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Author: Bryan Andrew Toth
Publisher:
ISBN: 9781124694764
Category :
Languages : en
Pages : 167
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Book Description
This dissertation expands on existing work to develop a dynamical state and parameter estimation methodology in non-linear systems. The field of parameter and state estimation, also known as inverse problem theory, is a mature discipline concerned with determining unmeasured states and parameters in experimental systems. This is important since measurement of some of the parameters and states may not be possible, yet knowledge of these unmeasured quantities is necessary for predictions of the future state of the system. This field has importance across a broad range of scientific disciplines, including geosciences, biosciences, nanoscience, and many others. he work presented here describes a state and parameter estimation method that relies on the idea of synchronization of nonlinear systems to control the conditional Lyapunov exponents of the model system. This method is generalized to address any dynamic system that can be described by a set of ordinary first-order differential equations. The Python programming language is used to develop scripts that take a simple text-file representation of the model vector field and output correctly formatted files for use with readily available optimization software. With the use of these Python scripts, examples of the dynamic state and parameter estimation method are shown for a range of neurobiological models, ranging from simple to highly complicated, using simulated data. In this way, the strengths and weaknesses of this methodology are explored, in order to expand the applicability to complex experimental systems.
Author: Bryan Andrew Toth
Publisher:
ISBN: 9781124694764
Category :
Languages : en
Pages : 167
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Book Description
This dissertation expands on existing work to develop a dynamical state and parameter estimation methodology in non-linear systems. The field of parameter and state estimation, also known as inverse problem theory, is a mature discipline concerned with determining unmeasured states and parameters in experimental systems. This is important since measurement of some of the parameters and states may not be possible, yet knowledge of these unmeasured quantities is necessary for predictions of the future state of the system. This field has importance across a broad range of scientific disciplines, including geosciences, biosciences, nanoscience, and many others. he work presented here describes a state and parameter estimation method that relies on the idea of synchronization of nonlinear systems to control the conditional Lyapunov exponents of the model system. This method is generalized to address any dynamic system that can be described by a set of ordinary first-order differential equations. The Python programming language is used to develop scripts that take a simple text-file representation of the model vector field and output correctly formatted files for use with readily available optimization software. With the use of these Python scripts, examples of the dynamic state and parameter estimation method are shown for a range of neurobiological models, ranging from simple to highly complicated, using simulated data. In this way, the strengths and weaknesses of this methodology are explored, in order to expand the applicability to complex experimental systems.
Author: John R. Hauser
Publisher: Springer Science & Business Media
ISBN: 1402099207
Category : Technology & Engineering
Languages : en
Pages : 1013
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Book Description
There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.
Author: Dr Ranadheer Donthi
Publisher:
ISBN:
Category :
Languages : en
Pages : 7
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Book Description
The literature on numerical methods for fitting nonlinear regression model has grown enormously in the fast five decades. An important phase in nonlinear regression problems is the exploration of the relation between the independent and dependent variables. A largely unexplored area of research in nonlinear regression models concerns the finite sample properties of nonlinear parameters. The main object of this research study is to pro- pose some nonlinear methods of estimation of nonlinear regression models, namely Newton- Raphson method, Gauss-Newton method, Method of scoring, Quadratic Hill-Climbing and Conjugate Gradient methods. In 2005, G.E. Hovland et al. In his research article, presented a parameter estimation of physical time-varying parameters for combined-cycle power plant models. B. Mahaboob et al. (see [6]), in their research paper, proposed some computational methods based on numerical analysis to estimate the parameters of nonlinear regression model. S.J. Juliear et al., in their research paper, developed the method of unscented transformation (UT) to propagate mean and covariance information through nonlinear transformations.
Author: Christopher G. Small
Publisher: OUP Oxford
ISBN: 0191545090
Category : Mathematics
Languages : en
Pages : 324
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Book Description
Nonlinearity arises in statistical inference in various ways, with varying degrees of severity, as an obstacle to statistical analysis. More entrenched forms of nonlinearity often require intensive numerical methods to construct estimators, and the use of root search algorithms, or one-step estimators, is a standard method of solution. This book provides a comprehensive study of nonlinear estimating equations and artificial likelihoods for statistical inference. It provides extensive coverage and comparison of hill climbing algorithms, which, when started at points of nonconcavity often have very poor convergence properties, and for additional flexibility proposes a number of modifications to the standard methods for solving these algorithms. The book also extends beyond simple root search algorithms to include a discussion of the testing of roots for consistency, and the modification of available estimating functions to provide greater stability in inference. A variety of examples from practical applications are included to illustrate the problems and possibilities thus making this text ideal for the research statistician and graduate student. This is the latest in the well-established and authoritative Oxford Statistical Science Series, which includes texts and monographs covering many topics of current research interest in pure and applied statistics. Each title has an original slant even if the material included is not specifically original. The authors are leading researchers and the topics covered will be of interest to all professional statisticians, whether they be in industry, government department or research institute. Other books in the series include 23. W.J.Krzanowski: Principles of multivariate analysis: a user's perspective updated edition 24. J.Durbin and S.J.Koopman: Time series analysis by State Space Models 25. Peter J. Diggle, Patrick Heagerty, Kung-Yee Liang, Scott L. Zeger: Analysis of Longitudinal Data 2/e 26. J.K. Lindsey: Nonlinear Models in Medical Statistics 27. Peter J. Green, Nils L. Hjort & Sylvia Richardson: Highly Structured Stochastic Systems 28. Margaret S. Pepe: The Statistical Evaluation of Medical Tests for Classification and Prediction
Author: Hans Georg Bock
Publisher: Springer Science & Business Media
ISBN: 3642303676
Category : Mathematics
Languages : en
Pages : 342
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Book Description
This judicious selection of articles combines mathematical and numerical methods to apply parameter estimation and optimum experimental design in a range of contexts. These include fields as diverse as biology, medicine, chemistry, environmental physics, image processing and computer vision. The material chosen was presented at a multidisciplinary workshop on parameter estimation held in 2009 in Heidelberg. The contributions show how indispensable efficient methods of applied mathematics and computer-based modeling can be to enhancing the quality of interdisciplinary research. The use of scientific computing to model, simulate, and optimize complex processes has become a standard methodology in many scientific fields, as well as in industry. Demonstrating that the use of state-of-the-art optimization techniques in a number of research areas has much potential for improvement, this book provides advanced numerical methods and the very latest results for the applications under consideration.
