Exponential Families in Theory and Practice

Erscheinungsjahr 2022
ISBN: 978-1-108-48890-7
Verlag: Cambridge University Press

Buch, Englisch, 200 Seiten, Format (B × H): 154 mm x 233 mm, Gewicht: 516 g

Reihe: Institute of Mathematical Statistics Textbooks

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.

Autoren/Hrsg.

Efron, Bradley

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Forschungsmethodik, Wissenschaftliche Ausstattung
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen

Inhaltsverzeichnis

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.

Über Autor(innen)

Efron, Bradley
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.