Modeling and Estimation of Discrete-Time Reciprocal Processes via   Probabilistic Graphical Models
  Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this paper, we provide a probabilistic graphical model for reciprocal processes. This leads to a principled solution of the smoothing problem via message passing algorithms. For the finite state space case, convergence analysis is revisited via the Hilbert metric. 
Francesca Paola Carli
stat.ML math.OC