Joint Bayesian model selection and estimation of noisy sinusoids via reversible jump MCMC

In this paper, the problem of joint Bayesian model selection and parameter estimation for sinusoids in white Gaussian noise is addressed. An original Bayesian model is proposed that allows us to define a posterior distribution on the parameter space. All Bayesian inference is then based on this distribution. Unfortunately, a direct evaluation of this distribution and of its features, including posterior model probabilities, requires evaluation of some complicated high-dimensional integrals. We develop an efficient stochastic algorithm based on reversible jump Markov chain Monte Carlo methods to perform the Bayesian computation. A convergence result for this algorithm is established. In simulation, it appears that the performance of detection based on posterior model probabilities outperforms conventional detection schemes.