Statistical Modelling by Exponential Families

A readable, digestible introduction to essential theory and wealth of applications, with a vast set of examples and numerous exercises.

Rolf Sundberg (Author)

9781108701112, Cambridge University Press

Paperback / softback, published 29 August 2019

296 pages, 22 b/w illus. 100 exercises
22.8 x 15.2 x 1.7 cm, 0.43 kg

'This book is perfect for an introductory theoretical graduate course but its parts could also definitely be used in a more applied course. The only prerequisite is basic mathematical statistics. The book is also very handy as a general reference on exponential families. To keep the content simple, the author sometimes avoids the most technical details; however, all necessary references are provided for the reader's convenience. In this sense the book can be used by any researcher interested in exponential families from either a more theoretical or more applied point of view.' Piotr Zwiernik, MathSciNet

This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exercises embedded within the text as well as at the ends of chapters.

1. What is an exponential family?
2. Examples of exponential families
3. Regularity conditions and basic properties
4. Asymptotic properties of the MLE
5. Testing model-reducing hypotheses
6. Boltzmann's law in statistics
7. Curved exponential families
8. Extension to incomplete data
9. Generalized linear models
10. Graphical models for conditional independence structures
11. Exponential family models for social networks
12. Rasch models for item response and related models
13. Models for processes in space or time
14. More modelling exercises
Appendix A. Statistical concepts and principles
Appendix B. Useful mathematics.

Subject Areas: Probability & statistics [PBT], Epidemiology & medical statistics [MBNS], Economic statistics [KCHS]