Exponential Families in Theory and Practice

Exponential families have gained prominence in parametric statistical inference, with logistic regression being a widely used methodology in medical statistics, computer-based prediction algorithms, and the social sciences. This book provides a comprehensive introduction to univariate and multivariate exponential families, generalized linear models, and their applications, emphasizing geometrical ideas, computational practice, and connections with other statistical methodologies. It is suitable for first-year Ph.D. and advanced master's students with no advanced mathematical preparation.

Format: Hardback
Length: 200 pages
Publication date: 15 December 2022
Publisher: Cambridge University Press

Over the past fifty years, exponential families have emerged as a pivotal framework in parametric statistical inference, garnering significant theoretical advancements and remarkable practical applications. These families have found widespread use in medical statistics, computer-based prediction algorithms, and the social sciences, with logistic regression alone becoming a dominant methodology. This comprehensive book is designed for first-year Ph.D. and advanced master's students, covering a one-semester course. It begins by introducing the fundamental structure of univariate and multivariate exponential families, extending their application to generalized linear models such as logistic and Poisson regression. Geometric concepts, computational techniques, and comparisons with ordinary linear regression are emphasized throughout. The book also establishes connections with various contemporary statistical methodologies, including missing data analysis, survival analysis, proportional hazards, false discovery rates, bootstrapping, and empirical Bayes analysis. By seamlessly bridging exponential family theory and its practical applications, this book aims to provide a comprehensive and accessible introduction to the field for students with a background in statistics.

Weight: 524g
Dimension: 237 x 158 x 21 (mm)
ISBN-13: 9781108488907