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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2011, 16(2), 382-391; https://doi.org/10.3390/mca16020382

Recovering Sinusoids from Noisy Data Using Bayesian Inference with Simulated Annealing

The Department of Mathematics, Faculty of Science and Arts Marmara University, 34722, Kadıköy, Istanbul, Turkey
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Published: 1 August 2011
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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
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Üstündağ, D.; Cevri, M. Recovering Sinusoids from Noisy Data Using Bayesian Inference with Simulated Annealing. Math. Comput. Appl. 2011, 16, 382-391.

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