Bayesian estimation of sinusoidal signals via parallel tempering

Authors:
M. Cevri;D. Üstündaǧ
Affiliations:
The Department of Mathematics, The Faculty of Science and Arts, The University of Marmara, Istanbul, Turkey;The Department of Mathematics, The Faculty of Science and Arts, The University of Marmara, Istanbul, Turkey
Venue:
WAV'09 Proceedings of the 3rd WSEAS international symposium on Wavelets theory and applications in applied mathematics, signal processing & modern science
Year:
2009

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Abstract

This paper deals with a parameter estimation problem within a Bayesian framework. Performing Bayesian inference about the parameters is a challenging computational problem and requires an evaluation of complicated high-dimensional integrals. In this context, we make an attempt to improve an efficient stochastic procedure, proposed by Gregory, which is based on a parallel tempering Markov Chain Monte Carlo method (MCMC). We code its algorithm in Mathematica and then test it for estimating parameters of sinusoids corrupted by a random noise. Computer simulations support its effectiveness.