2018
Journal article
Open Access
Beyond trans-dimensional RJMCMC with a case study in impulsive data modeling
Karakus O., Kuruoglu E. E., Altinkaya M. A.
Electrical Engineering and Systems Science - Signal Processing FOS: Electrical engineering Computer Vision and Pattern Recognition Student's t distribution Reversible jump MCMC PLC impulsive noise modeling Wavelet coefficients modeling Signal Processing Control and Systems Engineering electronic engineering Electrical and Electronic Engineering Signal Processing (eess.SP) Impulsive data modeling Software Generalized Gaussian distribution Symmetric alpha-stable distribution information engineering
Reversible jump Markov chain Monte Carlo (RJMCMC) is a Bayesian model estimation method, which has been generally used for trans-dimensional sampling and model order selection studies in the literature. In this study, we draw attention to unexplored potentials of RJMCMC beyond trans-dimensional sampling. the proposed usage, which we call trans-space RJMCMC exploits the original formulation to explore spaces of different classes or structures. This provides flexibility in using different types of candidate classes in the combined model space such as spaces of linear and nonlinear models or of various distribution families. As an application, we looked into a special case of trans-space sampling, namely trans-distributional RJMCMC in impulsive data modeling. In many areas such as seismology, radar, image, using Gaussian models is a common practice due to analytical ease. However, many noise processes do not follow a Gaussian character and generally exhibit events too impulsive to be successfully described by the Gaussian model. We test the proposed usage of RJMCMC to choose between various impulsive distribution families to model both synthetically generated noise processes and real-life measurements on power line communications impulsive noises and 2-D discrete wavelet transform coefficients. (C) 2018 Elsevier B.V. All rights reserved.
Source: Signal processing (Print) 153 (2018): 396–410. doi:10.1016/j.sigpro.2018.07.028
Publisher: Elsevier, Amsterdam , Paesi Bassi
1. S. A. Bhatti, Q. Shan, I. A. Glover, R. Atkinson, I. E. Portugues, P. J. Moore, R. Rutherford, Impulsive noise modelling and prediction of its impact on the performance of WLAN receiver, in: Signal Processing Conference, 2009 17th European, IEEE, 2009, pp. 1680-1684.
2. K. L. Blackard, T. S. Rappaport, C. W. Bostian, Measurements and models of radio frequency impulsive noise for indoor wireless communications, IEEE Journal on selected areas in communications 11 (7) (1993) 991-1001.
3. J. Lin, M. Nassar, B. L. Evans, Impulsive noise mitigation in powerline communications using sparse Bayesian learning, IEEE Journal on Selected Areas in Communications 31 (7) (2013) 1172-1183.
4. E. Alsusa, K. M. Rabie, Dynamic peak-based threshold estimation method for mitigating impulsive noise in power-line communication systems, IEEE Transactions on Power Delivery 28 (4) (2013) 2201-2208.
5. T. Y. Al-Naffouri, A. A. Quadeer, G. Caire, Impulsive noise estimation and cancellation in DSL using orthogonal clustering, in: Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on, IEEE, 2011, pp. 2841-2845.
6. R. Fantacci, A. Tani, D. Tarchi, Impulse noise mitigation techniques for xDSL systems in a real environment, IEEE Transactions on Consumer Electronics 56 (4) (2010) 2106-2114.
7. E. P. Simoncelli, Statistical models for images: Compression, restoration and synthesis, in: Signals, Systems & Computers, 1997. Conference Record of the Thirty-First Asilomar Conference on, Vol. 1, IEEE Computer Society, 1997, pp. 673-678.
8. A. Achim, P. Tsakalides, A. Bezerianos, SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling, IEEE Transactions on Geoscience and Remote Sensing 41 (8) (2003) 1773-1784.
9. B. Yue, Z. Peng, A validation study of a-stable distribution characteristic for seismic data, Signal Processing 106 (2015) 1-9.
