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Lois bayésiennes a priori dans un plan binomial séquentiel

Abstract : The reformulation by R. de Cristofaro of the Bayes theorem allows to integrate the information on the experimental design in the prior distribution. In accepting to transgress the Likelihood and Stopping Rules principles, a new framework allows to move on the issue of sequenciality in the Bayesian inference. Considering that the information on the design is contained in the Fisher information, a new family of priors is derived from a likelihood directly related to the sampling rule. The case of the study of a proportion in the sequential context of successive Binomial samplings leads to consider the Beta-J distribution. The study on several sequential designs allows to state that the "corrected Jeffreys prior" compensates the bias induced on the observed proportion. An application in the estimation shows the relationship between the parameters of the Beta-J and Beta distributions in the fixed sampling. The mean and mode of the posterior distributions show remarkable frequentist properties. As well, the corrected Jeffreys interval has an optimal covering rates as the correction compensates the effect of stopping rule on the limits. Last, a test procedure, whose the errors are interpreted in terms of both bayesian probabilities of hypotheses and frequentist risks, is designed with a rule for stopping and rejecting H0 based on a limit value of the Bayes factor. It is shown how the corrected Jeffreys prior compensates the ratio of evidences and guarantees the unicity of solutions, even when the null hypothesis is composite.
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Submitted on : Thursday, November 25, 2010 - 1:53:23 PM
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  • HAL Id : tel-00539868, version 1


Pierre Bunouf. Lois bayésiennes a priori dans un plan binomial séquentiel. Mathématiques [math]. Université de Rouen, 2006. Français. ⟨tel-00539868⟩



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