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.Read more
- Expands and extends the theory and application of exponential families within one concise volume
- Uses recurrent themes in examples and exercises to build familiarity with the models
- Gives a concise account of the philosophy of Per Martin-Löf, connecting statistical modelling with ideas in statistical physics
Reviews & endorsements
'Rolf Sundberg's book gives attractive properties of the exponential family and illustrates them for a wide variety of applications. Definitions are concise and most propositions look directly appealing. The writing reflects the author's experience in deriving results that are essential for good modelling and convincing inference. Thus, this book is indispensable for all data scientists, be they graduate students or experienced researchers.' Nanny Wermuth, Chalmers tekniska högskola, Sweden
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- Publication planned for: October 2019
- format: Paperback
- isbn: 9781108701112
- length: 296 pages
- dimensions: 228 x 152 x 17 mm
- weight: 0.43kg
- contains: 22 b/w illus. 100 exercises
- availability: Available
Table of Contents
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.
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