Plenary Lecture

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

Professor Dursun Ustundag
The Faculty of Science and Arts,
The Department of Mathematics,
Marmara University,
Istanbul, Turkey
E-mail: dustundag@marmara.edu.tr

Abstract: In this paper, we consider a problem of detecting and estimating of sinusoids corrupted by random noise. Within a Bayesian framework, a posterior probability distribution on the parameter space is defined. Unfortunately, all Bayesian inference based on this probability distributions 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 methods. The algorithm coded in Mathematica programming language is evaluated in simulation studies on a number of synthetic data sets. The simulations results support the effectiveness of the method.