The marginalization paradox does not imply inconsistency for improper priors

Abstract

The marginalization paradox involves a disagreement between two Bayesians who use two different procedures for calculating a posterior in the presence of an improper prior. We show that the argument used to justify the procedure of one of the Bayesians is inapplicable. There is therefore no reason to expect agreement, no paradox, and no evidence that improper priors are inherently inconsistent. We show further that the procedure in question can be interpreted as the cancellation of infinities in the formal posterior. We suggest that the implicit use of this formal procedure is the source of the observed disagreement.