Model order selection of damped sinusoids by predictive densities

In this paper, we investigate the problem of model order selection of damped sinusoids from a Bayesian perspective. We derive a maximum a posteriori (MAP) criterion through a combination of Bayesian inference and predictive densities. The MAP criterion is more appropriate for damped sinusoidal models (and transient data models in general) than are the SVD based information theoretic criteria in [1]. Simulation results are provided that display the breakdown of the AIC and MDL when the data record length is not properly coupled with the information bearing portion of the data model. This deterioration in performance is related to both, the underlying asymptotics upon which the AIC and MDL rules were originally based, and to their invalid penalty terms. Conversely, the MAP criterion is not based on asymptotics, and proves to be more reliable and consistent when the observation length is varied.