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Statistical Modelling by Exponential Families

Statistical Modelling by Exponential Families

Wydawnictwo Cambridge University Press
Data wydania 01/08/2019
Wydanie Pierwsze
Liczba stron 296
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla szkół wyższych i kształcenia podyplomowego
Język angielski
ISBN 9781108701112
Kategorie Prawdopodobieństwo i statystyka
157.15 PLN (z VAT)
$42.05 / €35.10 / £31.49 /
Produkt na zamówienie
Dostawa 3-4 tygodnie
Do schowka

Opis książki

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. '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 hoegskola, Sweden 'This is an excellent book on exponential families. It covers not only the basic properties of exponential families but also several modern topics such as graphical models and random networks. The author blends theories and applications elegantly and provides several useful examples from various scientific domains. It is suitable for a one-semester graduate-level course and will be an excellent reference for topic courses such as stochastic modeling and parametric models.' Yen-Chi Chen, Journal of the American Statistical Association

Statistical Modelling by Exponential Families

Spis treści

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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