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Article

Recovering Sinusoids from Noisy Data Using Bayesian Inference with Simulated Annealing

by
Dursun Üstündağ
* and
Mehmet Cevri
The Department of Mathematics, Faculty of Science and Arts Marmara University, 34722, Kadıköy, Istanbul, Turkey
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2011, 16(2), 382-391; https://doi.org/10.3390/mca16020382
Published: 1 August 2011
Versions Notes

Abstract

In this paper, we studied Bayesian analysis proposed by Bretthorst[6] for a general signal model equation and combined it with a simulated annealing (SA) algorithm to obtain a global maximum of a posterior probability density function (PDF) for frequencies. Thus, this analysis offers different approach to finding parameter values through a directed, but random, search of the parameter space. For this purpose, we developed a Mathematica code of this Bayesian approach together with SA and used it for recovering sinusoids from noisy data. Simulations results support its effectiveness.
Keywords: Bayesian Statistical Inference Simulated Annealing; Parameter Estimations; Power Spectral Density; Cramér-Rao lower bound Bayesian Statistical Inference Simulated Annealing; Parameter Estimations; Power Spectral Density; Cramér-Rao lower bound

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MDPI and ACS Style

Üstündağ, D.; Cevri, M. Recovering Sinusoids from Noisy Data Using Bayesian Inference with Simulated Annealing. Math. Comput. Appl. 2011, 16, 382-391. https://doi.org/10.3390/mca16020382

AMA Style

Üstündağ D, Cevri M. Recovering Sinusoids from Noisy Data Using Bayesian Inference with Simulated Annealing. Mathematical and Computational Applications. 2011; 16(2):382-391. https://doi.org/10.3390/mca16020382

Chicago/Turabian Style

Üstündağ, Dursun, and Mehmet Cevri. 2011. "Recovering Sinusoids from Noisy Data Using Bayesian Inference with Simulated Annealing" Mathematical and Computational Applications 16, no. 2: 382-391. https://doi.org/10.3390/mca16020382

APA Style

Üstündağ, D., & Cevri, M. (2011). Recovering Sinusoids from Noisy Data Using Bayesian Inference with Simulated Annealing. Mathematical and Computational Applications, 16(2), 382-391. https://doi.org/10.3390/mca16020382

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