Approximated adjusted fractional Bayes factors: A general method for testing informative hypotheses

X. Gu*, J. Mulder, H. Hoijtink

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

15 Citations (Scopus)

Abstract

Informative hypotheses are increasingly being used in psychological sciences because they adequately capture researchers’ theories and expectations. In the Bayesian framework, the evaluation of informative hypotheses often makes use of default Bayes factors such as the fractional Bayes factor. This paper approximates and adjusts the fractional Bayes factor such that it can be used to evaluate informative hypotheses in general statistical models. In the fractional Bayes factor a fraction parameter must be specified which controls the amount of information in the data used for specifying an implicit prior. The remaining fraction is used for testing the informative hypotheses. We discuss different choices of this parameter and present a scheme for setting it. Furthermore, a software package is described which computes the approximated adjusted fractional Bayes factor. Using this software package, psychological researchers can evaluate informative hypotheses by means of Bayes factors in an easy manner. Two empirical examples are used to illustrate the procedure.
Original languageEnglish
Pages (from-to)229-261
JournalBritish Journal of Mathematical and Statistical Psychology
Volume71
Issue number2
DOIs
Publication statusPublished - 2018

Keywords

  • CONSISTENCY
  • DIMENSION
  • INEQUALITY CONSTRAINED HYPOTHESES
  • LINEAR-MODELS
  • MODEL SELECTION
  • PRIOR DISTRIBUTIONS
  • RATIO
  • VARIABLE SELECTION
  • fractional Bayes factor
  • informative hypothesis
  • normal approximation
  • prior sensitivity

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