Model selection and comparison for independents sinusoids

In the signal processing literature, many methods have been proposed for estimating the number of sinusoidal basis functions from a noisy data set. The most popular method is the asymptotic MAP criterion, which is sometimes also referred to as the BIC. In this paper, we extend and improve this method by considering the problem in a full Bayesian framework instead of the approximate formulation, on which the asymptotic MAP criterion is based. This leads to a new model selection and comparison method, the lp-BIC, whose computational complexity is of the same order as the asymptotic MAP criterion. Through simulations, we demonstrate that the lp-BIC outperforms the asymptotic MAP criterion and other state of the art methods in terms of model selection, de-noising and prediction performance. The simulation code is available online.