Author: Josif A. Boguslavskiy
Publisher: Springer
ISBN: 3319040367
Category : Science
Languages : en
Pages : 219
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Book Description
This monograph is an exposition of a novel method for solving inverse problems, a method of parameter estimation for time series data collected from simulations of real experiments. These time series might be generated by measuring the dynamics of aircraft in flight, by the function of a hidden Markov model used in bioinformatics or speech recognition or when analyzing the dynamics of asset pricing provided by the nonlinear models of financial mathematics. Dynamic Systems Models demonstrates the use of algorithms based on polynomial approximation which have weaker requirements than already-popular iterative methods. Specifically, they do not require a first approximation of a root vector and they allow non-differentiable elements in the vector functions being approximated. The text covers all the points necessary for the understanding and use of polynomial approximation from the mathematical fundamentals, through algorithm development to the application of the method in, for instance, aeroplane flight dynamics or biological sequence analysis. The technical material is illustrated by the use of worked examples and methods for training the algorithms are included. Dynamic Systems Models provides researchers in aerospatial engineering, bioinformatics and financial mathematics (as well as computer scientists interested in any of these fields) with a reliable and effective numerical method for nonlinear estimation and solving boundary problems when carrying out control design. It will also be of interest to academic researchers studying inverse problems and their solution.
Author: John F. Monahan
Publisher: Cambridge University Press
ISBN: 1139498002
Category : Computers
Languages : en
Pages : 465
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Book Description
This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder–Mead search algorithm.
Author: Zhengming Wang
Publisher: CRC Press
ISBN: 1439853789
Category : Mathematics
Languages : en
Pages : 556
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Book Description
Measurement Data Modeling and Parameter Estimation integrates mathematical theory with engineering practice in the field of measurement data processing. Presenting the first-hand insights and experiences of the authors and their research group, it summarizes cutting-edge research to facilitate the application of mathematical theory in measurement and control engineering, particularly for those interested in aeronautics, astronautics, instrumentation, and economics. Requiring a basic knowledge of linear algebra, computing, and probability and statistics, the book illustrates key lessons with tables, examples, and exercises. It emphasizes the mathematical processing methods of measurement data and avoids the derivation procedures of specific formulas to help readers grasp key points quickly and easily. Employing the theories and methods of parameter estimation as the fundamental analysis tool, this reference: Introduces the basic concepts of measurements and errors Applies ideas from mathematical branches, such as numerical analysis and statistics, to the modeling and processing of measurement data Examines methods of regression analysis that are closely related to the mathematical processing of dynamic measurement data Covers Kalman filtering with colored noises and its applications Converting time series models into problems of parameter estimation, the authors discuss modeling methods for the true signals to be estimated as well as systematic errors. They provide comprehensive coverage that includes model establishment, parameter estimation, abnormal data detection, hypothesis tests, systematic errors, trajectory parameters, and modeling of radar measurement data. Although the book is based on the authors’ research and teaching experience in aeronautics and astronautics data processing, the theories and methods introduced are applicable to processing dynamic measurement data across a wide range of fields.
Author: Gavin J.S. Ross
Publisher: Springer Science & Business Media
ISBN: 1461234123
Category : Mathematics
Languages : en
Pages : 198
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Book Description
Non-Linear Estimation is a handbook for the practical statistician or modeller interested in fitting and interpreting non-linear models with the aid of a computer. A major theme of the book is the use of 'stable parameter systems'; these provide rapid convergence of optimization algorithms, more reliable dispersion matrices and confidence regions for parameters, and easier comparison of rival models. The book provides insights into why some models are difficult to fit, how to combine fits over different data sets, how to improve data collection to reduce prediction variance, and how to program particular models to handle a full range of data sets. The book combines an algebraic, a geometric and a computational approach, and is illustrated with practical examples. A final chapter shows how this approach is implemented in the author's Maximum Likelihood Program, MLP.
Author: Curtis R. Vogel
Publisher: SIAM
ISBN: 0898717574
Category : Mathematics
Languages : en
Pages : 195
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Book Description
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
