Bayesian Inference in Wavelet-Based ModelsPeter Müller, Brani Vidakovic This volume presents an overview of Bayesian methods for inference in the wavelet domain. The papers in this volume are divided into six parts: The first two papers introduce basic concepts. Chapters in Part II explore different approaches to prior modeling, using independent priors. Papers in the Part III discuss decision theoretic aspects of such prior models. In Part IV, some aspects of prior modeling using priors that account for dependence are explored. Part V considers the use of 2-dimensional wavelet decomposition in spatial modeling. Chapters in Part VI discuss the use of empirical Bayes estimation in wavelet based models. Part VII concludes the volume with a discussion of case studies using wavelet based Bayesian approaches. The cooperation of all contributors in the timely preparation of their manuscripts is greatly recognized. We decided early on that it was impor tant to referee and critically evaluate the papers which were submitted for inclusion in this volume. For this substantial task, we relied on the service of numerous referees to whom we are most indebted. We are also grateful to John Kimmel and the Springer-Verlag referees for considering our proposal in a very timely manner. Our special thanks go to our spouses, Gautami and Draga, for their support. |
Contents
| 1 | |
| 10 | |
Spectral View of Wavelets and Nonlinear Regression | 19 |
PRIOR MODELS INDEPENDENT CASE | 33 |
EMPIRICAL BAYES | 44 |
Some Observations on the Tractability of Certain | 51 |
Bayesian Analysis of ChangePoint Models | 67 |
Prior Elicitation in the Wavelet Domain | 83 |
PRIOR MODELS DEPENDENT CASE | 173 |
SPATIAL MODELS | 203 |
Geometrical Priors for Noisefree Wavelet Coefficients | 223 |
Multiscale Hidden Markov Models for Bayesian | 243 |
Wavelets for Object Representation and Recognition | 266 |
Bayesian Denoising of Visual Images in | 291 |
Empirical Bayes Estimation in Wavelet | 309 |
Nonparametric Empirical Bayes Estimation | 323 |
Wavelet Nonparametric Regression Using | 95 |
An Overview of Wavelet Regularization | 109 |
Minimax Restoration and Deconvolution | 115 |
Best Basis Representations with Prior | 155 |
CASE STUDIES | 341 |
Low Dimensional Turbulent Transport Mechanics | 361 |
Latent Structure Analyses of Turbulence Data Using | 381 |
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Abramovich algorithm applied assume Bayes estimator Bayes factors Bayesian approach Bayesian wavelet Besov spaces change-point Chipman choice Clyde components computed conditional consider corresponding covariance Crouse Daubechies deconvolution defined denoising diagonal discrete wavelet transform discussed Donoho and Johnstone empirical Bayes estimator example factorization Figure filter Fourier basis function given graphical models Haar wavelet hard thresholding hyperparameters independent inverse Johnstone 1994 Kolaczyk likelihood linear Mallat marginal likelihood Markov matrix methods MHMM minimax mixture multi-scale models multiresolution noise nonparametric regression normal Nowak orthogonal orthonormal posterior distribution posterior mean posterior probability prior distribution prior model prior probability probability problem reconstruction representation resolution level risk Ruggeri scale Section Signal Processing simulation smooth spatial specific Statistics stochastic structure Theorem thresholding estimator thresholding rule Tinf tion tractability values Vannucci variance vector Vidakovic 1998 wavelet basis wavelet coefficients wavelet shrinkage wavelet thresholding wj,k Xj,k zero