Objective priors for hypothesis testing in one-way random effects models

The Bayes factor is a key tool in hypothesis testing. Nevertheless, the important issue of which priors should be used to develop objective Bayes factors remains open. The authors consider this problem in the context of the one-way random effects model. They use concepts such as orthogonality, predi...

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Bibliographic Details
Published in:Canadian journal of statistics 2007-06, Vol.35 (2), p.303-320
Main Authors: García-Donato, Gonzalo, Sun, Dongchu
Format: Article
Language:English
Subjects:
A priori knowledge
Bayesian analysis
Bayesian inference
Bayesian method
consistency
Datasets
divergence-based prior
Frequentism
Hypotheses
Hypothesis testing
intrinsic prior
Linear models
model selection
Modeling
objective Bayes factor
orthogonality
P values
Parametric models
predictive matching prior
Significance tests
Statistical discrepancies
Statistical methods
Statistical models
Statistics
Studies
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Summary:The Bayes factor is a key tool in hypothesis testing. Nevertheless, the important issue of which priors should be used to develop objective Bayes factors remains open. The authors consider this problem in the context of the one-way random effects model. They use concepts such as orthogonality, predictive matching and invariance to justify a specific form of the priors for common parameters and derive the intrinsic and divergence based prior for the new parameter. The authors show that both intrinsic priors or divergence-based priors produce consistent Bayes factors. They illustrate the methods and compare them with other proposals. /// Le facteur de Bayes joue un rôle clef en théorie des tests. Subsiste toutefois l'épineuse question de l'identification de lois a priori menant à un facteur de Bayes objectif. Les auteurs abordent ce problème dans le cadre du modèle à effets aléatoires à un facteur. Ils exploitent des concepts tels que l'orthogonalité, le pairage prédictif et l'invariance afin de justifier des lois a priori d'une forme particulière pour les paramètres communs et d'identifier, pour le nouveau paramètre, des lois a priori intrinsèques ou déduites de la notion de divergence. Les auteurs démontrent la convergence du facteur de Bayes associé aux lois a priori intrinsèques et à celles déduites de la notion de divergence. Ils illustrent ces méthodes et les comparent à d'autres options.
ISSN:0319-5724
1708-945X
DOI:10.1002/cjs.5550350207