10. P. J. Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika 82 (4) (1995) 711-732. doi:10.1093/biomet/82.4.711.
11. P. T. Troughton, S. J. Godsill, A reversible jump sampler for autoregressive time series, in: Acoustics, Speech and Signal Processing, 1998. Proceedings of the 1998 IEEE International Conference on, Vol. 4, IEEE, 1998, pp. 2257-2260.
14. S. Richardson, P. J. Green, On Bayesian analysis of mixtures with an unknown number of components (with discussion), Journal of the Royal Statistical Society: series B (statistical methodology) 59 (4) (1997) 731-792.
15. V. Viallefont, S. Richardson, P. J. Green, Bayesian analysis of Poisson mixtures, Journal of nonparametric statistics 14 (1-2) (2002) 181-202.
16. D. Salas-Gonzalez, E. E. Kuruoglu, D. P. Ruiz, Finite mixture of a-stable distributions, Digital Signal Processing 19 (2) (2009) 250-264.
17. O. Karakus¸, E. E. Kuruog˘lu, M. A. Altınkaya, Estimation of the nonlinearity degree for polynomial autoregressive processes with RJMCMC, in: 23rd European Signal Processing Conference (EUSIPCO), IEEE, 2015, pp. 953-957.
18. O. Karakus¸, E. E. Kuruog˘lu, M. A. Altınkaya, Bayesian estimation of polynomial moving average models with unknown degree of nonlinearity, in: 24th European Signal Processing Conference (EUSIPCO), IEEE, 2016, pp. 1543-1547.
19. O. Karakus¸, E. E. Kuruog˘lu, M. A. Altınkaya, Nonlinear Model Selection for PARMA Processes Using RJMCMC, in: 25th European Signal Processing Conference (EUSIPCO), IEEE, 2017, pp. 2110-2114.
20. O. Karakus¸, E. E. Kuruog˘lu, M. A. Altınkaya, Bayesian Volterra System Identification Using Reversible Jump MCMC Algorithm, Signal Processing 141 (2017) 125-136.
21. J. A. Cortes, L. Diez, F. J. Canete, J. J. Sanchez-Martinez, Analysis of the indoor broadband power-line noise scenario, IEEE Transactions on electromagnetic compatibility 52 (4) (2010) 849-858.
22. P. A. Lopes, J. M. Pinto, J. B. Gerald, Dealing with unknown impedance and impulsive noise in the power-line communications channel, IEEE Transactions on power delivery 28 (1) (2013) 58-66.
23. Artemis, SAR solutions, image samples, http://artemisinc.net/media.php (2017).
24. MRI image of brain with gadolinium contrast showing enhancing mass in the right, http://mri-scan-img.info/mri-image-ofbrain-with-gadolinium-contrast-showing-enhancing-mass-in-the-right (2017).
25. C. Martinez Lara, M. Martin Perez, I. Martin Garcia, R. Blanco Herna´ndez, B. Sa´nchez Sa´nchez, J. Sevillano Sa´nchez, Radiological findings invasive lobular carcinoma, in: European Congress of Radiology (ECR), 2012, pp. C-1062. doi:10.1594/ecr2012/C-1062.
26. L. Knorr-Held, G. Raßer, Bayesian detection of clusters and discontinuities in disease maps, Biometrics 56 (1) (2000) 13-21.
27. D. J. Lunn, N. Best, J. C. Whittaker, Generic reversible jump MCMC using graphical models, Statistics and Computing 19 (4) (2009) 395-408.
28. P. Dellaportas, J. J. Forster, Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models, Biometrika 86 (3) (1999) 615-633.
29. F. Van Der Meulen, M. Schauer, H. Van Zanten, Reversible jump MCMC for nonparametric drift estimation for diffusion processes, Computational Statistics & Data Analysis 71 (2014) 615-632.
30. B. Rannala, Z. Yang, Improved reversible jump algorithms for Bayesian species delimitation, Genetics 194 (1) (2013) 245-253.
