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We incorporate discrete and continuous time Markov processes as buildingblocks into probabilistic graphical models with latent and observed variables.We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm(Mider et al., 2021) for programmable inference on latent states and modelparameters. Our starting point is a generative model, a forward description ofthe probabilistic process dynamics. We backpropagate the information providedby observations through the model to transform the generative (forward) modelinto a pre-conditional model guided by the data. It approximates the actualconditional model with known likelihood-ratio between the two. The backwardfilter and the forward change of measure are suitable to be incorporated into aprobabilistic programming context because they can be formulated as a set oftransformation rules.  The guided generative model can be incorporated in different approaches toefficiently sample latent states and parameters conditional on observations. Weshow applicability in a variety of settings, including Markov chains withdiscrete state space, interacting particle systems, state space models,branching diffusions and Gamma processes.

Automatic Backward Filtering Forward Guiding for Markov processes and graphical models