Dynamic Data Analysis : Modeling Data with Differential Equations. 1st ed. 2017

種類:

電子ブック

責任表示:

by James Ramsay, Giles Hooker

出版情報:

New York, NY : Springer New York : Imprint: Springer, 2017

著者名:

• Ramsay, James.
• Hooker, Giles.
• SpringerLink (Online service)

シリーズ名:

Springer Series in Statistics ;

ISBN:

9781493971909 [1493971905]    

注記:

1 Introduction to Dynamic Models -- 2 DE notation and types -- 3 Linear Differential Equations and Systems -- 4 Nonlinear Differential Equations -- 5 Numerical Solutions -- 6 Qualitative Behavior -- 7 Trajectory Matching -- 8 Gradient Matching -- 9 Profiling for Linear Systems -- 10 Nonlinear Profiling -- References -- Glossary -- Index.
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

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