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.
Table of Contents
2. Problems With Parameter Redundancy
3. Parameter Redundancy and Identifiability Definitions and Theory
4. Practical General Methods for Detecting Parameter Redundancy and Identifiability
5. Detecting Parameter Redundancy and Identifiability in Complex Models
6. Bayesian Identifiability
7. Identifiability in Continuous State-Space Models
8. Identifiability in Discrete State-Space Models
9. Detecting Parameter Redundancy in Ecological Models
10. Concluding Remarks
Appendix A. Maple Code
Appendix B. Winbugs and R Code
Diana Cole is a Senior Lecturer in Statistics at the University of Kent. She has written and co-authored 15 papers on parameter redundancy and identifiability, including general theory and ecological applications.
"This is an interesting book which concentrates on a relatively narrow, but certainly important and unfortunately often neglected topic of identifiability in statistical (and generic mathematical) models...In principle, it is certainly accessible to a wide audience, from students to practicing statisticians, or even to quantitatively oriented non-statistical scientists...Very nicely, the book reads somewhat as a story, going from simpler things to the more complicated, ultimately leading to fascinating and far-reaching things like design considerations with respect to extrinsic parameter redundancy, as well as practical implications for what the author calls integrated population models."
- Marek Brabec, ISCB News, December 2020