31. C. S. Oedekoven, R. King, S. T. Buckland, M. L. Mackenzie, K. Evans, L. Burger, Using hierarchical centering to facilitate a reversible jump MCMC algorithm for random effects models, Computational Statistics & Data Analysis 98 (2016) 79-90.
33. W. Hastings, Monte carlo samping methods using markov chains and their applications, Biometrika 57 (1970) 97-109. doi:10.1093/biomet/57.1.97.
34. G. Laguna-Sanchez, M. Lopez-Guerrero, On the use of alpha-stable distributions in noise modeling for PLC, IEEE Transactions on Power Delivery 30 (4) (2015) 1863-1870.
35. E. E. Kuruoglu, W. J. Fitzgerald, P. J. Rayner, Near optimal detection of signals in impulsive noise modeled with a symmetric a-stable distribution, IEEE Communications Letters 2 (10) (1998) 282-284.
36. H. Sadreazami, M. O. Ahmad, M. S. Swamy, A study of multiplicative watermark detection in the contourlet domain using alpha-stable distributions, IEEE Transactions on Image Processing 23 (10) (2014) 4348-4360.
37. N. Farsad, W. Guo, C.-B. Chae, A. Eckford, Stable distributions as noise models for molecular communication, in: Global Communications Conference (GLOBECOM), 2015 IEEE, IEEE, 2015, pp. 1-6.
38. G. Tzagkarakis, P. Tsakalides, Greedy sparse reconstruction of non-negative signals using symmetric alpha-stable distributions, in: Signal Processing Conference, 2010 18th European, IEEE, 2010, pp. 417-421.
39. J. Nolan, Bibliography on stable distributions, processes and related topics, Tech. rep., Technical report (2010).
40. M. N. Do, M. Vetterli, Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance, IEEE transactions on image processing 11 (2) (2002) 146-158.
41. C. Bouman, K. Sauer, A generalized Gaussian image model for edge-preserving MAP estimation, IEEE Transactions on Image Processing 2 (3) (1993) 296-310.
42. G. Verdoolaege, P. Scheunders, Geodesics on the manifold of multivariate generalized Gaussian distributions with an application to multicomponent texture discrimination, International Journal of Computer Vision 95 (3) (2011) 265-286.
43. S. Le Cam, A. Belghith, C. Collet, F. Salzenstein, Wheezing sounds detection using multivariate generalized Gaussian distributions, in: Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on, IEEE, 2009, pp. 541-544.
44. M. Novey, T. Adali, A. Roy, A complex generalized Gaussian distribution-Characterization, generation, and estimation, IEEE Transactions on Signal Processing 58 (3) (2010) 1427-1433.
45. A. J. Patton, Modelling asymmetric exchange rate dependence, International economic review 47 (2) (2006) 527-556.
46. R. F. Engle, T. Bollerslev, Modelling the persistence of conditional variances, Econometric reviews 5 (1) (1986) 1-50.
47. A. Aravkin, T. Van Leeuwen, F. Herrmann, Robust full-waveform inversion using the Student's t-distribution, in: SEG Technical Program Expanded Abstracts 2011, Society of Exploration Geophysicists, 2011, pp. 2669-2673.
48. Y. Liang, G. Chen, S. Naqvi, J. A. Chambers, Independent vector analysis with multivariate student's t-distribution source prior for speech separation, Electronics Letters 49 (16) (2013) 1035-1036.
49. T. M. Nguyen, Q. J. Wu, Robust student's-t mixture model with spatial constraints and its application in medical image segmentation, IEEE Transactions on Medical Imaging 31 (1) (2012) 103-116.
50. Z. Zhang, K. Lai, Z. Lu, X. Tong, Bayesian inference and application of robust growth curve models using student's t distribution, Structural Equation Modeling: A Multidisciplinary Journal 20 (1) (2013) 47-78.
51. D. I. Hastie, P. J. Green, Model choice using reversible jump Markov chain Monte Carlo, Statistica Neerlandica 66 (3) (2012) 309-338.
