Bayesian Inference in Wavelet-Based Models

Bayesian Inference in Wavelet-Based Models
Author: Peter Müller
Publisher: Springer Science & Business Media
Total Pages: 406
Release: 2012-12-06
Genre: Mathematics
ISBN: 1461205670

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.

Bayesian Thinking, Modeling and Computation

Bayesian Thinking, Modeling and Computation
Author:
Publisher: Elsevier
Total Pages: 1062
Release: 2005-11-29
Genre: Mathematics
ISBN: 0080461174

This volume describes how to develop Bayesian thinking, modelling and computation both from philosophical, methodological and application point of view. It further describes parametric and nonparametric Bayesian methods for modelling and how to use modern computational methods to summarize inferences using simulation. The book covers wide range of topics including objective and subjective Bayesian inferences with a variety of applications in modelling categorical, survival, spatial, spatiotemporal, Epidemiological, software reliability, small area and micro array data. The book concludes with a chapter on how to teach Bayesian thoughts to nonstatisticians. Critical thinking on causal effects Objective Bayesian philosophy Nonparametric Bayesian methodology Simulation based computing techniques Bioinformatics and Biostatistics

Multiscale Signal Analysis and Modeling

Multiscale Signal Analysis and Modeling
Author: Xiaoping Shen
Publisher: Springer Science & Business Media
Total Pages: 388
Release: 2012-09-18
Genre: Technology & Engineering
ISBN: 1461441447

Multiscale Signal Analysis and Modeling presents recent advances in multiscale analysis and modeling using wavelets and other systems. This book also presents applications in digital signal processing using sampling theory and techniques from various function spaces, filter design, feature extraction and classification, signal and image representation/transmission, coding, nonparametric statistical signal processing, and statistical learning theory.

Statistical Modeling by Wavelets

Statistical Modeling by Wavelets
Author: Brani Vidakovic
Publisher: John Wiley & Sons
Total Pages: 410
Release: 2009-09-25
Genre: Mathematics
ISBN: 0470317868

A comprehensive, step-by-step introduction to wavelets in statistics. What are wavelets? What makes them increasingly indispensable in statistical nonparametrics? Why are they suitable for "time-scale" applications? How are they used to solve such problems as denoising, regression, or density estimation? Where can one find up-to-date information on these newly "discovered" mathematical objects? These are some of the questions Brani Vidakovic answers in Statistical Modeling by Wavelets. Providing a much-needed introduction to the latest tools afforded statisticians by wavelet theory, Vidakovic compiles, organizes, and explains in depth research data previously available only in disparate journal articles. He carefully balances both statistical and mathematical techniques, supplementing the material with a wealth of examples, more than 100 illustrations, and extensive references-with data sets and S-Plus wavelet overviews made available for downloading over the Internet. Both introductory and data-oriented modeling topics are featured, including: * Continuous and discrete wavelet transformations. * Statistical optimality properties of wavelet shrinkage. * Theoretical aspects of wavelet density estimation. * Bayesian modeling in the wavelet domain. * Properties of wavelet-based random functions and densities. * Several novel and important wavelet applications in statistics. * Wavelet methods in time series. Accessible to anyone with a background in advanced calculus and algebra, Statistical Modeling by Wavelets promises to become the standard reference for statisticians and engineers seeking a comprehensive introduction to an emerging field.

The Oxford Handbook of Applied Bayesian Analysis

The Oxford Handbook of Applied Bayesian Analysis
Author: Anthony O' Hagan
Publisher: OUP Oxford
Total Pages: 924
Release: 2010-03-18
Genre: Mathematics
ISBN: 0191613894

Bayesian analysis has developed rapidly in applications in the last two decades and research in Bayesian methods remains dynamic and fast-growing. Dramatic advances in modelling concepts and computational technologies now enable routine application of Bayesian analysis using increasingly realistic stochastic models, and this drives the adoption of Bayesian approaches in many areas of science, technology, commerce, and industry. This Handbook explores contemporary Bayesian analysis across a variety of application areas. Chapters written by leading exponents of applied Bayesian analysis showcase the scientific ease and natural application of Bayesian modelling, and present solutions to real, engaging, societally important and demanding problems. The chapters are grouped into five general areas: Biomedical & Health Sciences; Industry, Economics & Finance; Environment & Ecology; Policy, Political & Social Sciences; and Natural & Engineering Sciences, and Appendix material in each touches on key concepts, models, and techniques of the chapter that are also of broader pedagogic and applied interest.

Wavelet Methods in Statistics with R

Wavelet Methods in Statistics with R
Author: Guy Nason
Publisher: Springer Science & Business Media
Total Pages: 259
Release: 2010-07-25
Genre: Mathematics
ISBN: 0387759611

This book contains information on how to tackle many important problems using a multiscale statistical approach. It focuses on how to use multiscale methods and discusses methodological and applied considerations.

An Introduction to Bayesian Analysis

An Introduction to Bayesian Analysis
Author: Jayanta K. Ghosh
Publisher: Springer Science & Business Media
Total Pages: 356
Release: 2007-07-03
Genre: Mathematics
ISBN: 0387354336

This is a graduate-level textbook on Bayesian analysis blending modern Bayesian theory, methods, and applications. Starting from basic statistics, undergraduate calculus and linear algebra, ideas of both subjective and objective Bayesian analysis are developed to a level where real-life data can be analyzed using the current techniques of statistical computing. Advances in both low-dimensional and high-dimensional problems are covered, as well as important topics such as empirical Bayes and hierarchical Bayes methods and Markov chain Monte Carlo (MCMC) techniques. Many topics are at the cutting edge of statistical research. Solutions to common inference problems appear throughout the text along with discussion of what prior to choose. There is a discussion of elicitation of a subjective prior as well as the motivation, applicability, and limitations of objective priors. By way of important applications the book presents microarrays, nonparametric regression via wavelets as well as DMA mixtures of normals, and spatial analysis with illustrations using simulated and real data. Theoretical topics at the cutting edge include high-dimensional model selection and Intrinsic Bayes Factors, which the authors have successfully applied to geological mapping. The style is informal but clear. Asymptotics is used to supplement simulation or understand some aspects of the posterior.

Case Studies in Bayesian Statistics

Case Studies in Bayesian Statistics
Author: Constantine Gatsonis
Publisher: Springer
Total Pages: 384
Release: 2018-08-17
Genre: Mathematics
ISBN: 1461220785

This volume contains invited case studies with the accompanying discussion as well as contributed papers selected by a refereeing process of 6th Workshop on Case Studies in Bayesian Statistics was held at the Carnegie Mellon University in October, 2001.

Energy Minimization Methods in Computer Vision and Pattern Recognition

Energy Minimization Methods in Computer Vision and Pattern Recognition
Author: Anand Rangarajan
Publisher: Springer
Total Pages: 540
Release: 2003-10-02
Genre: Computers
ISBN: 3540450637

This book constitutes the refereed proceedings of the 4th International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2003, held in Lisbon, Portugal in July 2003.The 33 revised full papers presented were carefully reviewed and selected from 66 submissions. The papers are organized in topical sections on unsupervised learning and matching, probabilistic modeling, segmentation and grouping, shape modeling, restoration and reconstruction, and graphs and graph-based methods.