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- W2024159897 abstract "A multi-level model allows the possibility of marginalization across levels in different ways, yielding more than one possible marginal likelihood. Since log-likelihoods are often used in classical model comparison, the question to ask is which likelihood should be chosen for a given model. The authors employ a Bayesian framework to shed some light on qualitative comparison of the likelihoods associated with a given model. They connect these results to related issues of the effective number of parameters, penalty function, and consistent definition of a likelihood-based model choice criterion. In particular, with a two-stage model they show that, very generally, regardless of hyperprior specification or how much data is collected or what the realized values are, a priori, the first-stage likelihood is expected to be smaller than the marginal likelihood. A posteriori, these expectations are reversed and the disparities worsen with increasing sample size and with increasing number of model levels. Dans un modèle multi-couches, il y a plusieurs façons de procéder à une marginalisation, et donc plus d'une vraisemblance marginale. Sachant que les log-vraisemblances sont souvent employées pour comparer des modèles entre eux, on se demande quelle vraisemblance choisir pour un modèle particulier. Adoptant une approche bayésienne, les auteurs jettent un éclairage nouveau sur la comparaison qualitative des diverses vraisemblances associées à un modèle donné. Ils lient ces résultats à des questions périphéri-ques concernant le nombre de paramètres, la pénalisation et la définition d'un critère de choix de modèle cohérent avec la vraisemblance. Dans le cadre particulier d'un modèle à deux couches, ils montrent que sous des conditions très générales, l'espérance de la vraisemblance de premier niveau est, a priori, plus petite que celle de la vraisemblance marginale, et ce peu importe le choix de la loi a priori sur les hyper-paramètres, le nombre ou la valeur des observations recueillies. A posteriori, l'inégalité est renversée et l'écart se creuse à mesure qu'augmentent la taille échantillonnale et le nombre de couches du modèle." @default.
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- W2024159897 date "2003-09-01" @default.
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- W2024159897 title "Inequalities between expected marginal log-likelihoods, with implications for likelihood-based model complexity and comparison measures" @default.
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- W2024159897 doi "https://doi.org/10.2307/3316084" @default.
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