Coherent Inferences and Improper Priors

Abstract

Formal posteriors for improper priors are investigated in connection with coherence, both in the sense of Regazzini and of Heath and Sudderth. Those priors $\pi$ which are linked with the improper prior $\gamma$ by the relation $\pi(B) = 0$ whenever $\gamma(B) < +\infty$ are studied in particular. Moreover, a characterization of the inferences which are coherent according to Heath and Sudderth is found, and several examples, exhibiting several phenomena, are given.