Model Selection

  • Agustín Blasco


In Chaps.  6 and  7, before making inferences about parameters of interest (e.g. before comparing treatments), we wrote a model containing ‘noise’ effects and effects of interest and we described which was the prior information of these effects, or in a frequentist context whether they were ‘fixed’ or ‘random’. We have assumed we know the right model without discussing whether there was a more appropriate model for our inferences. We can think that a better model could have been used to get better inferences. We can also think that we have underestimated our uncertainty, since we have some uncertainty about which is the best model for our inferences that we have not taken into account. The first problem is the goal of this chapter: how to choose the best model. The second problem has a difficult solution, since we cannot take into account all possible models to describe a natural phenomenon.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bernardo JM (2005) Reference analysis. In: Dey DK, Rao CR (eds) Handbook of statistics, vol 25. Elsevier, Amsterdam, pp 17–90Google Scholar
  2. Bernardo JM, Smith FM (1994) Bayesian theory. Wiley, ChichesterCrossRefGoogle Scholar
  3. Blasco A, Piles M, Varona L (2003) A Bayesian analysis of the effect of selection for growth rate on growth curves in rabbits. Genet Sel Evol 35:21–42CrossRefGoogle Scholar
  4. Burnham KP, Anderson KR (2002) Model selection and multimodel inference. Springer, New YorkGoogle Scholar
  5. Edgeworth FY (1908) On the probable error of frequency constants. J R Stat Soc 71:381–397, 499–512, 651–678, Addendum in 1908, 72:81–90Google Scholar
  6. Fisher R (1925) Theory of statistical estimation. Proc Camb Philos Soc 22:700–725CrossRefGoogle Scholar
  7. Hald A (1998) A history of mathematical statistics from 1750 to 1930. Wiley, New YorkGoogle Scholar
  8. Johnson DH (1999) The insignificance of statistical significance testing. J Wildl Manag 63:763–772CrossRefGoogle Scholar
  9. Kass RE, Adrian ER (1995) Bayes factors. J Am Stat Assoc 90:773–795CrossRefGoogle Scholar
  10. Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22:79–86CrossRefGoogle Scholar
  11. Shanon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(379–423):623–656CrossRefGoogle Scholar
  12. Sober E (2016) Occam’s razor. Cambridge University Press, CambridgeGoogle Scholar
  13. Sorensen DA, Gianola D (2002) Likelihood, Bayesian and MCMC methods in quantitative genetics. Springer, New YorkCrossRefGoogle Scholar
  14. Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A (2002) Bayesian measures of model complexity and fit. J R Stat Soc B 64:583–639CrossRefGoogle Scholar
  15. Stove D (1982) Popper and after: four modern irrationalists. Pergamon, OxfordGoogle Scholar
  16. Wilks S (1938) The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann Math Stat 9:60–62CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Agustín Blasco
    • 1
  1. 1.Institute of Animal Science and TechnologyUniversitat Politècnica de ValènciaValènciaSpain

Personalised recommendations