Rolf Sundberg

Statistical Modelling by Exponential Families (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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-Lof 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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 29. August 2019
• Englisch
• ISBN-13: 9781108759915
• Artikelnr.: 62745763

Autorenporträt

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.

Inhaltsangabe

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.