Location Reparametrization and Default Priors for Statistical Analysis

This paper develops default priors for Bayesian analysis that reproduce familiar frequentist and Bayesian analyses for models that are exponential or location. For the vector parameter case there is an information adjustment that avoids the Bayesian marginalizationparadoxes and properly targets the prior on the parameter of interest thus adjusting for any complicating nonlinearity; the details of this vector Bayesian issue will be investigated in detail elsewhere. As in wide generality a statistical model has an inference componentstructure that is approximately exponential or approximately location to third order, this provides general default prior procedures that can be described as reweighting likelihood in accord with a Jeffreys’ prior based on observed information. Two asymptotic models, that have variable and parameter of the same dimension and agree at a data point to first derivative conditional on an approximate ancillary, produce the same p-values to third order for inferences concerning scalar interest parameters. With