A categorical foundation for bayesian probability

Abstract

Building on the work of Lawvere and others, we develop a categorical framework for Bayesian probability. This foundation will then allow for Bayesian representations of uncertainty to be integrated into other categorical modeling applications. The main result uses an existence theorem for regular conditional probabilities by Faden, which holds in more generality than the standard setting of Polish spaces. This more general setting is advantageous, as it allows for non-trivial decision rules (Eilenberg-Moore algebras) on finite (as well as non finite) spaces. In this way, we obtain a common framework for decision theory and Bayesian probability. © 2013 © Springer Science+Business Media Dordrecht (outside the USA).