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Multiscale Modeling

A Bayesian Perspective

  • Marco A. R. Ferreira
  • Herbert K. H. Lee

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Pages 3-5
    3. Pages 17-19
  3. Convolutions and Wavelets

    1. Front Matter
      Pages 21-24
    2. Pages 25-38
    3. Pages 39-53
  4. Explicit Multiscale Models

  5. Implicit Multiscale Models

    1. Front Matter
      Pages 153-153
    2. Pages 179-192
  6. Case Studies

    1. Front Matter
      Pages 191-191
    2. Pages 223-224
  7. Back Matter
    Pages 225-245

About this book

Introduction

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

Authors and affiliations

  • Marco A. R. Ferreira
    • 1
  • Herbert K. H. Lee
    • 2
  1. 1.University of MissouriColumbiaUSA
  2. 2.University of CaliforniaSanta CruzUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-70898-0
  • Copyright Information Springer Science+Business Media, LLC 2007
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-70897-3
  • Online ISBN 978-0-387-70898-0
  • Series Print ISSN 0172-7397
  • Buy this book on publisher's site