Model order selection of damped sinusoids in noise by predictive densities

We develop a procedure for the order selection of damped sinusoidal models based on the maximum a posteriori (MAP) criterion. The proposed method merges the concept of predictive densities with Bayesian inference to arrive at a complex multidimensional integral whose solution is achieved by way of the efficient Monte Carlo importance sampling technique. The importance function, a multivariate Cauchy probability density, is employed to produce stratified samples over the hypersurfaces support region. Centrality location parameters for the Cauchy are resolved by exploiting the special structure of the compressed likelihood function (CLF) and applying the fast maximum likelihood (FML) procedure of Umesh and Tufts. Simulation results allow for a comparison between our method and the singular value decomposition (SVD) based information theoretic criteria of Reddy and Biradar (see IEEE Trans. Signal Processing, vol.41, no.9, p.2872-81, 1993).