Parameter Redundancy and Identifiability
Parameter Redundancy and Identifiability

Author: Diana Cole

Publisher: CRC Press

Published: 2020-05-10

Total Pages: 273

ISBN-13: 1498720900

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Statistical and mathematical models are defined by parameters that describe different characteristics of those models. Ideally it would be possible to find parameter estimates for every parameter in that model, but, in some cases, this is not possible. For example, two parameters that only ever appear in the model as a product could not be estimated individually; only the product can be estimated. Such a model is said to be parameter redundant, or the parameters are described as non-identifiable. This book explains why parameter redundancy and non-identifiability is a problem and the different methods that can be used for detection, including in a Bayesian context. Key features of this book: Detailed discussion of the problems caused by parameter redundancy and non-identifiability Explanation of the different general methods for detecting parameter redundancy and non-identifiability, including symbolic algebra and numerical methods Chapter on Bayesian identifiability Throughout illustrative examples are used to clearly demonstrate each problem and method. Maple and R code are available for these examples More in-depth focus on the areas of discrete and continuous state-space models and ecological statistics, including methods that have been specifically developed for each of these areas This book is designed to make parameter redundancy and non-identifiability accessible and understandable to a wide audience from masters and PhD students to researchers, from mathematicians and statisticians to practitioners using mathematical or statistical models.

Modeling Demographic Processes in Marked Populations
Modeling Demographic Processes in Marked Populations

Author: David L. Thomson

Publisher: Springer Science & Business Media

Published: 2008-12-11

Total Pages: 1110

ISBN-13: 038778151X

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Here, biologists and statisticians come together in an interdisciplinary synthesis with the aim of developing new methods to overcome the most significant challenges and constraints faced by quantitative biologists seeking to model demographic rates.

Analysis of Capture-Recapture Data
Analysis of Capture-Recapture Data

Author: Rachel S. McCrea

Publisher: CRC Press

Published: 2014-08-01

Total Pages: 302

ISBN-13: 1439836604

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An important first step in studying the demography of wild animals is to identify the animals uniquely through applying markings, such as rings, tags, and bands. Once the animals are encountered again, researchers can study different forms of capture-recapture data to estimate features, such as the mortality and size of the populations. Capture-rec

Uncertainty Quantification
Uncertainty Quantification

Author: Ralph C. Smith

Publisher: SIAM

Published: 2024-09-13

Total Pages: 571

ISBN-13: 1611977843

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Uncertainty quantification serves a fundamental role when establishing the predictive capabilities of simulation models. This book provides a comprehensive and unified treatment of the mathematical, statistical, and computational theory and methods employed to quantify uncertainties associated with models from a wide range of applications. Expanded and reorganized, the second edition includes advances in the field and provides a comprehensive sensitivity analysis and uncertainty quantification framework for models from science and engineering. It contains new chapters on random field representations, observation models, parameter identifiability and influence, active subspace analysis, and statistical surrogate models, and a completely revised chapter on local sensitivity analysis. Other updates to the second edition are the inclusion of over 100 exercises and many new examples — several of which include data — and UQ Crimes listed throughout the text to identify common misconceptions and guide readers entering the field. Uncertainty Quantification: Theory, Implementation, and Applications, Second Edition is intended for advanced undergraduate and graduate students as well as researchers in mathematics, statistics, engineering, physical and biological sciences, operations research, and computer science. Readers are assumed to have a basic knowledge of probability, linear algebra, differential equations, and introductory numerical analysis. The book can be used as a primary text for a one-semester course on sensitivity analysis and uncertainty quantification or as a supplementary text for courses on surrogate and reduced-order model construction and parameter identifiability analysis.

