  Reference analysis produces objective Bayesian inference, in the sense that
inferential statements depend only on the assumed model and the available data,
and the prior distribution used to make an inference is least informative in a
certain information-theoretic sense. Reference priors have been rigorously
defined in specific contexts and heuristically defined in general, but a
rigorous general definition has been lacking. We produce a rigorous general
definition here and then show how an explicit expression for the reference
prior can be obtained under very weak regularity conditions. The explicit
expression can be used to derive new reference priors both analytically and
numerically.
