Bayesian Inference using the Symmetric Monoidal Closed Category Structure

2016/01/11 by Sturtz, Kirk
#Category Theory (math.CT) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1601.02593

Abstract

Using the symmetric monoidal closed category structure of the category of measurable spaces, in conjunction with the Giry monad which we show is a strong monad, we analyze Bayesian inference maps and their construction in relation to the tensor product probability. This perspective permits the inference maps to be seen as a pullback construction.

Related

• Bayesian machine learning via category theory
• The existence and utility of Giry algebras in probability theory
• Categorical Probability Theory
• Commutativity and liftings of codensity monads of probability measures
• A category theory framework for Bayesian learning