scholarly journals Comparison of Bayesian Methods for Recovering Sinusoids

2021 ◽  
Vol 15 ◽  
pp. 36-43
Author(s):  
Dursun Üstündağ ◽  
Mehmet Cevri
Keyword(s):  
Lower Bound ◽  
Gibbs Sampling ◽  
Bayesian Methods ◽  
Integral Method ◽  
Noisy Data ◽  
Parallel Tempering ◽  
Computational Schemes ◽  
Cramer Rao Lower Bound

In this paper, we study a problem of estimating parameters of sinusoids from noisy data within Bayesian inferential framework. In this context, three different computational schemes such as, Bretthorst’s integral method (BRETTHORST), Gibbs sampling (GIBBS) and parallel tempering (PT) are studied and modifications of their algorithms were tested on data generated from synthetic signals. In addition, our emphasis is given to a comparison of their performances with respect to Cramér-Rao lower bound (CRLB).

scholarly journals Performance Analysis of Gibbs Sampling for Bayesian Extracting Sinusoids

2021 ◽  
Vol 15 ◽  
pp. 148-154
Author(s):  
Mehmet Cevri ◽  
Dursun Üstündag
Keyword(s):  
Fourier Transform ◽  
Maximum Likelihood ◽  
Lower Bound ◽  
Gibbs Sampling ◽  
Signal To Noise Ratio ◽  
Noisy Data ◽  
Data Sampling ◽  
Signal To Noise ◽  
Amplitude Estimation ◽  
Simulation Results

This paper involves problems of estimating parameters of sinusoids from white noisy data by using Gibbs sampling (GS) in a Bayesian framework. Modifications of its algorithm is tested on data generated from synthetic signals and its performance is compared with conventional estimators such as Maximum Likelihood(ML) and Discrete Fourier Transform (DFT) under a variety of signal to noise ratio (SNR) and different length of data sampling (N), regarding to Cramér-Rao lower bound (CRLB). All simulation results show its effectiveness in frequency and amplitude estimation of sinusoids.

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