Exponential Families in Theory and Practice (Institute of Mathematical Statistics Textbooks)

Efron, Bradley

ISBN 10: 1108715664 / ISBN 13: 9781108715669

Published by Cambridge University Press, 2023

About this Item

Seller Inventory # I-9781108715669

Bibliographic Details

• Title: Exponential Families in Theory and Practice (Institute of Mathematical Statistics Textbooks)
• Publisher: Cambridge University Press
• Publication Date: 2023
• Language: English
• ISBN 10: 1108715664
• ISBN 13: 9781108715669
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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.

About the Author

Bradley Efron is Professor Emeritus of Statistics and Biomedical Data Science at Stanford University. He is the inventor of the bootstrap method for assessing statistical accuracy. He has published extensively on statistical theory and its applications, with particular attention to exponential families. A MacArthur fellow, he is a member of the National Academy of Sciences. He received the National Medal of Science in 2007.