Bayesian Inference in Wavelet-Based Models

1. Front Matter

   Pages i-xiii

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2. Introduction

   1. An Introduction to Wavelets

      • Brani Vidakovic, Peter Müller

      Pages 1-18

   2. Spectral View of Wavelets and Nonlinear Regression

      • J. S. Marron

      Pages 19-32

3. Prior Models-Independent Case

   1. Bayesian Approach to Wavelet Decomposition and Shrinkage

      • Felix Abramovich, Theofanis Sapatinas

      Pages 33-50

   2. Some Observations on the Tractability of Certain Multi-Scale Models

      • Eric D. Kolaczyk

      Pages 51-66

   3. Bayesian Analysis of Change-Point Models

      • R. Todd Ogden, James D. Lynch

      Pages 67-82

   4. Prior Elicitation in the Wavelet Domain

      • Hugh A. Chipman, Lara J. Wolfson

      Pages 83-94

   5. Wavelet Nonparametric Regression Using Basis Averaging

      • Paul Yau, Robert Kohn

      Pages 95-108

4. Decision Theoretic Wavelet Shrinkage

   1. An Overview of Wavelet Regularization

      • Yazhen Wang

      Pages 109-114

   2. Minimax Restoration and Deconvolution

      • Jérôme Kalifa, Stéphane Mallat

      Pages 115-138

   3. Robust Bayesian and Bayesian Decision Theoretic Wavelet Shrinkage

      • Fabrizio Ruggeri

      Pages 139-154

   4. Best Basis Representations with Prior Statistical Models

      • David Leporini, Jean-Christophe Pesquet, Hamid Krim

      Pages 155-172

5. Prior Models- Dependent Case

   1. Modeling Dependence in the Wavelet Domain

      • Marina Vannucci, Fabio Corradi

      Pages 173-186

   2. MCMC Methods in Wavelet Shrinkage: Non-Equally Spaced Regression, Density and Spectral Density Estimation

      • Peter Müller, Brani Vidakovic

      Pages 187-202

6. Spatial Models

   1. Empirical Bayesian Spatial Prediction Using Wavelets

      • Hsin-Cheng Huang, Noel Cressie

      Pages 203-222

   2. Geometrical Priors for Noisefree Wavelet Coefficients in Image Denoising

      • Maarten Jansen, Adhemar Bultheel

      Pages 223-242

   3. Multiscale Hidden Markov Models for Bayesian Image Analysis

      • Robert D. Nowak

      Pages 243-265

   4. Wavelets for Object Representation and Recognition in Computer Vision

      • Luis Pastor, Angel Rodríguez, David Ríos Insua

      Pages 267-290

   5. Bayesian Denoising of Visual Images in the Wavelet Domain

      • Eero P. Simoncelli

      Pages 291-308

7. Empirical Bayes

   1. Empirical Bayes Estimation in Wavelet Nonparametric Regression

      • Merlise A. Clyde, Edward I. George

      Pages 309-322

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.

• Markov model
• hidden Markov model
• linear regression
• modeling
• statistics
• time series

• Institute of Statistics and Decision Sciences, Duke University, Durham, England

  Peter Müller, Brani Vidakovic

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