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• W77950420 abstract "Abstract In this paper, we investigate the use of assessments of conditional previsions for modeling prior information on the parameter of a binomial model as a way of obtaining non-vacuous posterior previsions via natural extension. More specifically, we argue that a useful method for obtaining an imprecise prevision for the parameter θ of a binomial model, given a sample of size n showing r successes, is to assess imprecise previsions for θ which are conditional on samples having sizes larger than n. Inferences obtained using this approach are compared to Walley's proposal for learning from a bag of marbles. Keywords: conditional lower previsions, prior information modeling, natural extension, generalized Bayes rule, binomial model 1 Introduction Even if the theory of coherent lower previsions (CLP, Walley [1991]) is quite appealing for decision-making under uncertainty, there are still few published applications of this theory, in part because inferences obtained using natural extension tend to be excessively imprecise from the point of view of the practitioner. As was pointed out by Walley [1996b], this occurs when the assumptions and prior judgments are themselves excessively imprecise. However, one of the appealing features of CLP theory is the possibility of making inferences and taking rational decisions based on few other assumptions than coherence. If one still wants to base inferences on natural extension, the challenge therefore resides in developing, for various statistical models, strategies for encoding prior information efficiently, in the sense that few assessments of imprecise previsions be necessary to obtain useful results. The purpose of this paper is to propose and illustrate a simple method for using natural extension to obtain imprecise, but still useful, coherent posterior previsions for the parameter of a binomial model from a small number of prior judgments. It aims at showing the advantages of CLP theory, and in particular of natural extension, for the type of problems encountered by the practitioner who has to make inferences, and eventually take action, based on small samples. Various inference frameworks that have been proposed for the binomial model are reviewed and discussed in Section 2. In Section 3, we propose a different approach, based on a finite number of assessments of the conditional expectation of the parameter of the binomial model for sample sizes larger than the one at hand. These ideas are illustrated in Section 4, and compared to the approach for learning from a bag of marbles proposed by Walley [1996a]. Section 5 contains a general discussion and some conclusions." @default.
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• W77950420 date "2001-01-01" @default.
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• W77950420 title "Posterior previsions for the parameter of a binomial model via natural extension of a finite number of judgments" @default.
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