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http://dx.doi.org/10.5351/KJAS.2009.22.4.759

Separating Signals and Noises Using Mixture Model and Multiple Testing  

Park, Hae-Sang (Department of Industrial and Management Engineering POSTECH)
Yoo, Si-Won (Customer Satisfaction Improvement Team, NHN)
Jun, Chi-Hyuck (Department of Industrial and Management Engineering, POSTECH)
Publication Information
The Korean Journal of Applied Statistics / v.22, no.4, 2009 , pp. 759-770 More about this Journal
Abstract
A problem of separating signals from noises is considered, when they are randomly mixed in the observation. It is assumed that the noise follows a Gaussian distribution and the signal follows a Gamma distribution, thus the underlying distribution of an observation will be a mixture of Gaussian and Gamma distributions. The parameters of the mixture model will be estimated from the EM algorithm. Then the signals and noises will be classified by a fixed threshold approach based on multiple testing using positive false discovery rate and Bayes error. The proposed method is applied to a real optical emission spectroscopy data for the quantitative analysis of inclusions. A simulation is carried out to compare the performance with the existing method using 3 sigma rule.
Keywords
Signal; noise; EM algorithm; false discovery rate; mixture model; multiple testing;
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  • Reference
1 Hochberg, Y. and Tamhane, A. C. (1987). Multiple Comparison Procedures, Wiley, New York
2 Kuss, H. M., l.iiengen, S., Mueller, G. and Thurmann, U. (2002). Comparison of spark OES methods for analysis of inclusions in iron base matters, Analytical and Bioanalytical Chemistry, 374, 1242-1249   DOI   ScienceOn
3 Kuss, H. M., Mittelstaedt, H. and Muller, G. (2005). Inclusion mapping and estimation of inclusion contents in ferrous materials by fast scanning laser-induced optical emission spectrometry, Journal of Analytical Atomic Spectrometry, 20, 730-735   DOI   ScienceOn
4 Shin, Y. and Bae, J. S. (2003). Rapid determination of cleanliness for steel by optical emission spectrometer, IEEE Instrumentation and Measurement Technology Conference (IMTC 2003), 2, 1583-1586
5 Storey, J. D. (2002). A direct approach to false discovery rates, Journal of the Royal Statistical Society: Series B (Methodological), 64, 479-498   DOI   ScienceOn
6 Storey, J. D. (2003). The positive false discovery rate: A Bayesian interpretation and the q-value, The Annals of Statistics, 31, 2013-2035   DOI   ScienceOn
7 Bishop, M. C. (2006). Pattern Recognition and Machine Learning, Springer, New York
8 Abdi, H. (2007). Signal Detection Theory, In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics, Thousand Oaks (CA): Sage
9 Altman, D. and Bland, J. M. (1994). Statistics notes: Diagnostic tests 1: Sensitivity and specificity, British Medical Journal, 308, 1552   DOI
10 Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing, Journal of the Royal Statistical Society: Series B (Methodological), 57, 289-300
11 Choi, S. C. and Wette, R. (1969). Maximum likelihood estimation of the parameters of the gamma distribution and their bias, Technometrics, 11, 683-690   DOI   ScienceOn
12 Chong, I. G. and Jun, C. H. (2005). Performance of some variable selection methods when multicollinearity is present, Chemometrics and Intelligent Laboratory Systems, 78, 103-112   DOI   ScienceOn