[PDF] Parameter Redundancy And Identifiability eBook

Author : Diana Cole
Publisher : CRC Press
Page : 273 pages
File Size : 36,81 MB
Release : 2020-05-10
Category : Mathematics
ISBN : 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.

Author : David L. Thomson
Publisher : Springer Science & Business Media
Page : 1110 pages
File Size : 40,20 MB
Release : 2008-12-11
Category : Medical
ISBN : 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.

Author : Rachel S. McCrea
Publisher : CRC Press
Page : 302 pages
File Size : 18,99 MB
Release : 2014-08-01
Category : Mathematics
ISBN : 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

Author : Ralph C. Smith
Publisher : SIAM
Page : 571 pages
File Size : 42,84 MB
Release : 2024-09-13
Category : Mathematics
ISBN : 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.

Author : Aleš Prokop
Publisher : Springer Science & Business Media
Page : 569 pages
File Size : 18,51 MB
Release : 2013-08-28
Category : Medical
ISBN : 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.

Author : K. B. Newman
Publisher : Springer
Page : 223 pages
File Size : 10,36 MB
Release : 2014-07-16
Category : Medical
ISBN : 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.

Author : Bruce A. Tichenor
Publisher : ASTM International
Page : 408 pages
File Size : 43,35 MB
Release : 1996
Category : Indoor air pollution
ISBN : 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

Author : George A. F. Seber
Publisher : Springer
Page : 663 pages
File Size : 35,31 MB
Release : 2019-08-13
Category : Mathematics
ISBN : 3030181871

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This comprehensive book, rich with applications, offers a quantitative framework for the analysis of the various capture-recapture models for open animal populations, while also addressing associated computational methods. The state of our wildlife populations provides a litmus test for the state of our environment, especially in light of global warming and the increasing pollution of our land, seas, and air. In addition to monitoring our food resources such as fisheries, we need to protect endangered species from the effects of human activities (e.g. rhinos, whales, or encroachments on the habitat of orangutans). Pests must be be controlled, whether insects or viruses, and we need to cope with growing feral populations such as opossums, rabbits, and pigs. Accordingly, we need to obtain information about a given population’s dynamics, concerning e.g. mortality, birth, growth, breeding, sex, and migration, and determine whether the respective population is increasing , static, or declining. There are many methods for obtaining population information, but the most useful (and most work-intensive) is generically known as “capture-recapture,” where we mark or tag a representative sample of individuals from the population and follow that sample over time using recaptures, resightings, or dead recoveries. Marks can be natural, such as stripes, fin profiles, and even DNA; or artificial, such as spots on insects. Attached tags can, for example, be simple bands or streamers, or more sophisticated variants such as radio and sonic transmitters. To estimate population parameters, sophisticated and complex mathematical models have been devised on the basis of recapture information and computer packages. This book addresses the analysis of such models. It is primarily intended for ecologists and wildlife managers who wish to apply the methods to the types of problems discussed above, though it will also benefit researchers and graduate students in ecology. Familiarity with basic statistical concepts is essential.

Author : Michael Schaub
Publisher : Academic Press
Page : 640 pages
File Size : 29,19 MB
Release : 2021-11-12
Category : Science
ISBN : 0128209151

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Integrated Population Models: Theory and Ecological Applications with R and JAGS is the first book on integrated population models, which constitute a powerful framework for combining multiple data sets from the population and the individual levels to estimate demographic parameters, and population size and trends. These models identify drivers of population dynamics and forecast the composition and trajectory of a population. Written by two population ecologists with expertise on integrated population modeling, this book provides a comprehensive synthesis of the relevant theory of integrated population models with an extensive overview of practical applications, using Bayesian methods by means of case studies. The book contains fully-documented, complete code for fitting all models in the free software, R and JAGS. It also includes all required code for pre- and post-model-fitting analysis. Integrated Population Models is an invaluable reference for researchers and practitioners involved in population analysis, and for graduate-level students in ecology, conservation biology, wildlife management, and related fields. The text is ideal for self-study and advanced graduate-level courses. Offers practical and accessible ecological applications of IPMs (integrated population models) Provides full documentation of analyzed code in the Bayesian framework Written and structured for an easy approach to the subject, especially for non-statisticians