[Statlist] Séminaires de Statistique - Université de Neuchâtel

[KONDYLIS Atanassios]

Séminaires de Statistique 

Mardi 22-03-2005 - 11h 00 
Groupe de Statistique, Espace de l'Europe 4, Neuchâtel

Objective Bayesian Inference: A General Definition of a Reference Prior 
Jose-Miguel Bernardo
Universidad de Valencia, España 

Reference analysis produces objective Bayesian inference, that is Bayesian inferential statements which only depend on the assumed model and the available data. A reference prior function is a mathematical description of that situation where data would better dominate prior knowledge about the quantity of interest. Reference priors are not descriptions of personal beliefs; they are proposed as technical devices to produce reference posteriors for the quantities of interest, obtained by formal use of Bayes theorem with a reference prior function followed by appropriate probability operations. It is argued that reference posteriors encapsulate inferential statements over which there could be a general consensus and, therefore, may be used as standards for scientific communication. In this paper, statistical information theory is used to provide a general definition of a reference prior function from first principles. An explicit form for the reference prior is then obtained under very weak regularity conditions, and this is shown to contain the original reference algorithms as particular cases. Examples are given where a reference prior does not exist. Maximum entropy priors and Jeffreys priors are both obtained as particular cases under suitable conditions. This presentation concentrates on one parameter models, but the basic ideas are easily extended to multiparameter problems.