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Pré-Publication, Document De Travail Année : 2017

Two prior distributions for incorporating information on a parameter θ ∈ [0, 1]

Deux loi a priori pour incorporer de l'information sur un paramètre appartenant à [0,1]

Résumé

In Bayesian statistics, the available prior information on a statistical parameter θ is taken into account via a prior distribution. We consider the problem of incorporating prior information on a parameter θ ∈ [0, 1] consisting of a 95% credible interval and either the mean or the mode. Two prior distributions are considered for incorporated these two kinds of priors: the beta distribution and the two-sided power (TSP) distribution. It appears that the beta distribution is preferable to the TSP distribution when the prior involves the mean. The preference is reversed when the prior includes the mode. We show that, in this case, there exits a unique TSP distribution which allows us to incorporate such a prior. In all the other cases, results of existence are established, but uniqueness may not hold. That is why we advocate collecting from an expert the prior mode rather the prior mean, and incorporating the resulting prior via a TSP distribution.
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Dates et versions

hal-01534675 , version 1 (07-06-2017)

Identifiants

  • HAL Id : hal-01534675 , version 1

Citer

Jérôme Dupuis. Two prior distributions for incorporating information on a parameter θ ∈ [0, 1]. 2017. ⟨hal-01534675⟩
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