Detection and estimation of signals by reversible jump Markov chain Monte Carlo computations

Markov Chain Monte Carlo (MCMC) samplers have been a very powerful methodology for estimating signal parameters. With the introduction of the reversible jump MCMC sampler, which is a Metropolis-Hastings method adapted to general state spaces, the potential of the MCMC methods has risen to a new level. Consequently, the MCMC methods currently play a major role in many research activities. In this paper we propose a reversible jump MCMC sampler based on predictive distributions obtained by integrating out unwanted parameters. The proposal distributions are approximations of the posterior distributions of the remaining parameters and are computed by sampling importance resampling (SIR). We apply the method to the problem of signal detection and parameter estimation of signals. To illustrate the proposed procedure, we present an example of sinusoids embedded in noise.