  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; 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.
