In this paper we will review some properties of the ''belief propagation'' iterative map used to perform Bayesian inference in a distributed way. We use this algorithm as a starting point to address the inverse problem of encoding observation data into a probabilistic model. and focus on the situation when the data have many different statistical components, representing a variety of independent patterns. Asymptotic analysis reveals a connection with some Hopfield model. We then discuss the relevance of these results to the problem of reconstructing and predicting traffic states based on floating car data and show some experiments based on artificial and real data.