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Abstract:
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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 such dependence is necessary to produce objective priors that result in procedures with optimal properties. There are, however, many situations where one is simultaneously interested in all the parameters of the model or functions of them (prediction of future observables is one such scenario), and it would then be useful to have a single objective prior which could safely be used to produce reasonable marginal posteriors for all the quantities of interest. In this talk, 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 good approximation to the parameter-specific reference priors.
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