The Seven Pillars of Statistical Wisdom

The Seven Pillars of Statistical Wisdom PDF Author: Stephen M. Stigler
Publisher: Harvard University Press
ISBN: 9780674088917
Category : Social Science
Languages : en
Pages : 0

Book Description
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.

Statistics on the Table

Statistics on the Table PDF Author: Stephen M. Stigler
Publisher: Harvard University Press
ISBN: 9780674009790
Category : History
Languages : en
Pages : 514

Book Description
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.

The History of Statistics

The History of Statistics PDF Author: Stephen M. Stigler
Publisher: Harvard University Press
ISBN: 0674256859
Category : History
Languages : en
Pages : 436

Book Description
This magnificent book is the first comprehensive history of statistics from its beginnings around 1700 to its emergence as a distinct and mature discipline around 1900. Stephen M. Stigler shows how statistics arose from the interplay of mathematical concepts and the needs of several applied sciences including astronomy, geodesy, experimental psychology, genetics, and sociology. He addresses many intriguing questions: How did scientists learn to combine measurements made under different conditions? And how were they led to use probability theory to measure the accuracy of the result? Why were statistical methods used successfully in astronomy long before they began to play a significant role in the social sciences? How could the introduction of least squares predate the discovery of regression by more than eighty years? On what grounds can the major works of men such as Bernoulli, De Moivre, Bayes, Quetelet, and Lexis be considered partial failures, while those of Laplace, Galton, Edgeworth, Pearson, and Yule are counted as successes? How did Galton’s probability machine (the quincunx) provide him with the key to the major advance of the last half of the nineteenth century? Stigler’s emphasis is upon how, when, and where the methods of probability theory were developed for measuring uncertainty in experimental and observational science, for reducing uncertainty, and as a conceptual framework for quantitative studies in the social sciences. He describes with care the scientific context in which the different methods evolved and identifies the problems (conceptual or mathematical) that retarded the growth of mathematical statistics and the conceptual developments that permitted major breakthroughs. Statisticians, historians of science, and social and behavioral scientists will gain from this book a deeper understanding of the use of statistical methods and a better grasp of the promise and limitations of such techniques. The product of ten years of research, The History of Statistics will appeal to all who are interested in the humanistic study of science.

The Seven Pillars of Statistical Wisdom

The Seven Pillars of Statistical Wisdom PDF Author: Stephen M. Stigler
Publisher: Harvard University Press
ISBN: 0674970217
Category : Social Science
Languages : en
Pages : 214

Book Description
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.

Statistical Issues in Drug Development

Statistical Issues in Drug Development PDF Author: Stephen S. Senn
Publisher: John Wiley & Sons
ISBN: 9780470723579
Category : Medical
Languages : en
Pages : 523

Book Description
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.

The Calculus Story

The Calculus Story PDF Author: David Acheson
Publisher: Oxford University Press
ISBN: 0198804547
Category : Mathematics
Languages : en
Pages : 209

Book Description
"[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

Ten Great Ideas about Chance

Ten Great Ideas about Chance PDF Author: Persi Diaconis
Publisher: Princeton University Press
ISBN: 0691196397
Category : Mathematics
Languages : en
Pages : 270

Book Description
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.

Computer Age Statistical Inference

Computer Age Statistical Inference PDF Author: Bradley Efron
Publisher: Cambridge University Press
ISBN: 1108107958
Category : Mathematics
Languages : en
Pages : 496

Book Description
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.

Computer Age Statistical Inference, Student Edition

Computer Age Statistical Inference, Student Edition PDF Author: Bradley Efron
Publisher: Cambridge University Press
ISBN: 1108915876
Category : Mathematics
Languages : en
Pages : 514

Book Description
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.

Foundations of Statistics for Data Scientists

Foundations of Statistics for Data Scientists PDF Author: Alan Agresti
Publisher: CRC Press
ISBN: 1000462919
Category : Business & Economics
Languages : en
Pages : 486

Book Description
Foundations of Statistics for Data Scientists: With R and Python is designed as a textbook for a one- or two-term introduction to mathematical statistics for students training to become data scientists. It is an in-depth presentation of the topics in statistical science with which any data scientist should be familiar, including probability distributions, descriptive and inferential statistical methods, and linear modeling. The book assumes knowledge of basic calculus, so the presentation can focus on "why it works" as well as "how to do it." Compared to traditional "mathematical statistics" textbooks, however, the book has less emphasis on probability theory and more emphasis on using software to implement statistical methods and to conduct simulations to illustrate key concepts. All statistical analyses in the book use R software, with an appendix showing the same analyses with Python. The book also introduces modern topics that do not normally appear in mathematical statistics texts but are highly relevant for data scientists, such as Bayesian inference, generalized linear models for non-normal responses (e.g., logistic regression and Poisson loglinear models), and regularized model fitting. The nearly 500 exercises are grouped into "Data Analysis and Applications" and "Methods and Concepts." Appendices introduce R and Python and contain solutions for odd-numbered exercises. The book's website has expanded R, Python, and Matlab appendices and all data sets from the examples and exercises.
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