Probabilistic morphisms and Bayesian nonparametrics

Understand

In this paper we develop a functorial language of probabilistic morphisms and apply it to some basic problems in Bayesian nonparametrics.

• First we extend and unify the Kleisli category of probabilistic morphisms proposed by Lawvere and Giry with the category of statistical models proposed by Chentsov and Morse-Sacksteder.
• Then we introduce the notion of a Bayesian statistical model that formalizes the notion of a parameter space with a given prior distribution in Bayesian statistics.
• {We revisit the existence of a posterior distribution, using probabilistic morphisms}.