ESTIMATING PARAMETERS OF SINUSOIDS FROM NOISY DATA USING MAXIMUM LIKELIHOOD TOGETHER WITH MONTE-CARLO SIMULATIONS
Abstract
We consider here estimating parameters of signals from noisy data. For this purpose, a Mathematica program, in which an effective method based on the principle of maximum likelihood together with Monte-Carlo simulations is incorporated, was written and used for estimating the parameters of sinusoids corrupted by the Gaussian random noise.
Keywords
Maximum Likelihood Monte-Carlo Simulations Parameter Estimations Statistical Inference Simulated Annealing
References
- Bretthost, G. L.: “Bayesian Spectrum Analysis and Parameter Estimation”, Springer-Verlag, 12, (1997).
- Dou, L.; Hodgson, R.J.W.: “Bayesian Inference and Gibbs Sampling in Spectral Analysis and Parameter Estimation: I”, Inverse Problems, 11 (1995) 1069-1085.
- Andrieu, C.; Doucet, A.: “Joint Bayesian Model Selection and Estimation of Noisy Sinusoids via Reversible Jump MCMC”, IEEE Transactions on Signal Processing, Vol: 47, No: 10 (1999) 2667-2676.
- Capon, J.: “Maximum-likelihood spectral estimation”, Nonlinear Methods of Spectral Analysis, Springer-Verlag ( 1983).
- Gelman, A.; Carlin, J.B.; Stern, H.S.; Rubin, D.B.: “Bayesian Data Analysis”, Chapman & Hall/CRC, (2000).
- Cevri, M.: “Bayesian Parameter Estimation”, Yüksek Lisans Tezi, Marmara Üniv. Fen Bilimleri Enstitüsü, İstanbul, Türkiye, (2002).
- Fisher, R.A.: “Theory of Statistical Estimation”, Proceedings of the Cambridge Philosophy Society, 22 (1925), 700-725.
- Edwards, A.W.F.: “Likelihood”, Cambridge University Press, (1972).
- Press, W.H.; Flannery, B.P.; Teukolshy, S.A.; Vetterling, W.T.: “Numerical Recipes in C: The Art of Computing “, 2nd Ed.; Cambridge University Press, (1995).
- Kelly, J.J.: “Introduction to Data Analysis”, Essential Mathematica for Students of Science , (1998)
- Weillin, P.; Gayllord, R.; Kamin, S.: “An Introduction to Programming with Mathematica”, Cambridge University Press (2005).
- Tan, S.M.; Fox, C. ; Nicolls, G.K.: “Physics 707 Inverse Problems” (2006).
Ençok olabilirliğin monte-carlo simülasyonlarıyla birlikte kullanılmasıyla gürültülü verilerden sinüzoitlerin parametrelerinin kestirimi
Abstract
Bu makalede gürültülü verilerden sinyallerin parametrelerinin kestirimini düşünüyoruz. Bu amaç için, Monte-Carlo simülasyonları ile birlikte en çok olabilirlik prensibinin kullanımına dayanan etkili bir yöntemin uygulandığı bir Mathematica programı yazıldı ve Gauss dağılımlı gürültülerle bozulmuş sinüzoitlerin parametrelerinin kestirimi için kullanıldı.
Keywords
En Çok Olabilirlik Monte-Carlo Simülasyonları Parametre Kestirimleri İstatiksel Çıkarım Sahte sertleştirme.
References
- Bretthost, G. L.: “Bayesian Spectrum Analysis and Parameter Estimation”, Springer-Verlag, 12, (1997).
- Dou, L.; Hodgson, R.J.W.: “Bayesian Inference and Gibbs Sampling in Spectral Analysis and Parameter Estimation: I”, Inverse Problems, 11 (1995) 1069-1085.
- Andrieu, C.; Doucet, A.: “Joint Bayesian Model Selection and Estimation of Noisy Sinusoids via Reversible Jump MCMC”, IEEE Transactions on Signal Processing, Vol: 47, No: 10 (1999) 2667-2676.
- Capon, J.: “Maximum-likelihood spectral estimation”, Nonlinear Methods of Spectral Analysis, Springer-Verlag ( 1983).
- Gelman, A.; Carlin, J.B.; Stern, H.S.; Rubin, D.B.: “Bayesian Data Analysis”, Chapman & Hall/CRC, (2000).
- Cevri, M.: “Bayesian Parameter Estimation”, Yüksek Lisans Tezi, Marmara Üniv. Fen Bilimleri Enstitüsü, İstanbul, Türkiye, (2002).
- Fisher, R.A.: “Theory of Statistical Estimation”, Proceedings of the Cambridge Philosophy Society, 22 (1925), 700-725.
- Edwards, A.W.F.: “Likelihood”, Cambridge University Press, (1972).
- Press, W.H.; Flannery, B.P.; Teukolshy, S.A.; Vetterling, W.T.: “Numerical Recipes in C: The Art of Computing “, 2nd Ed.; Cambridge University Press, (1995).
- Kelly, J.J.: “Introduction to Data Analysis”, Essential Mathematica for Students of Science , (1998)
- Weillin, P.; Gayllord, R.; Kamin, S.: “An Introduction to Programming with Mathematica”, Cambridge University Press (2005).
- Tan, S.M.; Fox, C. ; Nicolls, G.K.: “Physics 707 Inverse Problems” (2006).
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | November 25, 2011 |
| Published in Issue | Year 2008 Volume: 20 Issue: 1 |
Cite
Marmara Journal of Pure and Applied Sciences
e-ISSN : 2146-5150