Joint Detection and Estimation of Noisy Sinusoids using Bayesian Inference with Reversible Jump MCMC Algorithm

In this paper, we consider a problem of detecting and estimating of sinusoids corrupted by random noise within a Bayesian framework. Unfortunately, all Bayesian inference drawn from posterior probability distributions of parameters requires evaluation of some complicated high-dimensional integrals. Therefore, an attempt for performing the Bayesian computation is made to Improve an efficient stochastic algorithm based on reversible jump Markov chain Monte Carlo (RJMCMC) methods. This algorithm, coded in Mathematica programming language is evaluated in simulation studies on synthetic data sets. All the simulations results support the effectiveness of the method.