  Probabilistic model checking for systems with large or unbounded state space
is a challenging computational problem in formal modelling and its
applications. Numerical algorithms require an explicit representation of the
state space, while statistical approaches require a large number of samples to
estimate the desired properties with high confidence. Here, we show how model
checking of time-bounded path properties can be recast exactly as a Bayesian
inference problem. In this novel formulation the problem can be efficiently
approximated using techniques from machine learning. Our approach is inspired
by a recent result in statistical physics which derived closed form
differential equations for the first-passage time distribution of stochastic
processes. We show on a number of non-trivial case studies that our method
achieves both high accuracy and significant computational gains compared to
statistical model checking.
