## Bayesian Inference in Wavelet-Based ModelsThis 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 |

Copyright | |

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Abramovich algorithm analysis applied approximation Bayes estimator Bayes factors Bayesian approach Bayesian wavelet BB search Besov spaces change-point Chipman Clyde components computed conditional consider corresponding covariance Crouse Daubechies DecompShrink deconvolution denoising density estimation diagonal discrete wavelet transform discussed Donoho and Johnstone EB estimation example factorization Figure filter function given graphical models Haar wavelet hard thresholding hyperparameters IEEE Trans independent inverse Johnstone 1994 Kolaczyk likelihood linear Mallat marginal likelihood Markov matrix methods MHMM minimax mirror wavelet mixture multiresolution multiscale parameters noise nonparametric regression normal Nowak optimal orthogonal orthonormal pixels posterior distribution posterior mean posterior probability prior distribution prior model prior probability problem random reconstruction representation resolution level Ruggeri Sapatinas scale Section Signal Processing Silverman simulation smooth spatial specific spectral density Statistics stochastic structure Theorem thresholding estimator thresholding rules tion values Vannucci variables variance vector wavelet basis wavelet coefficients wavelet shrinkage wavelet thresholding zero