A Mathematical Primer for Social Statistics

✍ Scribed by John Fox

• Publisher: SAGE Publications, Incorporated
• Year: 2020
• Tongue: English
• Leaves: 257
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

COVER
TITTLE PAGE
COPYRIGHT PAGE
CONTENTS
SERIES EDITOR’S INTRODUCTION
ACKNOWLEDGMENTS
PREFACE
ABOUT THE AUTHOR
CHAPTER 1 - MATRICES, LINEAR ALGEBRA, AND VECTOR GEOMETRY: THE BASICS
CHAPTER 2 - MATRIX DECOMPOSITIONS AND QUADRATIC FORMS
CHAPTER 3 - AN INTRODUCTION TO CALCULUS
CHAPTER 4 - ELEMENTARY PROBABILITY THEORY
CHAPTER 5 - COMMON PROBABILITY DISTRIBUTIONS
CHAPTER 6 - AN INTRODUCTION TO STATISTICAL THEORY
CHAPTER 7 - PUTTING THE MATH TO WORK: LINEAR LEAST-SQUARES REGRESSION
REFERENCES
INDEX