A generalization of the Savage-Dickey density ratio for equality and order constrained testing

Joris Mulder*, Eric-Jan Wagenmakers, Maarten Marsman

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

The Savage–Dickey density ratio is a specific expression of the Bayes factor when testing a precise (equality constrained) hypothesis against an unrestricted alternative. The expression greatly simplifies the computation of the Bayes factor at the cost of assuming a specific form of the prior under the precise hypothesis as a function of the unrestricted prior. A generalization was proposed by Verdinelli and Wasserman such that the priors can be freely specified under both hypotheses while keeping the computational advantage. This article presents an extension of this generalization when the hypothesis has equality as well as order constraints on the parameters of interest. The methodology is used for a constrained multivariate t-test using the JZS Bayes factor and a constrained hypothesis test under the multinomial model.
Original languageEnglish
Number of pages8
JournalThe American Statistician
DOIs
Publication statusE-pub ahead of print - 2021

Keywords

  • BAYES FACTORS
  • Bayes factors
  • Constrained hypotheses
  • Constrained multinomial models
  • Constrained multivariate Bayesiant-test
  • INEQUALITY

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