Dynamic Data Analysis

Modeling Data with Differential Equations

James Ramsay, Giles Hooker (Autoren)

Buch | Hardcover

230 Seiten

2017 | 1st ed. 2017
Springer-Verlag New York Inc.
978-1-4939-7188-6 (ISBN)

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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.

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.

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 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)

Erscheinungsdatum	18.07.2017
Reihe/Serie	Springer Series in Statistics
Zusatzinfo	50 Illustrations, color; 34 Illustrations, black and white; XVII, 230 p. 84 illus., 50 illus. in color.
Verlagsort	New York
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Datenbanken
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Differential Equations • Dynamic Models • functional data analysis • gradient matching • Linear Differential Equations • nonlinear differential equations • nonlinear profiling • numerical solutions • profiling for linear systems • qualitative behavior • trajectory matching
ISBN-10	1-4939-7188-3 / 1493971883
ISBN-13	978-1-4939-7188-6 / 9781493971886
Zustand	Neuware