The Seven Pillars Of Statistical Wisdom

What gives statistics its unity as a science? Stephen Stigler sets forth the seven foundational ideas of statistics—a scientific discipline related to but distinct from mathematics and computer science. Even the most basic idea—aggregation, exemplified by averaging—is counterintuitive. It allows one to gain information by discarding information, namely, the individuality of the observations. Stigler’s second pillar, information measurement, challenges the importance of “big data” by noting that observations are not all equally important: the amount of information in a data set is often proportional to only the square root of the number of observations, not the absolute number. The third idea is likelihood, the calibration of inferences with the use of probability. Intercomparison is the principle that statistical comparisons do not need to be made with respect to an external standard. The fifth pillar is regression, both a paradox (tall parents on average produce shorter children; tall children on average have shorter parents) and the basis of inference, including Bayesian inference and causal reasoning. The sixth concept captures the importance of experimental design—for example, by recognizing the gains to be had from a combinatorial approach with rigorous randomization. The seventh idea is the residual: the notion that a complicated phenomenon can be simplified by subtracting the effect of known causes, leaving a residual phenomenon that can be explained more easily. The Seven Pillars of Statistical Wisdom presents an original, unified account of statistical science that will fascinate the interested layperson and engage the professional statistician.

This lively collection of essays examines statistical ideas with an ironic eye for their essence and what their history can tell us for current disputes. The topics range from 17th-century medicine and the circulation of blood, to the cause of the Great Depression, to the determinations of the shape of the Earth and the speed of light.

Stigler shows how statistics arose from the interplay of mathematical concepts and the needs of several applied sciences. His emphasis is upon how methods of probability theory were developed for measuring uncertainty, for reducing uncertainty, and as a conceptual framework for quantitative studies in the social sciences.

What gives statistics its unity as a science? Stephen Stigler sets forth the seven foundational ideas of statistics—a scientific discipline related to but distinct from mathematics and computer science. Even the most basic idea—aggregation, exemplified by averaging—is counterintuitive. It allows one to gain information by discarding information, namely, the individuality of the observations. Stigler’s second pillar, information measurement, challenges the importance of “big data” by noting that observations are not all equally important: the amount of information in a data set is often proportional to only the square root of the number of observations, not the absolute number. The third idea is likelihood, the calibration of inferences with the use of probability. Intercomparison is the principle that statistical comparisons do not need to be made with respect to an external standard. The fifth pillar is regression, both a paradox (tall parents on average produce shorter children; tall children on average have shorter parents) and the basis of inference, including Bayesian inference and causal reasoning. The sixth concept captures the importance of experimental design—for example, by recognizing the gains to be had from a combinatorial approach with rigorous randomization. The seventh idea is the residual: the notion that a complicated phenomenon can be simplified by subtracting the effect of known causes, leaving a residual phenomenon that can be explained more easily. The Seven Pillars of Statistical Wisdom presents an original, unified account of statistical science that will fascinate the interested layperson and engage the professional statistician.

"[Acheson] introduces the fundamental ideas of calculus through the story of how the subject developed, from approximating π to imaginary numbers, and from Newton's falling apple to the vibrations of an electric guitar."--Back cover

Drug development is the process of finding and producingtherapeutically useful pharmaceuticals, turning them into safe andeffective medicine, and producing reliable information regardingthe appropriate dosage and dosing intervals. With regulatoryauthorities demanding increasingly higher standards in suchdevelopments, statistics has become an intrinsic and criticalelement in the design and conduct of drug development programmes. Statistical Issues in Drug Development presents anessential and thought provoking guide to the statistical issues andcontroversies involved in drug development. This highly readable second edition has been updated toinclude: Comprehensive coverage of the design and interpretation ofclinical trials. Expanded sections on missing data, equivalence, meta-analysisand dose finding. An examination of both Bayesian and frequentist methods. A new chapter on pharmacogenomics and expanded coverage ofpharmaco-epidemiology and pharmaco-economics. Coverage of the ICH guidelines, in particular ICH E9,Statistical Principles for Clinical Trials. It is hoped that the book will stimulate dialogue betweenstatisticians and life scientists working within the pharmaceuticalindustry. The accessible and wide-ranging coverage make itessential reading for both statisticians and non-statisticiansworking in the pharmaceutical industry, regulatory bodies andmedical research institutes. There is also much to benefitundergraduate and postgraduate students whose courses include amedical statistics component.

A daily glass of wine prolongs life—yet alcohol can cause life-threatening cancer. Some say raising the minimum wage will decrease inequality while others say it increases unemployment. Scientists once confidently claimed that hormone replacement therapy reduced the risk of heart disease but now they equally confidently claim it raises that risk. What should we make of this endless barrage of conflicting claims? Observation and Experiment is an introduction to causal inference by one of the field’s leading scholars. An award-winning professor at Wharton, Paul Rosenbaum explains key concepts and methods through lively examples that make abstract principles accessible. He draws his examples from clinical medicine, economics, public health, epidemiology, clinical psychology, and psychiatry to explain how randomized control trials are conceived and designed, how they differ from observational studies, and what techniques are available to mitigate their bias. “Carefully and precisely written...reflecting superb statistical understanding, all communicated with the skill of a master teacher.” —Stephen M. Stigler, author of The Seven Pillars of Statistical Wisdom “An excellent introduction...Well-written and thoughtful...from one of causal inference’s noted experts.” —Journal of the American Statistical Association “Rosenbaum is a gifted expositor...an outstanding introduction to the topic for anyone who is interested in understanding the basic ideas and approaches to causal inference.” —Psychometrika “A very valuable contribution...Highly recommended.” —International Statistical Review

The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and in influence. 'Big data', 'data science', and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? This book takes us on an exhilarating journey through the revolution in data analysis following the introduction of electronic computation in the 1950s. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. The book ends with speculation on the future direction of statistics and data science.

In the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact.

The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and influence. 'Data science' and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? How does it all fit together? Now in paperback and fortified with exercises, this book delivers a concentrated course in modern statistical thinking. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov Chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. Each chapter ends with class-tested exercises, and the book concludes with speculation on the future direction of statistics and data science.