A branch of Bayesian inference involves the analysis of so-called "Bayesian networks", defined as directed acyclic networks composed of probabilistic connections. We extend this class of networks to consider cyclic Bayesian networks, which incorporate every pair of inverse conditional probabilities or probability density functions, thereby enabling the application of Bayesian updating around the network. The networks are assumed Markovian, although this assumption can be relaxed when necessary. The analysis of probabilistic cycles reveals a deep connection to the mutual information between pairs of variables on the network. Analysis of a four-parameter network - of the form of a commutative diagram - is shown to enable thedevelopment of a new branch of Bayesian inference using a reduced order model (coarse-graining) framework.

### S³: Bayesian Cyclic Networks, Mutual Information and Reduced-Order Bayesian Inference

Séminaire le 17 Juillet 2015, 10h30 à CentraleSupelec (Gif-sur-Yvette) Salle des séminaires du L2S

**Robert Niven, University of New South Wales, Canberra, Australia**