Comments on “Joint Bayesian Model Selection and Estimation of Noisy Sinusoids Via Reversible Jump MCMC”

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 the so-called Metropolis–Hastings–Green (MHG) ratio, which determines the acceptance probability for the proposed moves. It turns out that the expression of the MHG ratio that was given in the paper of Andrieu and Doucet for “Birth-or-Death” moves is erroneous and has been reproduced in many subsequent papers dealing with RJ-MCMC sampling in the signal processing literature. This note fixes the erroneous expression and briefly discusses its cause and consequences.