Bayesian procedure for the detection of damped signals

Multiple hypotheses testing arises in many signal processing applications. It can be viewed as a model selection problem, and as such, is commonly resolved by invoking the popular MDL or AIC rules. These rules are very often inappropriately applied however, particularly when the signal models violate the underlying conditions on which the rules are based. The tools of Bayesian inference provide a mechanism for the specification of more accurate criteria for model selection. Through appropriate approximations of the prior predictive densities, one can develop rules similar in form to the AIC and MDL, but with a more complete penalty term. The derived rules are approximations of the maximum a posteriori criterion (MAP), which for a uniform cost function is known to be optimal. We present a general solution to the problem followed by a consideration of the special case of damped signals in white Gaussian noise. In particular, we investigate models whose signal components are comprised of damped sinusoids. Monte Carlo simulations are performed, the results of which indicate a marked improvement over both, the AIC and MDL.