Evidential Decision Theory via Partial Markov Categories

TL;DR

This paper introduces partial Markov categories to model constrained stochastic processes, proves a synthetic Bayes theorem, and formalizes Evidential Decision Theory within this framework, with practical examples.

Contribution

It develops the concept of partial Markov categories, enabling the encoding of constraints and observations in stochastic processes, and formalizes Evidential Decision Theory using this new framework.

Findings

Synthetic Bayes theorem proved for partial Markov categories

Normalisations of partial theories can be computed within original categories

Implemented examples demonstrate the practical application of the theory

Abstract

We introduce partial Markov categories. In the same way that Markov categories encode stochastic processes, partial Markov categories encode stochastic processes with constraints, observations and updates. In particular, we prove a synthetic Bayes theorem and we apply it to define a syntactic partial theory of observations on any Markov category, whose normalisations can be computed in the original Markov category. Finally, we formalise Evidential Decision Theory in terms of partial Markov categories, and provide implemented examples.