52. R. J. Barker, W. A. Link, Bayesian multimodel inference by RJMCMC: A Gibbs sampling approach, The American Statistician 67 (3) (2013) 150-156.
53. G. A. Tsihrintzis, C. L. Nikias, Fast estimation of the parameters of alpha-stable impulsive interference, IEEE Transactions on Signal Processing 44 (6) (1996) 1492-1503.
54. X. Ma, C. L. Nikias, Parameter estimation and blind channel identification in impulsive signal environments, IEEE transactions on signal processing 43 (12) (1995) 2884-2897.
55. E. E. Kuruoglu, Density parameter estimation of skewed a-stable distributions, IEEE transactions on signal processing 49 (10) (2001) 2192-2201.
56. N. Andreadou, F.-N. Pavlidou, Modeling the noise on the OFDM power-line communications system, IEEE Transactions on Power Delivery 25 (1) (2010) 150-157.
57. T. H. Tran, D. D. Do, T. H. Huynh, PLC impulsive noise in industrial zone: measurement and characterization, International Journal of Computer and Electrical Engineering 5 (1) (2013) 48.
58. S. Kullback, Information theory and statistics, Courier Corporation, 1997.
59. J. R. Hershey, P. A. Olsen, Approximating the Kullback Leibler divergence between Gaussian mixture models, in: Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on, Vol. 4, IEEE, 2007, pp. IV-317.
60. K. P. Burnham, D. R. Anderson, Model selection and multimodel inference: a practical information-theoretic approach, Springer Science & Business Media, 2003.
61. F. J. Massey Jr, The Kolmogorov-Smirnov test for goodness of fit, Journal of the American statistical Association 46 (253) (1951) 68-78.
62. L. A. Goodman, Kolmogorov-Smirnov tests for psychological research., Psychological bulletin 51 (2) (1954) 160.
63. R. Wilcox, Kolmogorov-Smirnov test, Encyclopedia of biostatistics.
64. J. Wang, W. W. Tsang, G. Marsaglia, Evaluating Kolmogorov's distribution, Journal of Statistical Software 8 (18).
65. W. H. Press, Numerical recipes 3rd edition: The art of scientific computing, Cambridge university press, 2007.
66. L. Tong, J. Yang, R. S. Cooper, Efficient calculation of p-value and power for quadratic form statistics in multilocus association testing, Annals of human genetics 74 (3) (2010) 275-285.
67. M. A. Stephens, Use of the Kolmogorov-Smirnov, Crame´r-Von Mises and related statistics without extensive tables, Journal of the Royal Statistical Society. Series B (Methodological) (1970) 115-122.
2. K. L. Blackard, T. S. Rappaport, C. W. Bostian, Measurements and models of radio frequency impulsive noise for indoor wireless communications, IEEE Journal on selected areas in communications 11 (7) (1993) 991-1001.
3. J. Lin, M. Nassar, B. L. Evans, Impulsive noise mitigation in powerline communications using sparse Bayesian learning, IEEE Journal on Selected Areas in Communications 31 (7) (2013) 1172-1183.
4. E. Alsusa, K. M. Rabie, Dynamic peak-based threshold estimation method for mitigating impulsive noise in power-line communication systems, IEEE Transactions on Power Delivery 28 (4) (2013) 2201-2208.
5. T. Y. Al-Naffouri, A. A. Quadeer, G. Caire, Impulsive noise estimation and cancellation in DSL using orthogonal clustering, in: Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on, IEEE, 2011, pp. 2841-2845.
6. R. Fantacci, A. Tani, D. Tarchi, Impulse noise mitigation techniques for xDSL systems in a real environment, IEEE Transactions on Consumer Electronics 56 (4) (2010) 2106-2114.
