Summary A procedure is proposed to derive reference posterior distributions which approximately describe the inferential content of the data without incorporating any other information. More explicitly, operational priors, derived from information‐theoretical considerations, are used to obtain reference posteriors which may be expected to approximate the posteriors which would have been obtained with the use of proper priors describing vague initial states of knowledge. The results obtained unify and generalize some previous work and seem to overcome criticisms to which this has been subject.

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In multi-parameter models, reference priors typically depend on the parameter or quantity of interest, and it is well known that this is necessary to produce objective posterior distributions with optimal properties. There are, however, many situations where one is simultaneously interested in all the parameters of the model or, more realistically, in functions of them that include aspects such as prediction, and it would then be useful to have a single objective prior that could safely be used to produce reasonable posterior inferences for all the quantities of interest. In this paper, we consider three methods for selecting a single objective prior and study, in a variety of problems including the multinomial problem, whether or not the resulting prior is a reasonable overall prior.Comment: Published at http://dx.doi.org/10.1214/14-BA915 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY Noninformative priors are developed, using the reference prior approach, for multiparameter problems in which there may be parameters of interest and nuisance parameters. For a given grouping of parameters and ordering of the groups, intuitively, according to inferential importance, an algorithm for determining the associated reference prior is presented. The algorithm is illustrated on the multinomial problem, with discussion of the variety and success of various groupings and ordering strategies.Some key words: Bayesian inference; Multiparameter problem; Noninformative prior.This content downloaded from 62.122.76.48 on Tue