Lecture Notes in Statistics : LECTURE NOTES IN STATISTICS - Peter MÃ¼ller

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Lecture Notes in Statistics

By: Peter MÃ¼ller (Editor), Brani Vidakovic (Editor)

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Paperback | 1 August 1999

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416 Pages

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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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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Probability & Statistics Medicine Medicine in General Applied Mathematics Gardening

Introduction
An Introduction to Wavelets	p. 1
Spectral View of Wavelets and Nonlinear Regression	p. 19
Prior Models - Independent Case
Bayesian Approach to Wavelet Decomposition and Shrinkage	p. 33
Some Observations on the Tractability of Certain Multi-Scale Models	p. 51
Bayesian Analysis of Change-Point Models	p. 67
Prior Elicitation in the Wavelet Domain	p. 83
Wavelet Nonparametric Regression Using Basis Averaging	p. 95
Decision Theoretic Wavelet Shrinkage
An Overview of Wavelet Regularization	p. 109
Minimax Restoration and Deconvolution	p. 115
Robust Bayesian and Bayesian Decision Theoretic Wavelet Shrinkage	p. 139
Best Basis Representations with Prior Statistical Models	p. 155
Prior Models - Dependent Case
Modeling Dependence in the Wavelet Domain	p. 173
MCMC Methods in Wavelet Shrinkage	p. 187
Spatial Models
Empirical Bayesian Spatial Prediction Using Wavelets	p. 203
Geometrical Priors for Noisefree Wavelet Coefficients in Image Denoising	p. 223
Multiscale Hidden Markov Models for Bayesian Image Analysis	p. 243
Wavelets for Object Representation and Recognition in Computer Vision	p. 267
Bayesian Denoising of Visual Images in the Wavelet Domain	p. 291
Empirical Bayes
Empirical Bayes Estimation in Wavelet Nonparametric Regression	p. 309
Nonparametric Empirical Bayes Estimation via Wavelets	p. 323
Case Studies
Multiresolution Wavelet Analyses in Hierarchical Bayesian Turbulence Models	p. 341
Low Dimensional Turbulent Transport Mechanics Near the Forest-Atmosphere Interface	p. 361
Latent Structure Analyses of Turbulence Data Using Wavelets and Time Series Decompositions	p. 381
Table of Contents provided by Blackwell. All Rights Reserved.

Lecture Notes in Statistics

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