Introduction to Modeling in Physiology and Medicine
Introduction to Modeling in Physiology and Medicine

Author: Claudio Cobelli

Publisher: Elsevier

Published: 2008-02-06

Total Pages: 337

ISBN-13: 0080559980

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This unified modeling textbook for students of biomedical engineering provides a complete course text on the foundations, theory and practice of modeling and simulation in physiology and medicine. It is dedicated to the needs of biomedical engineering and clinical students, supported by applied BME applications and examples. Developed for biomedical engineering and related courses: speaks to BME students at a level and in a language appropriate to their needs, with an interdisciplinary clinical/engineering approach, quantitative basis, and many applied examples to enhance learning Delivers a quantitative approach to modeling and also covers simulation: the perfect foundation text for studies across BME and medicine Extensive case studies and engineering applications from BME, plus end-of-chapter exercises

Systems Biology
Systems Biology

Author: Aleš Prokop

Publisher: Springer Science & Business Media

Published: 2013-08-28

Total Pages: 569

ISBN-13: 9400768036

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Growth in the pharmaceutical market has slowed down – almost to a standstill. One reason is that governments and other payers are cutting costs in a faltering world economy. But a more fundamental problem is the failure of major companies to discover, develop and market new drugs. Major drugs losing patent protection or being withdrawn from the market are simply not being replaced by new therapies – the pharmaceutical market model is no longer functioning effectively and most pharmaceutical companies are failing to produce the innovation needed for success. This multi-authored new book looks at a vital strategy which can bring innovation to a market in need of new ideas and new products: Systems Biology (SB). Modeling is a significant task of systems biology. SB aims to develop and use efficient algorithms, data structures, visualization and communication tools to orchestrate the integration of large quantities of biological data with the goal of computer modeling. It involves the use of computer simulations of biological systems, such as the networks of metabolites comprise signal transduction pathways and gene regulatory networks to both analyze and visualize the complex connections of these cellular processes. SB involves a series of operational protocols used for performing research, namely a cycle composed of theoretical, analytic or computational modeling to propose specific testable hypotheses about a biological system, experimental validation, and then using the newly acquired quantitative description of cells or cell processes to refine the computational model or theory.

Modelling Population Dynamics
Modelling Population Dynamics

Author: K. B. Newman

Publisher: Springer

Published: 2014-07-16

Total Pages: 223

ISBN-13: 1493909770

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This book gives a unifying framework for estimating the abundance of open populations: populations subject to births, deaths and movement, given imperfect measurements or samples of the populations. The focus is primarily on populations of vertebrates for which dynamics are typically modelled within the framework of an annual cycle, and for which stochastic variability in the demographic processes is usually modest. Discrete-time models are developed in which animals can be assigned to discrete states such as age class, gender, maturity, population (within a metapopulation), or species (for multi-species models). The book goes well beyond estimation of abundance, allowing inference on underlying population processes such as birth or recruitment, survival and movement. This requires the formulation and fitting of population dynamics models. The resulting fitted models yield both estimates of abundance and estimates of parameters characterizing the underlying processes.

Model Identification and Data Analysis
Model Identification and Data Analysis

Author: Sergio Bittanti

Publisher: John Wiley & Sons

Published: 2019-04-02

Total Pages: 416

ISBN-13: 1119546362

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This book is about constructing models from experimental data. It covers a range of topics, from statistical data prediction to Kalman filtering, from black-box model identification to parameter estimation, from spectral analysis to predictive control. Written for graduate students, this textbook offers an approach that has proven successful throughout the many years during which its author has taught these topics at his University. The book: Contains accessible methods explained step-by-step in simple terms Offers an essential tool useful in a variety of fields, especially engineering, statistics, and mathematics Includes an overview on random variables and stationary processes, as well as an introduction to discrete time models and matrix analysis Incorporates historical commentaries to put into perspective the developments that have brought the discipline to its current state Provides many examples and solved problems to complement the presentation and facilitate comprehension of the techniques presented

Characterizing Sources of Indoor Air Pollution and Related Sink Effects
Characterizing Sources of Indoor Air Pollution and Related Sink Effects

Author: Bruce A. Tichenor

Publisher: ASTM International

Published: 1996

Total Pages: 408

ISBN-13: 0803120303

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Based on presentations at a 1994 Symposium, these detailed papers review source/sink characterization; design, construction, characterization, and operation of test chambers and facilities; testing protocols for determining emission factors and sink absorption/desorption rates; models for predicting