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Statistical Modelling by Exponential Families
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'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 hgskola, Sweden
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Rolf Sundberg is Professor Emeritus of Statistical Science at Stockholms Universitet. His work embraces both theoretical and applied statistics, including principles of statistics, exponential families, regression, chemometrics, stereology, survey sampling inference, molecular biology, and paleoclimatology. In 2003, with M. Linder, he won the award for best theoretical paper in the Journal of Chemometrics for their work on multivariate calibration, and in 2017 he was named Statistician of the Year by the Swedish Statistical Society.
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.