Bayesian sigmoid shrinkage with improper variance priors and an application to wavelet denoising

Computational Statistics and Data Analysis

Volumn 51, Issue 2, 2006, Pages 1232-1242

  ter Braak, Cajo J F ^a  

^a WAGENINGEN UNIVERSITY   (Netherlands)

Author keywords

Bayesian model; Improper prior; Shrinkage rule; Wavelet denoising

Indexed keywords

COMPUTATION THEORY; ERROR ANALYSIS; LEAST SQUARES APPROXIMATIONS; REGRESSION ANALYSIS; SHRINKAGE; WAVELET TRANSFORMS;

BAYESIAN MODELS; IMPROPER PRIOR; SHRINKAGE RULE; WAVELET DENOISING;

LINEAR SYSTEMS;

EID: 33750286670     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2006.06.011     Document Type: Article

References (31)

1. Abramovich F., Sapatinas T., and Silverman B.W. Wavelet thresholding via a Bayesian approach. J. R. Statist. Soc. B 60 (1998) 725-749
2. Abramovich F., Amato U., and Angelini C. On optimality of Bayesian wavelet estimators. Scand. J. Statist. 31 (2004) 217-234
3. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1972), Dover Publications, New York
4. Box G.E.P., and Tiao G.C. Bayesian Inference in Statistical Analysis (1973), Wiley Classics, New York
5. Breiman L. Better subset regression using the nonnegative garrote. Technometrics 37 (1995) 373-384
6. Breiman L., and Friedman J.H. Predicting multivariate responses in multiple linear regression. J. R. Statist. Soc. B. 59 (1997) 3-54
7. Brown P.J., Vannucci M., and Fearn T. Bayes model averaging with selection of regressors. J. R. Statist. Soc. B. 64 (2002) 519-536
8. Cai T.T. Adaptive wavelet estimation: a block thresholding and oracle inequality approach. Ann. Statist. 27 (1999) 898-924
9. Clyde M., Parmigiani G., and Vidakovic B. Multiple shrinkage and subset selection in wavelets. Biometrika 85 (1998) 391-401
10. Copas J.B. Regression, prediction and shrinkage (with discussion). J. R. Statist. Soc. B 45 (1983) 311-354
11. Cutillo, L., Jung, Y. Y., Ruggeri, F., Vidakovic, B., 2005. Larger posterior mode wavelet thresholding and applications. Technical Report 14/2005, Georgia Institute of Technology, Atlanta, USA.
12. De Canditiis D., and Vidakovic B. Wavelet Bayesian block shrinkage via mixtures of normal-inverse gamma priors. J. Comput. Graph. Statist. 13 (2004) 383-398
13. Donoho D.L., and Johnstone I.M. Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 (1994) 425-455
14. Donoho D.L., and Johnstone I.M. Adapting to unknown smoothness via wavelet shrinkage. J. Am. Statist. Assoc. 90 (1995) 1200-1224
15. Efron B. The estimation of prediction error: covariance penalties and cross-validation. J. Am. Statist. Assoc. 99 (2004) 619-642
16. Efron B., and Morris C. Stein's estimation rule and its competitors-an empirical Bayes approach. J. Am. Statist. Assoc. 68 (1973) 117-130
17. Gelfand A.E., and Sahu K. Identifiability, improper priors, and Gibbs sampling for generalized linear models. J. Am. Statist. Assoc. 94 (1999) 247-253
18. Hardy D.W., and Walker C.L. Workplace notebook. Doing Mathematics with Scientific Workplace & Scientific Notebook (version 3.5) (2000), MacKichan, Poulsbo, WA
19. Hastie T., Tibshirani R., and Friedman J.H. The elements of statistical learning. Data Mining, Inference and Prediction (2001), Springer, New York
20. Hoerl A.E., and Kennard R.W. Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12 (1970) 55-57
21. Holmes C.C., and Denison D.G.T. Bayesian wavelet analysis with a model complexity prior. In: Bernardo J.M., Berger J.O., Dawid A.P., and Smith A.F.M. (Eds). Bayesian Statistics vol. 6 (1999), Clarendon Press, Oxford 769-776
22. Jansen, M., 2001. Noise Reduction by Wavelet Thresholding, vol. 61, Springer, New York.
23. Johnstone, I.M., Silverman, B.W., 2002. Ebayesthresh: R and S-plus software for empirical Bayes thresholding. Available from www.Bernardsilverman.Com.
24. Johnstone I.M., and Silverman B.W. Needles and straw in haystacks: empirical Bayes estimates of possibly sparse sequences. Ann. Statist. 32 (2004) 1594-1649
25. Johnstone I.M., and Silverman B.W. Empirical Bayes selection of wavelet thresholds. Ann. Statist. 33 (2005) 1700-1752
26. O'Hagan, A., 1994. Bayesian Inference, vol. 2B. Arnold, London.
27. Ogden R.T. Essential Wavelets for Statitistical Applications and Data Analysis (1997), Birkhäuser, Boston
28. Semadeni C., Davison A.C., and Hinkley D.V. Posterior probability intervals in Bayesian wavelet estimation. Biometrika 91 (2004) 497-505
29. ter Braak C.J.F., Boer M.P., and Bink M.C.A.M. Extending Xu's Bayesian model for estimating polygenic effects using markers of the entire genome. Genetics 170 (2005) 1435-1438
30. Tibshirani R. Regression shrinkage and selection via the lasso. J. R. Statist. Soc. B 58 (1996) 267-288
31. Xu S. Estimating polygenic effects using markers of the entire genome. Genetics 163 (2003) 789-801