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.Comment: Published in at http://dx.doi.org/10.1214/07-AOS587 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Amount of information, intrinsic discrepancy, Bayesian asymptotics, confidence intervals, Fisher information, HPD regions, interval estimation, Jeffreys priors, LPL regions, objective priors, reference priors, point estimation, probability centred intervals, region estimation, Primary 62F15, Secondary 62F25, 62B10,

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