7. E. P. Simoncelli, Statistical models for images: Compression, restoration and synthesis, in: Signals, Systems & Computers, 1997. Conference Record of the Thirty-First Asilomar Conference on, Vol. 1, IEEE Computer Society, 1997, pp. 673-678.
8. A. Achim, P. Tsakalides, A. Bezerianos, SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling, IEEE Transactions on Geoscience and Remote Sensing 41 (8) (2003) 1773-1784.
9. B. Yue, Z. Peng, A validation study of a-stable distribution characteristic for seismic data, Signal Processing 106 (2015) 1-9.
10. P. J. Green, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika 82 (4) (1995) 711-732. doi:10.1093/biomet/82.4.711.
11. P. T. Troughton, S. J. Godsill, A reversible jump sampler for autoregressive time series, in: Acoustics, Speech and Signal Processing, 1998. Proceedings of the 1998 IEEE International Conference on, Vol. 4, IEEE, 1998, pp. 2257-2260.
14. S. Richardson, P. J. Green, On Bayesian analysis of mixtures with an unknown number of components (with discussion), Journal of the Royal Statistical Society: series B (statistical methodology) 59 (4) (1997) 731-792.
15. V. Viallefont, S. Richardson, P. J. Green, Bayesian analysis of Poisson mixtures, Journal of nonparametric statistics 14 (1-2) (2002) 181-202.
16. D. Salas-Gonzalez, E. E. Kuruoglu, D. P. Ruiz, Finite mixture of a-stable distributions, Digital Signal Processing 19 (2) (2009) 250-264.
17. O. Karakus¸, E. E. Kuruog˘lu, M. A. Altınkaya, Estimation of the nonlinearity degree for polynomial autoregressive processes with RJMCMC, in: 23rd European Signal Processing Conference (EUSIPCO), IEEE, 2015, pp. 953-957.
18. O. Karakus¸, E. E. Kuruog˘lu, M. A. Altınkaya, Bayesian estimation of polynomial moving average models with unknown degree of nonlinearity, in: 24th European Signal Processing Conference (EUSIPCO), IEEE, 2016, pp. 1543-1547.
19. O. Karakus¸, E. E. Kuruog˘lu, M. A. Altınkaya, Nonlinear Model Selection for PARMA Processes Using RJMCMC, in: 25th European Signal Processing Conference (EUSIPCO), IEEE, 2017, pp. 2110-2114.
20. O. Karakus¸, E. E. Kuruog˘lu, M. A. Altınkaya, Bayesian Volterra System Identification Using Reversible Jump MCMC Algorithm, Signal Processing 141 (2017) 125-136.
21. J. A. Cortes, L. Diez, F. J. Canete, J. J. Sanchez-Martinez, Analysis of the indoor broadband power-line noise scenario, IEEE Transactions on electromagnetic compatibility 52 (4) (2010) 849-858.
22. P. A. Lopes, J. M. Pinto, J. B. Gerald, Dealing with unknown impedance and impulsive noise in the power-line communications channel, IEEE Transactions on power delivery 28 (1) (2013) 58-66.
23. Artemis, SAR solutions, image samples, http://artemisinc.net/media.php (2017).
24. MRI image of brain with gadolinium contrast showing enhancing mass in the right, http://mri-scan-img.info/mri-image-ofbrain-with-gadolinium-contrast-showing-enhancing-mass-in-the-right (2017).
25. C. Martinez Lara, M. Martin Perez, I. Martin Garcia, R. Blanco Herna´ndez, B. Sa´nchez Sa´nchez, J. Sevillano Sa´nchez, Radiological findings invasive lobular carcinoma, in: European Congress of Radiology (ECR), 2012, pp. C-1062. doi:10.1594/ecr2012/C-1062.
26. L. Knorr-Held, G. Raßer, Bayesian detection of clusters and discontinuities in disease maps, Biometrics 56 (1) (2000) 13-21.
27. D. J. Lunn, N. Best, J. C. Whittaker, Generic reversible jump MCMC using graphical models, Statistics and Computing 19 (4) (2009) 395-408.
