- Publisher: Cambridge University Press
- Online publication date: November 2022
- Print publication year: 2022
- Online ISBN: 9781108773157
- DOI: https://doi.org/10.1017/9781108773157
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.
Larry Wasserman - Carnegie Mellon University
Trevor Hastie - Stanford University
Stephen Stigler - University of Chicago
Nancy Reid - University of Toronto
David Blei - Columbia University
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