Finitely Additive Priors, Coherence and the Marginalization Paradox

The marginalization paradox does not imply inconsistency for improper priors

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....

Finitely Additive Equivalent

Let L be a linear space of real bounded random variables on the probability space (Ω,A, P0). There is a finitely additive probability P on A, such that P ∼ P0 and EP (X) = 0 for all X ∈ L, if and only if c EQ(X) ≤ ess sup(−X), X ∈ L, for some constant c > 0 and (countably additive) probability Q on A such that Q ∼ P0. A necessary condition for such a P to exist is L− L∞ ∩ L∞ = {0}, where the cl...

Finitely Additive Supermartingales

The concept of finitely additive supermartingales, originally due to Bochner, is revived and developed. We exploit it to study measure decompositions over filtered probability spaces and the properties of the associated Doléans-Dade measure. We obtain versions of the Doob Meyer decomposition and, as an application, we establish a version of the Bichteler and Dellacherie theorem with no exogenou...

On finitely additive vector measures.

In this paper we extend the well-known Vitali-Hahn-Saks and Nikodým theorems for measures to finitely additive vector-valued set functions.

Representing Finitely Additive Invariant Probabilities