  The interpretation of data in terms of multi-parameter models of new physics,
using the Bayesian approach, requires the construction of multi-parameter
priors. We propose a construction that uses elements of Bayesian reference
analysis. Our idea is to initiate the chain of inference with the reference
prior for a likelihood function that depends on a single parameter of interest
that is a function of the parameters of the physics model. The reference
posterior density of the parameter of interest induces on the parameter space
of the physics model a class of posterior densities. We propose to continue the
chain of inference with a particular density from this class, namely, the one
for which indistinguishable models are equiprobable and use it as the prior for
subsequent analysis. We illustrate our method by applying it to the constrained
minimal supersymmetric Standard Model and two non-universal variants of it.
