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  • © 2007

Multiscale Modeling

A Bayesian Perspective

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  • 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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  • ISBN: 978-0-387-70898-0
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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xii
  2. Introduction

    1. Front Matter

      Pages 1-1
    2. Introduction

      Pages 3-5
    3. Illustrative Example

      Pages 17-19
  3. Convolutions and Wavelets

    1. Front Matter

      Pages 21-24
    2. Convolution Methods

      Pages 25-38
    3. Wavelet Methods

      Pages 39-53
  4. Explicit Multiscale Models

    1. Front Matter

      Pages 55-55
    2. Multiscale Time Series

      Pages 113-143
    3. Change of Support Models

      Pages 145-152
  5. Implicit Multiscale Models

    1. Front Matter

      Pages 153-153
    2. Genetic Algorithms

      Pages 179-192

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.

The book is aimed at statisticians, applied mathematicians, and engineers working on problems dealing with multiscale processes in time and/or space, such as in engineering, finance, and environmetrics. The book will also be of interest to those working on multiscale computation research. The main prerequisites are knowledge of Bayesian statistics and basic Markov chain Monte Carlo methods. A number of real-world examples are thoroughly analyzed in order to demonstrate the methods and to assist the readers in applying these methods to their own work. To further assist readers, the authors are making source code (for R) available for many of the basic methods discussed herein.

Marco A. R. Ferreira is an Assistant Professor of Statistics at the University of Missouri, Columbia. Herbert K. H. Lee is an Associate Professor of Applied Mathematics and Statistics at the University of California, Santa Cruz, and authored the book Bayesian Nonparametrics via Neural Networks.

Keywords

  • Monte Carlo
  • Time series
  • aggregation
  • bayesian analysis
  • bayesian statistics
  • computed tomography (CT)
  • geographic data
  • image analysis
  • model
  • modeling
  • multiresolution modeling
  • multiscale analysis
  • statistics

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 for illustration, 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

  • University of Missouri, Columbia, USA

    Marco A. R. Ferreira

  • University of California, Santa Cruz, USA

    Herbert K. H. Lee

Bibliographic Information

Buying options

eBook
USD 129.00
Price excludes VAT (USA)
  • ISBN: 978-0-387-70898-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 169.00
Price excludes VAT (USA)
Hardcover Book
USD 169.99
Price excludes VAT (USA)