Factor Graph-Based Online Bayesian Identification and Component Evaluation for Multivariate Autoregressive Exogenous Input Models.

We present a Forney-style factor graph representation for the class of multivariate autoregressive models with exogenous inputs, and we propose an online Bayesian parameter-identification procedure based on message passing within this graph. We derive message-update rules for (1) a custom factor node that represents the multivariate autoregressive likelihood function and (2) the matrix normal Wishart distribution over the parameters. The flow of messages reveals how parameter uncertainty propagates into predictive uncertainty over the system outputs and how individual factor nodes and edges contribute to the overall model evidence. We evaluate the message-passing-based procedure on (i) a simulated autoregressive system, demonstrating convergence, and (ii) on a benchmark task, demonstrating strong predictive performance.