  We define and study an inference algorithm based on "belief propagation" (BP)
and the Bethe approximation. The idea is to encode into a graph an a priori
information composed of correlations or marginal probabilities of variables,
and to use a message passing procedure to estimate the actual state from some
extra real-time information. This method is originally designed for traffic
prediction and is particularly suitable in settings where the only information
available is floating car data. We propose a discretized traffic description,
based on the Ising model of statistical physics, in order to both reconstruct
and predict the traffic in real time. General properties of BP are addressed in
this context. In particular, a detailed study of stability is proposed with
respect to the a priori data and the graph topology. The behavior of the
algorithm is illustrated by numerical studies on a simple traffic toy model.
How this approach can be generalized to encode superposition of many traffic
patterns is discussed.
