Ebook: Bayesian Inference in Wavelet-Based Models

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.

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This volume provides a thorough introduction and reference for any researcher who is interested in Bayesian inference for wavelet-based models, but is not necessarily an expert in either. To achieve this goal the book starts with an extensive introductory chapter providing a self-contained introduction to the use of wavelet decompositions and the relation to Bayesian inference. The remaining papers in this volume are divided into six parts: independent prior modeling; decision theoretic aspects; dependent prior modeling; spatial models using bivariate wavelet bases; empirical Bayes approaches; and case studies. Chapters are written by experts who published the original research papers establishing the use of wavelet-based models in Bayesian inference. Peter Muller is Associate Professor and Brani Vidakovic is Assistant Professor of Statistics at Duke University.

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This volume provides a thorough introduction and reference for any researcher who is interested in Bayesian inference for wavelet-based models, but is not necessarily an expert in either. To achieve this goal the book starts with an extensive introductory chapter providing a self-contained introduction to the use of wavelet decompositions and the relation to Bayesian inference. The remaining papers in this volume are divided into six parts: independent prior modeling; decision theoretic aspects; dependent prior modeling; spatial models using bivariate wavelet bases; empirical Bayes approaches; and case studies. Chapters are written by experts who published the original research papers establishing the use of wavelet-based models in Bayesian inference. Peter Muller is Associate Professor and Brani Vidakovic is Assistant Professor of Statistics at Duke University.
Content:
Front Matter....Pages i-xiii
An Introduction to Wavelets....Pages 1-18
Spectral View of Wavelets and Nonlinear Regression....Pages 19-32
Bayesian Approach to Wavelet Decomposition and Shrinkage....Pages 33-50
Some Observations on the Tractability of Certain Multi-Scale Models....Pages 51-66
Bayesian Analysis of Change-Point Models....Pages 67-82
Prior Elicitation in the Wavelet Domain....Pages 83-94
Wavelet Nonparametric Regression Using Basis Averaging....Pages 95-108
An Overview of Wavelet Regularization....Pages 109-114
Minimax Restoration and Deconvolution....Pages 115-138
Robust Bayesian and Bayesian Decision Theoretic Wavelet Shrinkage....Pages 139-154
Best Basis Representations with Prior Statistical Models....Pages 155-172
Modeling Dependence in the Wavelet Domain....Pages 173-186
MCMC Methods in Wavelet Shrinkage: Non-Equally Spaced Regression, Density and Spectral Density Estimation....Pages 187-202
Empirical Bayesian Spatial Prediction Using Wavelets....Pages 203-222
Geometrical Priors for Noisefree Wavelet Coefficients in Image Denoising....Pages 223-242
Multiscale Hidden Markov Models for Bayesian Image Analysis....Pages 243-265
Wavelets for Object Representation and Recognition in Computer Vision....Pages 267-290
Bayesian Denoising of Visual Images in the Wavelet Domain....Pages 291-308
Empirical Bayes Estimation in Wavelet Nonparametric Regression....Pages 309-322
Nonparametric Empirical Bayes Estimation via Wavelets....Pages 323-340
Multiresolution Wavelet Analyses in Hierarchical Bayesian Turbulence Models....Pages 341-359
Low Dimensional Turbulent Transport Mechanics Near the Forest-Atmosphere Interface....Pages 361-380
Latent Structure Analyses of Turbulence Data Using Wavelets and Time Series Decompositions....Pages 381-394
Back Matter....Pages 395-396

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This volume provides a thorough introduction and reference for any researcher who is interested in Bayesian inference for wavelet-based models, but is not necessarily an expert in either. To achieve this goal the book starts with an extensive introductory chapter providing a self-contained introduction to the use of wavelet decompositions and the relation to Bayesian inference. The remaining papers in this volume are divided into six parts: independent prior modeling; decision theoretic aspects; dependent prior modeling; spatial models using bivariate wavelet bases; empirical Bayes approaches; and case studies. Chapters are written by experts who published the original research papers establishing the use of wavelet-based models in Bayesian inference. Peter Muller is Associate Professor and Brani Vidakovic is Assistant Professor of Statistics at Duke University.
Content:
Front Matter....Pages i-xiii
An Introduction to Wavelets....Pages 1-18
Spectral View of Wavelets and Nonlinear Regression....Pages 19-32
Bayesian Approach to Wavelet Decomposition and Shrinkage....Pages 33-50
Some Observations on the Tractability of Certain Multi-Scale Models....Pages 51-66
Bayesian Analysis of Change-Point Models....Pages 67-82
Prior Elicitation in the Wavelet Domain....Pages 83-94
Wavelet Nonparametric Regression Using Basis Averaging....Pages 95-108
An Overview of Wavelet Regularization....Pages 109-114
Minimax Restoration and Deconvolution....Pages 115-138
Robust Bayesian and Bayesian Decision Theoretic Wavelet Shrinkage....Pages 139-154
Best Basis Representations with Prior Statistical Models....Pages 155-172
Modeling Dependence in the Wavelet Domain....Pages 173-186
MCMC Methods in Wavelet Shrinkage: Non-Equally Spaced Regression, Density and Spectral Density Estimation....Pages 187-202
Empirical Bayesian Spatial Prediction Using Wavelets....Pages 203-222
Geometrical Priors for Noisefree Wavelet Coefficients in Image Denoising....Pages 223-242
Multiscale Hidden Markov Models for Bayesian Image Analysis....Pages 243-265
Wavelets for Object Representation and Recognition in Computer Vision....Pages 267-290
Bayesian Denoising of Visual Images in the Wavelet Domain....Pages 291-308
Empirical Bayes Estimation in Wavelet Nonparametric Regression....Pages 309-322
Nonparametric Empirical Bayes Estimation via Wavelets....Pages 323-340
Multiresolution Wavelet Analyses in Hierarchical Bayesian Turbulence Models....Pages 341-359
Low Dimensional Turbulent Transport Mechanics Near the Forest-Atmosphere Interface....Pages 361-380
Latent Structure Analyses of Turbulence Data Using Wavelets and Time Series Decompositions....Pages 381-394
Back Matter....Pages 395-396
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