Parameter Estimation in Nonlinear Models of Biological Systems PDF Download
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Author: William Robert Smith
Publisher:
ISBN:
Category : Biological systems
Languages : en
Pages : 180
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Book Description
Author: William Robert Smith
Publisher:
ISBN:
Category : Biological systems
Languages : en
Pages : 180
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Book Description
Author: W.R. Smith
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: Andrei Kramer
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832541950
Category : Computers
Languages : en
Pages : 164
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Book Description
Markov Chain Monte Carlo (MCMC) methods are sampling based techniques, which use random numbers to approximate deterministic but unknown values. They can be used to obtain expected values, estimate parameters or to simply inspect the properties of a non-standard, high dimensional probability distribution. Bayesian analysis of model parameters provides the mathematical foundation for parameter estimation using such probabilistic sampling. The strengths of these stochastic methods are their robustness and relative simplicity even for nonlinear problems with dozens of parameters as well as a built-in uncertainty analysis. Because Bayesian model analysis necessarily involves the notion of prior knowledge, the estimation of unidentifiable parameters can be regularised (by priors) in a straight forward way. This work draws the focus on typical cases in systems biology: relative data, nonlinear ordinary differential equation models and few data points. It also investigates the consequences of parameter estimation from steady state data; consequences such as performance benefits. In biology the data is almost exclusively relative, the raw measurements (e.g. western blot intensities) are normalised by control experiments or a reference value within a series and require the model to do the same when comparing its output to the data. Several sampling algorithms are compared in terms of effective sampling speed and necessary adaptations to relative and steady state data are explained.
Author: Harvey Motulsky
Publisher: Oxford University Press
ISBN: 9780198038344
Category : Mathematics
Languages : en
Pages : 352
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Book Description
Most biologists use nonlinear regression more than any other statistical technique, but there are very few places to learn about curve-fitting. This book, by the author of the very successful Intuitive Biostatistics, addresses this relatively focused need of an extraordinarily broad range of scientists.
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: 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: J. Perkins
Publisher: Createspace Independent Publishing Platform
ISBN: 9781983526428
Category :
Languages : en
Pages : 438
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Book Description
SimBiology provides an app and programmatic tools to model, simulate, and analyze dynamic systems, focusing on pharmacokinetic/pharmacodynamic (PK/PD) and systems biology applications. It provides a block diagram editor for building models, or you can create models programmatically using the MATLAB language. SimBiology includes a library of common PK models, which you can customize and integrate with mechanistic systems biology models. A variety of model exploration techniques let you identify optimal dosing schedules and putative drug targets in cellular pathways. SimBiology uses ordinary differential equations (ODEs) and stochastic solvers to simulate the time course profile of drug exposure, drug efficacy, and enzyme and metabolite levels. You can investigate system dynamics and guide experimentation using parameter sweeps and sensitivity analysis. You can also use single subject or population data to estimate model parameters. The fundamental content of this book is the following: -App for PK/PD and mechanistic systems biology modeling -Ordinary differential equations (ODEs) and stochastic solvers -Library of PK models -Parameter estimation techniques for single-subject and population data, including nonlinear mixed-effects models -Sensitivity analysis and parameter sweeps for investigating parameter effects on system dynamics -Diagnostic plots for individual and population fits -Methods for creating and optimizing dosing schedules
Author: Joel Barry Swartz
Publisher:
ISBN:
Category : Biological models
Languages : en
Pages : 590
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Book Description
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: W. J. H. Stortelder
Publisher:
ISBN:
Category : Differentiable dynamical systems
Languages : en
Pages : 196
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Book Description
