  This paper exploits extended Bayesian networks for uncertainty reasoning on
Petri nets, where firing of transitions is probabilistic. In particular,
Bayesian networks are used as symbolic representations of probability
distributions, modelling the observer's knowledge about the tokens in the net.
The observer can study the net by monitoring successful and failed steps.
  An update mechanism for Bayesian nets is enabled by relaxing some of their
restrictions, leading to modular Bayesian nets that can conveniently be
represented and modified. As for every symbolic representation, the question is
how to derive information - in this case marginal probability distributions -
from a modular Bayesian net. We show how to do this by generalizing the known
method of variable elimination.
  The approach is illustrated by examples about the spreading of diseases (SIR
model) and information diffusion in social networks. We have implemented our
approach and provide runtime results.
