Bayesian Inference in Wavelet-Based Models

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Peter Müller, Brani Vidakovic
Springer New York, Aug 1, 1999 - Mathematics - 396 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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Contents

An Introduction to Wavelets
1
Spectral View of Wavelets and Nonlinear Regression
19
PRIOR MODELS INDEPENDENT CASE
33
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About the author (1999)

Peter Muller is a Professor in the Department of Biostatistics and Applied Mathematics at the University of Texas M. D. Anderson Cancer Center. His research interests and contributions are in the areas of Markov chain Monte Carlo posterior simulation, nonparametric Bayesian inference, hierarchical models, mixture models and Bayesian decisions problems.

Paul H. Kvam, PhD, is Professor of Industrial and Systems Engineering at Georgia Institute of Technology. His research interests include nonparametric estimation, statistical reliability with applications to engineering, and analysis of complex and dependent systems. He has written over fifty refereed articles and was named a Fellow of the American Statistical Association in 2006.

Brani Vidakovic, PhD, is Professor of Statistics and Director of the Center for Bioengineering Statistics at The Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology. He has authored or co-authored three books and has published more than four dozen refereed articles. His areas of interest include wavelets, Bayesian inference, biostatistics, statistical methods in environmental research, and statistical education.

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