alternative Bayes factors for model selection. Canadian Journal of Statistics, 25, 503–515 (1997)zbMATHCrossRefGoogle Scholar
  11. [11]
    Dudley, R.M., Haughton, D.: Information criteria for multiple data sets and restricted parameters. Statistica Sinica, 7, 265–284 (1997)zbMATHMathSciNetGoogle Scholar
  12. [12]
    Giron, F.J., Moreno E., Casella, G.: Objective Bayesian analysis of multiple changepoints models (with discussion). Bayesian Statistics 9. Oxford, Oxford University Press (2006)Google Scholar
  13. [13]
    Huntjens, R.J.C., Peters, M.L., Woertman, L., Bovenschen, L.M., Martin, R.C., Postma, A.: Inter-identity amnesia in dissociative identity disorder: A simulated memory impairment? Psychological Medicine, 36, 857–863 (2006)CrossRefGoogle Scholar
  14. [14]
    Jeffreys, H.: Theory of Probability (3rd. ed.). Oxford, Oxford University Press (1961)zbMATHGoogle Scholar
  15. [15]
    Kato, B.S., Hoijtink, H.: A Bayesian approach to inequality constrained linear mixed models: Estimation and model selection. Statistical Modelling, 6, 231–249 (2006)CrossRefMathSciNetGoogle Scholar
  16. [16]
    Klugkist, I., Hoijtink, H.: The Bayes factor for inequality and about equality constrained models. Computational Statistics and Data Analysis, 51, 6367–6379 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    Laudy, O., Hoijtink, H.: Bayesian methods for the analysis of inequality constrained contingency tables. Statistical Methods in Medical Research, 16, 123–138 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    Lempers, F.B.: Posterior Probabilities of Alternative Linear Models. Rotterdam, University of Rotterdam Press (1971)zbMATHGoogle Scholar
  19. [19]
    O’Hagan, A.: Fractional Bayes factors for model comparisons. Journal of the Royal Statistical Society, Series B, 57, 115–149 (1995)MathSciNetGoogle Scholar
  20. [20]
    Pericchi, L.R.: Model selection and hypothesis testing based on objective probabilities and Bayes factors. In Dey, D.P., Rao, C.R. (eds) Bayesian Thinking, Modeling and Computation. Handbook of Statistics, Vol. 25. Amsterdam, Elsevier (2005) pp. 115–149Google Scholar
  21. [21]
    Zellner, A., Siow, A.: Posterior odds for selected regression hypothesis. In Bernardo, J.M. et al. (eds) Bayesian Statistics 1. Valencia, Valencia University Press (1980), pp. 585-603Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Luis Raúl Pericchi Guerra
    • 1
    Email author
  • Guimei Liu
    • 1
  • David Torres Núñez
    • 1
  1. 1.Department of MathematicsUniversity of Puerto Rico at Rio Piedras CampusSan JuanPuerto Rico

Personalised recommendations