Authors:
- Stochastic models for processes that live and can possibly be observed at different levels of resolution
- The models in this book allow different degrees of smoothness of the stochastic processes at the different levels of resolution
- The statistical analysis of multiscale models based on the Bayesian paradigm in the book allow a full amount of uncertainty
- Contains implicit multiscale models implementable with parallel computation and genetic algorithms
Part of the book series: Springer Series in Statistics (SSS)
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Table of contents (18 chapters)
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Front Matter
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Introduction
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Front Matter
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Convolutions and Wavelets
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Front Matter
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Implicit Multiscale Models
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Front Matter
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About this book
A wide variety of processes occur on multiple scales, either naturally or as a consequence of measurement. This book contains methodology for the analysis of data that arise from such multiscale processes. The book brings together a number of recent developments and makes them accessible to a wider audience. Taking a Bayesian approach allows for full accounting of uncertainty, and also addresses the delicate issue of uncertainty at multiple scales. The Bayesian approach also facilitates the use of knowledge from prior experience or data, and these methods can handle different amounts of prior knowledge at different scales, as often occurs in practice.
Reviews
From the reviews:
"Readership: Students and practitioners of Multiscale Modeling and Analysis by Bayesian methods.… This is a wonderfully written review of what is known about multiscale modelling and associated Bayesian inference.… The models are very clearly described and discussed with a lot of insight. The computational details are also discussed well. The book is very well written… ." (Jayanta K. Ghosh, International Statistical Review, Vol. 76 (1), 2008)
"In general, the book discusses various statistical tools, which can be used to link the information at different scales and assess the associated uncertainties. Approaches to speed up the computations are also presented. The basic computer codes for many of the methods discussed in the book are made available through the website of one of the authors. This is a very good introductory book for nonexperts as well as for experts working in this field." (Yalchin Efendiev, Journal of the American Statistical Association, March 2009, Vol. 104, No. 485)
“A multitude of natural processes occur in multiple scales giving rise to complicated phenomenon often modeled by processes, algorithms, and data structured by scale. However, a ‘real’ book that summarizes these for a wider audience, particularly geostatisticians, has been lacking. I personally thank Professors Ferreira and Lee for filling this void with this commendable book, a nicely organized exploration of multiscale methods developed using a Bayesian paradigm. … Multiscale Modeling: A Bayesian Perspective is not really a textbook… . It is more like an advanced-level reference book for graduate students and geostatistical researchers interested in learning about the advances in this field. For any PhD-level graduate statistics course in advanced multiscale models, this book…is automatically the book of choice. The detailed theoretical exposition of the methods, motivating examples forillustration, easy-to-understand R programs, and other features will enable any instructor to introduce the topic in the classroom setting. Several Chapters can provide sufficient insight to choose a PhD dissertation topic. The extensive bibliography at the end of the book will complement the learning curve. The book is a seminal work in this direction, the first of its kind, and I highly recommend it.” (Technometrics, May 2010, Vol. 52, No. 2)Authors and Affiliations
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University of Missouri, Columbia, USA
Marco A. R. Ferreira
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University of California, Santa Cruz, USA
Herbert K. H. Lee
Bibliographic Information
Book Title: Multiscale Modeling
Book Subtitle: A Bayesian Perspective
Authors: Marco A. R. Ferreira, Herbert K. H. Lee
Series Title: Springer Series in Statistics
DOI: https://doi.org/10.1007/978-0-387-70898-0
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2007
Hardcover ISBN: 978-0-387-70897-3Published: 27 July 2007
Softcover ISBN: 978-1-4419-2426-1Published: 19 November 2010
eBook ISBN: 978-0-387-70898-0Published: 17 July 2007
Series ISSN: 0172-7397
Series E-ISSN: 2197-568X
Edition Number: 1
Number of Pages: XII, 245
Topics: Statistical Theory and Methods, Probability Theory and Stochastic Processes, Econometrics, Simulation and Modeling, Image Processing and Computer Vision, Geography, general