28. P. Dellaportas, J. J. Forster, Markov chain Monte Carlo model determination for hierarchical and graphical log-linear models, Biometrika 86 (3) (1999) 615-633.
29. F. Van Der Meulen, M. Schauer, H. Van Zanten, Reversible jump MCMC for nonparametric drift estimation for diffusion processes, Computational Statistics & Data Analysis 71 (2014) 615-632.
30. B. Rannala, Z. Yang, Improved reversible jump algorithms for Bayesian species delimitation, Genetics 194 (1) (2013) 245-253.
31. C. S. Oedekoven, R. King, S. T. Buckland, M. L. Mackenzie, K. Evans, L. Burger, Using hierarchical centering to facilitate a reversible jump MCMC algorithm for random effects models, Computational Statistics & Data Analysis 98 (2016) 79-90.
33. W. Hastings, Monte carlo samping methods using markov chains and their applications, Biometrika 57 (1970) 97-109. doi:10.1093/biomet/57.1.97.
34. G. Laguna-Sanchez, M. Lopez-Guerrero, On the use of alpha-stable distributions in noise modeling for PLC, IEEE Transactions on Power Delivery 30 (4) (2015) 1863-1870.
35. E. E. Kuruoglu, W. J. Fitzgerald, P. J. Rayner, Near optimal detection of signals in impulsive noise modeled with a symmetric a-stable distribution, IEEE Communications Letters 2 (10) (1998) 282-284.
36. H. Sadreazami, M. O. Ahmad, M. S. Swamy, A study of multiplicative watermark detection in the contourlet domain using alpha-stable distributions, IEEE Transactions on Image Processing 23 (10) (2014) 4348-4360.
37. N. Farsad, W. Guo, C.-B. Chae, A. Eckford, Stable distributions as noise models for molecular communication, in: Global Communications Conference (GLOBECOM), 2015 IEEE, IEEE, 2015, pp. 1-6.
38. G. Tzagkarakis, P. Tsakalides, Greedy sparse reconstruction of non-negative signals using symmetric alpha-stable distributions, in: Signal Processing Conference, 2010 18th European, IEEE, 2010, pp. 417-421.
39. J. Nolan, Bibliography on stable distributions, processes and related topics, Tech. rep., Technical report (2010).
40. M. N. Do, M. Vetterli, Wavelet-based texture retrieval using generalized Gaussian density and Kullback-Leibler distance, IEEE transactions on image processing 11 (2) (2002) 146-158.
41. C. Bouman, K. Sauer, A generalized Gaussian image model for edge-preserving MAP estimation, IEEE Transactions on Image Processing 2 (3) (1993) 296-310.
42. G. Verdoolaege, P. Scheunders, Geodesics on the manifold of multivariate generalized Gaussian distributions with an application to multicomponent texture discrimination, International Journal of Computer Vision 95 (3) (2011) 265-286.
43. S. Le Cam, A. Belghith, C. Collet, F. Salzenstein, Wheezing sounds detection using multivariate generalized Gaussian distributions, in: Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on, IEEE, 2009, pp. 541-544.
44. M. Novey, T. Adali, A. Roy, A complex generalized Gaussian distribution-Characterization, generation, and estimation, IEEE Transactions on Signal Processing 58 (3) (2010) 1427-1433.
45. A. J. Patton, Modelling asymmetric exchange rate dependence, International economic review 47 (2) (2006) 527-556.
46. R. F. Engle, T. Bollerslev, Modelling the persistence of conditional variances, Econometric reviews 5 (1) (1986) 1-50.
47. A. Aravkin, T. Van Leeuwen, F. Herrmann, Robust full-waveform inversion using the Student's t-distribution, in: SEG Technical Program Expanded Abstracts 2011, Society of Exploration Geophysicists, 2011, pp. 2669-2673.
