A prior predictive loss function for the evaluation of inequality constrained hypotheses

Rens van de Schoot*, Herbert Hoijtink, Jan-Willem Romeijn, Daniel Brugman

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)
31 Downloads (Pure)


In many types of statistical modeling, inequality constraints are imposed between the parameters of interest. As we will show in this paper, the DIC (i.e., posterior Deviance Information Criterium as proposed as a Bayesian model selection tool by Spiegelhalter, Best, Carlin, & Van Der Linde, 2002) fails when comparing inequality constrained hypotheses. In this paper, we will derive the prior DIC and show that it also fails when comparing inequality constrained hypotheses. However, it will be shown that a modification of the prior predictive loss function that is minimized by the prior DIC renders a criterion that does have the properties needed in order to be able to compare inequality constrained hypotheses. This new criterion will be called the Prior Information Criterion (PIC) and will be illustrated and evaluated using simulated data and examples. The PIC has a close connection with the marginal likelihood in combination with the encompassing prior approach and both methods will be compared. All in all, the main message of the current paper is: (1) do not use the classical DIC when evaluating inequality constrained hypotheses, better use the PIC; and (2) the PIC is considered a proper model selection tool in the context of evaluating inequality constrained hypotheses. (C) 2011 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)13-23
Number of pages11
JournalJournal of Mathematical Psychology
Issue number1
Publication statusPublished - Feb-2012


  • Bayesian model selection
  • Inequality constrained hypothesis
  • Deviance information criterion
  • DIC

Cite this