Online Bayesian system identification in multivariate autoregressive models via message passing

In multivariate autoregressive models with exogenous inputs (MARX), the evolution of the signal incorporates past observations and controls, producing substantial uncertainty during parameter estimation. Bayesian inference procedures can quantify this uncertainty and propagate it towards future predictions [5], [6]. Quantified uncertainty is valuable on its own, but also useful to sensor fusion, optimal experimental design and adaptive control [7], [8], [9], [10], [11]. We present an exact recursive Bayesian estimator whose computation is distributed over a probabilistic graphical model. Bayesian inference in multivariate autoregressive models has a rich history, especially in econometrics [1], [3].