Bayesian Model Selection of Exponential Time Series Through Adaptive Importance Sampling

Abstract

Information provided by the accurate model selection of exponential time series is indispensable in many areas of science and engineering. This paper presents a method for the simultaneous detection and estimation of signals composed of sums of damped exponentials in additive noise. The method is entirely Bayesian in that the utility of a marginalized posterior probability density allows for the formulation of a maximum a posteriori (MAP) model selection criterion. Numerical integrations are accomplished through the application of a computationally efficient algorithm known as Adaptive Importance Sampling (AIS). This procedure, which requires no knowledge regarding the functional form of the integrands and enforces parameter constraints with relative ease, presents itself as a welcome alternative to constrained multidimensional optimization. Monte-Carlo simulations on two component synthesized data indicate a n e table improvement in selection performance of the MAP over both, the AIC and MDL.