Bayesian Inference using the Symmetric Monoidal Closed Category Structure

TL;DR

This paper explores Bayesian inference through the lens of symmetric monoidal closed category structures and the Giry monad, providing a categorical perspective on inference maps as pullback constructions.

Contribution

It introduces a novel categorical framework for Bayesian inference using symmetric monoidal closed categories and the Giry monad, highlighting the pullback construction of inference maps.

Findings

Giry monad is shown to be a strong monad

Inference maps can be characterized as pullback constructions

Provides a categorical foundation for Bayesian inference

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.