Preprint #97-9
The concept of Bayesian deviance functions is introduced for the purpose of assessing the precictive ability of fully parametric models. Bayesian deviance is formulated as a ratio of predictive densities, similar to the Bayes factor, except that only one of these densities corresponds to a valid model. The other, taken as the denominator in the ratio, is constructed for a 'maximal' model which is formed by choosing that prior that maximizes the predictive density for a given observation. Bayesian deviance thus does not depend on positing a legitimate alternative model to be compared with a hypothesized model, but rather is based strictly on the observed data, within the probabilistic framework dictated by the hypothesized model. Bayesian deviance is developed for exponential family models with conjugate prior distributions on the natural parameter, and is compared with several modified versions of the Bayes factor that have appeared in the literature.
Key words and phrases: Exponential families, Bayes factor, Model assessment
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