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.

Table of Contents:
I Introduction.- 1 An Introduction to Wavelets.- 2 Spectral View of Wavelets and Nonlinear Regression.- II Prior Models - Independent Case.- 3 Bayesian Approach to Wavelet Decomposition and Shrinkage.- 4 Some Observations on the Iractability of Certain Multi-Scale Models..- 5 Bayesian Analysis of Change-Point Models.- 6 Prior Elicitation in the Wavelet Domain.- 7 Wavelet Nonparametric Regression Using Basis Averaging.- III Decision Theoretic Wavelet Shrinkage.- 8 An Overview of Wavelet Regularization.- 9 Minimax Restoration and Deconvolution.- 10 Robust Bayesian and Bayesian Decision Theoretic Wavelet Shrinkage.- 11 Best Basis Representations with Prior Statistical Models.- IV Prior Models — Dependent Case.- 12 Modeling Dependence in the Wavelet Domain.- 13 MCMC Methods in Wavelet Shrinkage.- V Spatial Models.- 14 Empirical Bayesian Spatial Prediction Using Wavelets.- 15 Geometrical Priors for Noisefree Wavelet Coefficients in Image Denoising.- 16 Multiscale Hidden Markov Models for Bayesian Image Analysis.- 17 Wavelets for Object Representation and Recognition in Computer Vision.- 18 Bayesian Denoising of Visual Images in the Wavelet Domain.- VI Empirical Bayes.- 19 Empirical Bayes Estimation in Wavelet Nonparametric Regression.- 20 Nonparametric Empirical Bayes Estimation via Wavelets.- VII Case Studies.- 21 Multiresolution Wavelet Analyses in Hierarchical Bayesian Turbulence Models.- 22 Low Dimensional Turbulent Transport Mechanics Near the Forest-Atmosphere Interface.- 23 Latent Structure Analyses of Turbulence Data Using Wavelets and Time Series Decompositions.