Parameter Redundancy And Identifiability
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Parameter Redundancy and Identifiability
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.
Analysis of Capture-Recapture Data
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-recapture methods are also used in other areas, including epidemiology and sociology. With an emphasis on ecology, Analysis of Capture-Recapture Data covers many modern developments of capture-recapture and related models and methods and places them in the historical context of research from the past 100 years. The book presents both classical and Bayesian methods. A range of real data sets motivates and illustrates the material and many examples illustrate biometry and applied statistics at work. In particular, the authors demonstrate several of the modeling approaches using one substantial data set from a population of great cormorants. The book also discusses which computer programs to use for implementing the models and contains 130 exercises that extend the main material. The data sets, computer programs, and other ancillaries are available at www.capturerecapture.co.uk. The book is accessible to advanced undergraduate and higher-level students, quantitative ecologists, and statisticians. It helps readers understand model formulation and applications, including the technicalities of model diagnostics and checking.
Quantitative Psychology
This book includes presentations given at the 88th annual meeting of the Psychometric Society, held in Maryland, USA on July 24–28, 2023. The proceeding covers a diverse set of psychometric topics. The topics include, but are not limited to item response theory, cognitive diagnostic models, Bayesian estimation, validity and reliability issues, and several applications within different fields. The authors are from all over the world, they work in different psychometrics areas, as well as having diverse professional and academic experiences.