Simultaneous credible bands for transfer function estimates

Abstract

This paper deals with simultaneous credible bands (SCBs) for transfer function estimates based on Gaussian posteriors of the impulse response vector derived from identification of high-order FIR models, where SCBs quantify estimation errors of functions over their entire domain. Though conservative, SCBs for step responses and gain/phase functions are obtained by maximizing and minimizing them over the uncertainty sets specified by critical values of ${\chi }^2$ statistics associated with the Gaussian posterior. This procedure also applies to deriving (exact) pointwise credible bands (PCBs) using relevant critical values. In numerical studies, we compute the failure rates that SCBs fail to include the true step response or gain function over their respective domains; thereby an empirical method for computing less conservative SCBs is developed.