Statistical Modelling by Exponential Families
Statistical Modelling by Exponential Families, authored by Rolf Sundberg and published by Cambridge University Press on August 29, 2019, offers a comprehensive introduction to exponential families in statistics. This 296-page book is presented in English and is designed for graduate students and researchers with a foundational understanding of statistical inference. It covers essential statistical models based on key distributions such as normal, gamma, binomial, Poisson, and negative binomial, while emphasizing practical applications across various fields.
Readers will find that the book not only presents the fundamental theory but also illustrates its practical implications through connections to areas like item response analysis, social network models, and generalized linear models. The text includes numerous examples and exercises to reinforce learning, as well as a concise discussion of Per Martin-Löf’s philosophy, linking statistical modeling to concepts in statistical physics. This edition serves as a valuable resource for those interested in the intersection of mathematics, probability, and statistics, particularly in medical, epidemiological, and economic contexts.
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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.
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