Abstract
A key sticking point of Bayesian analysis is the choice of prior
distribution, and there is a vast literature on potential defaults including
uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and
weakly informative priors. These methods, however, often manifest a key
conceptual tension in prior modeling: a model encoding true prior information
should be chosen without reference to the model of the measurement process, but
almost all common prior modeling techniques are implicitly motivated by a
reference likelihood. In this paper we resolve this apparent paradox by placing
the choice of prior into the context of the entire Bayesian analysis, from
inference to prediction to model evaluation.
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