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

X. Gu, J. Mulder, H. Hoijtink

Research output: Contribution to journalArticleScientificpeer-review

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

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Fractional Bayes Factor
Testing
Statistical Models
Bayes Factor
Software Package
Evaluate
Statistical Model
Hypothesis Testing
Evaluation

Keywords

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

Cite this

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title = "Approximated adjusted fractional Bayes factors: A general method for testing informative hypotheses",
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.",
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language = "English",
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journal = "British Journal of Mathematical and Statistical Psychology",
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Approximated adjusted fractional Bayes factors : A general method for testing informative hypotheses. / Gu, X.; Mulder, J.; Hoijtink, H.

In: British Journal of Mathematical and Statistical Psychology, Vol. 71, No. 2, 2018, p. 229-261.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Approximated adjusted fractional Bayes factors

T2 - A general method for testing informative hypotheses

AU - Gu, X.

AU - Mulder, J.

AU - Hoijtink, H.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - CONSISTENCY

KW - DIMENSION

KW - INEQUALITY CONSTRAINED HYPOTHESES

KW - LINEAR-MODELS

KW - MODEL SELECTION

KW - PRIOR DISTRIBUTIONS

KW - RATIO

KW - VARIABLE SELECTION

KW - fractional Bayes factor

KW - informative hypothesis

KW - normal approximation

KW - prior sensitivity

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DO - 10.1111/bmsp.12110

M3 - Article

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EP - 261

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