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Approximating Bayesian Inference by Weighted Likelihood

Xiaogang Wang
The Canadian Journal of Statistics / La Revue Canadienne de Statistique
Vol. 34, No. 2 (Jun., 2006), pp. 279-298
Stable URL: http://www.jstor.org/stable/20445201
Page Count: 20
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Approximating Bayesian Inference by Weighted Likelihood
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Abstract

The author proposes to use weighted likelihood to approximate Bayesian inference when no external or prior information is available. He proposes a weighted likelihood estimator that minimizes the empirical Bayes risk under relative entropy loss. He discusses connections among the weighted likelihood, empirical Bayes and James-Stein estimators. Both simulated and real data sets are used for illustration purposes. /// L'auteur propose l'emploi de la vraisemblance pondérée pour approximer l'inférence bayésienne en l'absence d'information externe ou a priori. Il propose un estimateur de vraisemblance pondérée qui minimise le risque de Bayes empirique sous l'entropie relative. Il établit des liens entre les estimateurs de vraisemblance pondérée, de Bayes empirique et de James-Stein. Des jeux de données réelles et simulées illustrent son propos.

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