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Bayesian Inference in Wavelet-Based Models

  • Book
  • © 1999

Overview

Editors:
  1. Peter Müller

    1. Institute of Statistics and Decision Sciences, Duke University, Durham, England

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    You can also search for this editor in PubMed   Google Scholar

  2. Brani Vidakovic

    1. Institute of Statistics and Decision Sciences, Duke University, Durham, England

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Statistics (LNS, volume 141)

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Table of contents (23 chapters)

  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
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Keywords

About this book

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.

Editors and Affiliations

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

    Peter Müller, Brani Vidakovic

Bibliographic Information

  • Book Title: Bayesian Inference in Wavelet-Based Models

  • Editors: Peter Müller, Brani Vidakovic

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-0567-8

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1999

  • Softcover ISBN: 978-0-387-98885-6Published: 22 June 1999

  • eBook ISBN: 978-1-4612-0567-8Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: XIV, 396

  • Topics: Applications of Mathematics

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