The formal definition of reference priors
Abstract
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 informationtheoretic 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2009
 arXiv:
 arXiv:0904.0156
 Bibcode:
 2009arXiv0904.0156B
 Keywords:

 Mathematics  Statistics;
 62F15 (Primary) 62A01;
 62B10 (Secondary)
 EPrint:
 Published in at http://dx.doi.org/10.1214/07AOS587 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)