Inherent difficulties of non-Bayesian likelihood-based inference, as revealed by an examination of a recent book by Aitkin
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14 avril 2015
- handle: 10670/1.2uyrr2
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Statistics & Risk Modeling
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30
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2
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2013
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105-120
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De Gruyter
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http://dx.doi.org/10.1524/strm.2013.1113
Mots-clés
Foundations Bayes factor Bayesian model choice testing of hypotheses improper priors 519 Probabilités et mathématiques appliquéesSujets proches
Induction, Ampliative Ampliative induction Inference (Logic) Pattern ModelCiter ce document
Andrew Gelman et al., « Inherent difficulties of non-Bayesian likelihood-based inference, as revealed by an examination of a recent book by Aitkin », IFD : Chaire Les Particuliers face aux risques : Analyse et réponse des marchés, ID : 10670/1.2uyrr2
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For many decades, statisticians have made attempts to prepare the Bayesian omelette without breaking the Bayesian eggs; that is, to obtain probabilistic likelihood-based inferences without relying on informative prior distributions. A recent example is Murray Aitkin´s recent book, Statistical Inference, which presents an approach to statistical hypothesis testing based on comparisons of posterior distributions of likelihoods under competing models. Aitkin develops and illustrates his method using some simple examples of inference from iid data and two-way tests of independence. We analyze in this note some consequences of the inferential paradigm adopted therein, discussing why the approach is incompatible with a Bayesian perspective and why we do not find it relevant for applied work.