Skip to main content
SpringerLink
Log in
Book cover

Dynamic Data Analysis

Modeling Data with Differential Equations

  • Book
  • © 2017

Overview

Authors:
  1. James Ramsay

    1. Ottawa, Canada

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Giles Hooker

    1. Computational Biology, Cornell University Dept. Biological Statistics &, Ithaca, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Offers an accessible text to those with little or no exposure to differential equations as modeling objects
  • Updates and builds on techniques from the popular Functional Data Analysis (Ramsay and Silverman, 2005)
  • Opens up new opportunities for dynamical systems and presents additional applications for previously analyzed data
  • Includes supplementary material: sn.pub/extras

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvii
    Download chapter PDF

  2. Introduction to Dynamic Models

    • James Ramsay, Giles Hooker
    Pages 1-15

  3. Differential Equations: Notation and Architecture

    • James Ramsay, Giles Hooker
    Pages 17-30

  4. Linear Differential Equations and Systems

    • James Ramsay, Giles Hooker
    Pages 31-51

  5. Nonlinear Differential Equations and Systems

    • James Ramsay, Giles Hooker
    Pages 53-68

  6. Numerical Solutions

    • James Ramsay, Giles Hooker
    Pages 69-81

  7. Qualitative Behavior

    • James Ramsay, Giles Hooker
    Pages 83-102

  8. Nonlinear Least Squares or Trajectory Matching

    • James Ramsay, Giles Hooker
    Pages 103-136

  9. Two-Stage Least Squares or Gradient Matching

    • James Ramsay, Giles Hooker
    Pages 137-160

  10. Profiled Estimation for Linear Systems Estimated by Least Squares Fitting

    • James Ramsay, Giles Hooker
    Pages 161-200

  11. Profiled Estimation for Nonlinear Systems

    • James Ramsay, Giles Hooker
    Pages 201-220

  12. Back Matter

    Pages 221-230
    Download chapter PDF
Back to top

Keywords

About this book

This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in the properties of differential equations estimated from data will find rather less to work with. This book fills that gap. 

Reviews

“This book is intended both for first year graduate students and for researchers in applied mathematics and/or statistics who want to check models with differential equations in data science. These kinds of models have a mechanistic approach, enlarging the classes of models for statisticians, and giving techniques for estimation of parameters, assessing the adequacy of models and planning experiments for applied mathematicians.” (Sylvie Viguier-Pla, Mathematical Reviews, August, 2018)​

Authors and Affiliations

  • Ottawa, Canada

    James Ramsay

  • Computational Biology, Cornell University Dept. Biological Statistics &, Ithaca, USA

    Giles Hooker

About the authors

Jim Ramsay, PhD, is Professor Emeritus of Psychology and an Associate Member in the Department of Mathematics and Statistics at McGill University. He received his PhD from Princeton University in 1966 in quantitative psychology. He has been President of the Psychometric Society and the Statistical Society of Canada. He received the Gold Medal in 1998 for his contributions to psychometrics and functional data analysis and Honorary Membership in 2012 from the Statistical Society of Canada.

Giles Hooker, PhD, is Associate Professor of Biological Statistics and Computational Biology at Cornell University. In addition to differential equation models, he has published extensively on functional data analysis and uncertainty quantification in machine learning. Much of his methodological work is inspired by collaborations in ecology and citizen science data.

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation