Statistics

This book provides an introduction to the mathematical and algorithmic foundations of data science, including machine learning, high-dimensional geometry, and analysis of large networks. Topics include the counterintuitive nature of data in high dimensions, important linear algebraic techniques such as singular value decomposition, the theory of random walks and Markov chains, the fundamentals of and important algorithms for machine learning, algorithms and analysis for clustering, probabilistic models for large networks, representation learning including topic modelling and non-negative matrix factorization, wavelets and compressed sensing. Important probabilistic techniques are developed including the law of large numbers, tail inequalities, analysis of random projections, generalization guarantees in machine learning, and moment methods for analysis of phase transitions in large random graphs. Additionally, important structural and complexity measures are discussed such as matrix norms and VC-dimension. This book is suitable for both undergraduate and graduate courses in the design and analysis of algorithms for data.

Reflecting a sea change in how empirical research has been conducted over the past three decades, Foundations of Agnostic Statistics presents an innovative treatment of modern statistical theory for the social and health sciences. This book develops the fundamentals of what the authors call agnostic statistics, which considers what can be learned about the world without assuming that there exists a simple generative model that can be known to be true. Aronow and Miller provide the foundations for statistical inference for researchers unwilling to make assumptions beyond what they or their audience would find credible. Building from first principles, the book covers topics including estimation theory, regression, maximum likelihood, missing data, and causal inference. Using these principles, readers will be able to formally articulate their targets of inquiry, distinguish substantive assumptions from statistical assumptions, and ultimately engage in cutting-edge quantitative empirical research that contributes to human knowledge.

The vast majority of statistics books delineate techniques used to analyze collected data. The Joy of Statistics is not one of these books. It consists of a series of 42 "short stories", each illustrating how statistical methods applied to data produce insight and solutions to the questionsthe data were collected to answer. Real-life and sometimes artificial data are used to demonstrate the often painless method and magic of statistics. In addition, the text contains brief histories of the evolution of statistical methods and a number of brief biographies of the most famousstatisticians of the 20th century. Sprinkled throughout are statistical jokes, puzzles and traditional stories. The levels of statistical texts span a spectrum, from elementary to introductory to application to theoretical to advanced mathematical.This book explores a variety of statistical applications using graphs and plots, along with detailed and intuitive descriptions, and occasionally a bit of 10th grade mathematics. Examples of a few of the topics included among these "short stories" are pet ownership, gambling games such as roulette,blackjack and lotteries, as well as more serious subjects such as comparison of black/white infant mortality risk, infant birth weight and maternal age, estimation of coronary heart disease risk and racial differences in Hodgkin disease. The statistical descriptions of these topics are in many casesaccompanied by easy to understand explanations labelled "How it Works."

This book is a stimulating panoramic tour - quite different from a textbook journey - of the world of statistics in both its theory and practice, for teachers, students and practitioners. At each stop on the tour, the authors investigate unusual and quirky aspects of statistics, highlighting historical, biographical and philosophical dimensions of this field of knowledge. Each chapter opens with perspectives on its theme, often from several points of view. Five original and thought-provoking questions follow. These aim at widening readers' knowledge and deepening their insight. Scattered among the questions are entertaining puzzles to solve and tantalising paradoxes to explain. Readers can compare their own statistical discoveries with the authors' detailed answers to all the questions. The writing is lively and inviting, the ideas are rewarding, and the material is extensively cross-referenced. A Panorama of Statistics: Leads readers to discover the fascinations of statistics. Is an enjoyable companion to an undergraduate statistics textbook. Is an enriching source of knowledge for statistics teachers and practitioners. Is unique among statistics books today for its memorable content and engaging style. Lending itself equally to reading through and to dipping into, A Panorama of Statistics will surprise teachers, students and practitioners by the variety of ways in which statistics can capture and hold their interest. Reviews: "As befits the authors' statement that 'this is not a textbook', the structure is unusual. There are twenty-five chapters organised in five sections, each beginning with a brief perspective of a theme in statistics and finishing with five questions related to that theme. The answers provided to the questions, in section six, are as discursive and illuminating as the main body of the text. Even if you are pretty sure you know the answer, it is always worth checking what the authors have to say. Chances are that you will learn something every time. The glimpses and insights given into this enormous and far-reaching discipline succeed in being bewitching, entertaining and inviting; coverage was never the aim."   "In summary, this splendid book lives up to the four 'p-values' of its title. It is panoramic in the scope of its survey of statistics, it is full of illuminating perspectives, it sets entertaining and challenging puzzles, and it explores fascinating paradoxes. Read it, enjoy it and learn from it." From Neil Sheldon, Teaching Statistics, volume 9, no. 2, May 2017

* This comprehensive text covers all the traditional topics in a first-semester course. * Divided into 67 short sections, this book makes the topics easy to digest. Students regularly get positive reinforcement as they check their mastery with exercises at the end of each section. * Each exercise is based on a humorous riddle. If the answer to a riddle makes sense, students know all their answers for that exercise are correct. If not, they know they need to check their answers. * Short sections make it easy to customize your course by assigning only those sections needed to fulfill your objectives. * A comprehensive basic math review at the end of this book may be used to help students whose math skills are rusty. * Thoroughly field-tested for student interest and comprehension. The short sections and humor-based, self-checking riddles are greatly appreciated by students. * Contains Part D on effect size, which provides technical solutions to issues raised in Part C (such as the limitations of inferential statistics). New to this edition: Section 1: Explains the importance of statistical techniques in the advancement of scientific knowledge. Section 11: Provides practice with the summation operation before using it in multiple statistical tests. Section 27: This section on z-scores explains how to translate a percentile rank into a raw score. Section 30: Underlines the importance of figural representations of data, explains how to identify the most appropriate figure, and discusses how to label figures effectively. Section 41: Provides a deeper understanding of the relationship between p-values and critical values in a statistical test. Appendix J: A summary table of all statistical equations and guidelines for choosing a particular statistical test. Table 1: The format and discussion for the Table of the Normal Curve has been changed to a more conventional presentation of this statistical tool.