Statistical modelling by exponential families
著者
書誌事項
Statistical modelling by exponential families
（Institute of Mathematical Statistics textbooks, 12）
Cambridge University Press, 2019
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注記
Includes bibliographical references (p. 271-277) and index
内容説明・目次
内容説明
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-Loef 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.
目次
- 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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