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 …

Reversible jump MCMC (RJ-MCMC) sampling techniques, which allow to jointly tackle
model selection and parameter estimation problems in a coherent Bayesian framework,
have become increasingly popular in the signal processing literature since the seminal
paper of Andrieu and Doucet [“Joint Bayesian model selection and estimation of noisy
sinusoids via reversible jump MCMC,” IEEE Trans. Signal Process, vol. 47, no. 10, pp. 2667–
2676, 1999]. Crucial to the implementation of any RJ-MCMC sampler is the computation of …