On the estimation of hyperparameters for Bayesian system identification with exponentially decaying kernels

A Bayesian formulation of system identification problems has become popular recently; this is mainly due to the introduction of a family of prior descriptions (kernels) which encode structural properties of dynamical systems such as stability. The simplest instance of this kernel prescribes that the impulse response coefficients are independent random variables with exponentially decaying variance. Selecting the most suitable kernel within this class, which involves tuning the rate at which variance decay, is an important step. This paper studies the properties of the so-called “marginal likelihood” approach providing an interpretation in terms of Mean Squared Error properties of the resulting estimators.