II. REFERENCE PRIORS In 1979, Bernardo [8] introduced a formal rule for constructing what he called a reference prior. The goal was to construct a prior which, in a sense to be made precise, contained as little information as possible relative to the statistical model under consideration. By statistical model he meant a representation of the entire experimental design, including the probability distribution of the data, the sampling space, and the stopping rule. Hence, by construction reference priors depend on all these aspects of a statistical model, and so will inferences derived from data with the help of a reference prior. This may seem to violate the so-called likelihood principle [14], according to which all the information about unknown model parameters obtainable from an experiment is contained in the likelihood function, i.e. the probability distribution of the data, evaluated at the observations and viewed as a function of the parameters. While this is formally true, it should be kept in mind that the likelihood principle applies after data have been observed, whereas reference priors are constructed at the experimental design stage. Their purpose is to approximate a consensus of opinions that is suitable for scientific communication. This is generally unproblematic in large-sample situations, where posterior inferences are dominated by the likelihood function. In small sample cases however, results obtained with reference priors should be considered preliminary, and a careful study should be conducted of the degree to which inferences about the physics model underlying the observations can be trusted. This can be achieved by examining the sensitivity of the results to changes in the prior, and subsequently assessing the need for additional observations. Reference priors have several desirable properties, including 1. generality: a well-defined algorithm exists to create a reference prior for almost any type of estimation problem, and the resulting posterior is proper; 2. invariance: given a one-to-one map from a parameter θ to a parameter φ , applying the reference prior construction separately to θ and φ yields posteriors that are related by the correct transformation law, π ( φ | x ) = π ( θ | x ) | ∂θ/∂φ | ; 3. sampling consistency: the posterior densities from an ensemble of experiments tend to cluster around the true values of the parameters; and 4. coherence: inferences derived from reference priors avoid marginalization paradoxes. 4