48. Y. Liang, G. Chen, S. Naqvi, J. A. Chambers, Independent vector analysis with multivariate student's t-distribution source prior for speech separation, Electronics Letters 49 (16) (2013) 1035-1036.
49. T. M. Nguyen, Q. J. Wu, Robust student's-t mixture model with spatial constraints and its application in medical image segmentation, IEEE Transactions on Medical Imaging 31 (1) (2012) 103-116.
50. Z. Zhang, K. Lai, Z. Lu, X. Tong, Bayesian inference and application of robust growth curve models using student's t distribution, Structural Equation Modeling: A Multidisciplinary Journal 20 (1) (2013) 47-78.
51. D. I. Hastie, P. J. Green, Model choice using reversible jump Markov chain Monte Carlo, Statistica Neerlandica 66 (3) (2012) 309-338.
52. R. J. Barker, W. A. Link, Bayesian multimodel inference by RJMCMC: A Gibbs sampling approach, The American Statistician 67 (3) (2013) 150-156.
53. G. A. Tsihrintzis, C. L. Nikias, Fast estimation of the parameters of alpha-stable impulsive interference, IEEE Transactions on Signal Processing 44 (6) (1996) 1492-1503.
54. X. Ma, C. L. Nikias, Parameter estimation and blind channel identification in impulsive signal environments, IEEE transactions on signal processing 43 (12) (1995) 2884-2897.
55. E. E. Kuruoglu, Density parameter estimation of skewed a-stable distributions, IEEE transactions on signal processing 49 (10) (2001) 2192-2201.
56. N. Andreadou, F.-N. Pavlidou, Modeling the noise on the OFDM power-line communications system, IEEE Transactions on Power Delivery 25 (1) (2010) 150-157.
57. T. H. Tran, D. D. Do, T. H. Huynh, PLC impulsive noise in industrial zone: measurement and characterization, International Journal of Computer and Electrical Engineering 5 (1) (2013) 48.
58. S. Kullback, Information theory and statistics, Courier Corporation, 1997.
59. J. R. Hershey, P. A. Olsen, Approximating the Kullback Leibler divergence between Gaussian mixture models, in: Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on, Vol. 4, IEEE, 2007, pp. IV-317.
60. K. P. Burnham, D. R. Anderson, Model selection and multimodel inference: a practical information-theoretic approach, Springer Science & Business Media, 2003.
61. F. J. Massey Jr, The Kolmogorov-Smirnov test for goodness of fit, Journal of the American statistical Association 46 (253) (1951) 68-78.
62. L. A. Goodman, Kolmogorov-Smirnov tests for psychological research., Psychological bulletin 51 (2) (1954) 160.
63. R. Wilcox, Kolmogorov-Smirnov test, Encyclopedia of biostatistics.
64. J. Wang, W. W. Tsang, G. Marsaglia, Evaluating Kolmogorov's distribution, Journal of Statistical Software 8 (18).
65. W. H. Press, Numerical recipes 3rd edition: The art of scientific computing, Cambridge university press, 2007.
66. L. Tong, J. Yang, R. S. Cooper, Efficient calculation of p-value and power for quadratic form statistics in multilocus association testing, Annals of human genetics 74 (3) (2010) 275-285.
67. M. A. Stephens, Use of the Kolmogorov-Smirnov, Crame´r-Von Mises and related statistics without extensive tables, Journal of the Royal Statistical Society. Series B (Methodological) (1970) 115-122.
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BibTeX entry
@article{oai:it.cnr:prodotti:398430,
title = {Beyond trans-dimensional RJMCMC with a case study in impulsive data modeling},
author = {Karakus O. and Kuruoglu E. E. and Altinkaya M. A.},
publisher = {Elsevier, Amsterdam , Paesi Bassi},
doi = {10.1016/j.sigpro.2018.07.028 and 10.48550/arxiv.1711.03633},
journal = {Signal processing (Print)},
volume = {153},
pages = {396–410},
year = {2018}
}CNR authorsLaboratories
0000-0002-2608-8034
