This volume provides a thorough introduction and reference for any researcher who is interested in Bayesian inference for wavelet-based models, but is not necessarily an expert in either. To achieve this goal the book starts with an extensive introductory chapter providing a self-contained introduction to the use of wavelet decompositions and the relation to Bayesian inference. The remaining papers in this volume are divided into six parts: independent prior modeling; decision theoretic aspects; dependent prior modeling; spatial models using bivariate wavelet bases; empirical Bayes approaches; and case studies. Chapters are written by experts who published the original research papers establishing the use of wavelet-based models in Bayesian inference. Peter Müller is Associate Professor and Brani Vidakovic is Assistant Professor of Statistics at Duke University.