This book is a readable, digestible introduction to exponential families, encompassing
statistical models based on the most useful distributions in statistical theory, such as
the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by
applications, it presents the essential theory and then demonstrates the theory’s
practical potential by connecting it with developments in areas such as item response
analysis, social network models, conditional independence and latent variable
structures, and point process models. Extensions to incomplete data models and
generalized linear models are also included. In addition, the author gives a concise
account of the philosophy of Per Martin-Lo¨f in order to connect statistical modelling
with ideas in statistical physics, such as Boltzmann’s law. Written for graduate
students and researchers with a background in basic statistical inference, the book
includes a vast set of examples demonstrating models for applications and numerous
exercises embedded within the text as well as at the ends of chapters.
Author(s): Rolf Sundberg
Series: Institute of Mathematical Statistics Textbooks (12)
Publisher: Cambridge University Press
Year: 2019
Language: English
Pages: 297
Cover......Page 1
Front Matter
......Page 2
Statistical Modelling by
Exponential Families......Page 4
Copyright
......Page 5
Dedication
......Page 6
Contents
......Page 7
Examples......Page 10
Preface......Page 13
1 What Is an Exponential Family?......Page 16
2 Examples of Exponential Families......Page 21
3 Regularity Conditions and Basic Properties......Page 39
4 Asymptotic Properties of the MLE......Page 79
5 Testing Model-Reducing Hypotheses......Page 90
6 Boltzmann’s Law in Statistics......Page 115
7 Curved Exponential Families......Page 133
8 Extension to Incomplete Data......Page 158
9 Generalized Linear Models......Page 179
10 Graphical Models for Conditional
Independence Structures......Page 206
11 Exponential Family Models for Graphs of
Social Networks......Page 225
12 Rasch Models for Item Response
and Related Model Types......Page 243
13 Models for Processes in Space or Time......Page 261
14 More Modelling Exercises......Page 273
Appendix A:
Statistical Concepts and Principles......Page 280
Appendix B:
Useful Mathematics......Page 283
Bibliography......Page 286
Index......Page 293
