Analysis and Probability seminar

Abstract: In category theory, optics have been proposed for modelling systems with bidirectional data flow. The bidirectional nature of the changes to the transition laws of Markov models under conditioning or control can be formalised through Doob’s h-transform. In this talk, I show how Doob’s h-transform composes optically and can be realised as a lax monoidal functor from a category of Markov kernels to a category of optics. I further explore how this framework extends to related constructions such as guided, controlled, or twisted processes, providing a categorical perspective on the compositional semantics of conditioning in probabilistic models.