Inference for partially observed stochastic processes on a graph

For a stochastic process evolving on a (directed) tree I will show that sampling from the smoothing distribution can essentially be done by defining forward and backward maps, together with composition rules for the pairing of these maps. If transitions over edges can be composed, then it is natural to ask whether the corresponding composition rule of the resulting pairing is equivalent to composition of the separate pairings. The answer is affirmative.

Based on joint work with Moritz Schauer