Exponential Families in Theory and Practice

This accessible course on a central player in modern statistical practice connects models with methodology, without need for advanced math.

Bradley Efron (Author)

9781108715669, Cambridge University Press

Paperback / softback, published 15 December 2022

262 pages
22.9 x 15.2 x 1.5 cm, 0.39 kg

'In this book, Brad Efron illuminates the exponential family as a practical, extendible, and crucial ingredient in all manners of data analysis, be they Bayesian, frequentist, or machine learning. He shows us how to shape, understand, and employ these distributions in both algorithms and analysis. The book is crisp, insightful, and indispensable.' David Blei, Columbia University

During the past half-century, exponential families have attained a position at the center of parametric statistical inference. Theoretical advances have been matched, and more than matched, in the world of applications, where logistic regression by itself has become the go-to methodology in medical statistics, computer-based prediction algorithms, and the social sciences. This book is based on a one-semester graduate course for first year Ph.D. and advanced master's students. After presenting the basic structure of univariate and multivariate exponential families, their application to generalized linear models including logistic and Poisson regression is described in detail, emphasizing geometrical ideas, computational practice, and the analogy with ordinary linear regression. Connections are made with a variety of current statistical methodologies: missing data, survival analysis and proportional hazards, false discovery rates, bootstrapping, and empirical Bayes analysis. The book connects exponential family theory with its applications in a way that doesn't require advanced mathematical preparation.

1. One-parameter exponential families
2. Multiparameter exponential families
3. Generalized linear models
4. Curved exponential families, eb, missing data, and the em algorithm
5. Bootstrap confidence intervals
Bibliography
Index.

Subject Areas: Machine learning [UYQM], Probability & statistics [PBT], Research methods: general [GPS]