A Mathematical Primer for Social Statistics, Second Edition presents mathematics central to learning and understanding statistical methods beyond the introductory level: the basic ‘language’ of matrices and linear algebra and its visual representation, vector geometry; differential and integral calculus; probability theory; common probability distributions; statistical estimation and inference, including likelihood-based and Bayesian methods. The volume concludes by applying mathematical concepts and operations to a familiar case, linear least-squares regression. The Second Edition pays more attention to visualization, including the elliptical geometry of quadratic forms and its application to statistics. It also covers some new topics, such as an introduction to Markov-Chain Monte Carlo methods, which are important in modern Bayesian statistics. A companion website includes materials that enable readers to use the R statistical computing environment to reproduce and explore computations and visualizations presented in the text. The book is an excellent companion to a ‘math camp’ or a course designed to provide foundational mathematics needed to understand relatively advanced statistical methods.
สารบัญ
About the Author
Series Editor Introduction
Acknowledgments
Preface
Matrices, Linear Algebra, and Vector Geometry: The Basics
Matrix Decompositions and Quadratic Forms
An Introduction to Calculus
Elementary Probability Theory
Common Probability Distributions
An Introduction to Statistical Theory
Putting the Math to Work: Linear Least-Squares Regression
References
Index
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John Fox received a BA from the City College of New York and a Ph D from the University of Michigan, both in Sociology. He is Professor Emeritus of Sociology at Mc Master University in Hamilton, Ontario, Canada, where he was previously the Senator William Mc Master Professor of Social Statistics. Prior to coming to Mc Master, he was Professor of Sociology, Professor of Mathematics and Statistics, and Coordinator of the Statistical Consulting Service at York University in Toronto. Professor Fox is the author of many articles and books on applied statistics, including /emph{Applied Regression Analysis and Generalized Linear Models, Third Edition} (Sage, 2016). He is an elected member of the R Foundation, an associate editor of the Journal of Statistical Software, a prior editor of R News and its successor the R Journal, and a prior editor of the Sage Quantitative Applications in the Social Sciences monograph series.
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