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Author: Aubrey Clayton
Publisher: Columbia University Press
ISBN: 0231553358
Category : Mathematics
Languages : en
Pages : 641
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Book Description
There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations. Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics. Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach—that is, to incorporate prior knowledge when reasoning with incomplete information—in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli’s Fallacy explains why something has gone wrong with how we use data—and how to fix it.
Author: Aubrey Clayton
Publisher: Columbia University Press
ISBN: 0231553358
Category : Mathematics
Languages : en
Pages : 641
Get Book
Book Description
There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations. Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics. Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach—that is, to incorporate prior knowledge when reasoning with incomplete information—in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli’s Fallacy explains why something has gone wrong with how we use data—and how to fix it.
Author:
Publisher:
ISBN: 9780231199957
Category :
Languages : en
Pages :
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Book Description
Author: Aubrey Clayton
Publisher:
ISBN: 9780231199940
Category : Mathematics
Languages : en
Pages : 368
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Book Description
Aubrey Clayton traces the history of the flaw that underlies modern statistics, beginning with the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Ranging across math, philosophy, and culture, Bernoulli's Fallacy explains why something has gone wrong with how we use data--and how to fix it.
Author: Jacob Bernoulli
Publisher: JHU Press
ISBN: 9780801882357
Category : Mathematics
Languages : en
Pages : 468
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Book Description
"Part I reprints and reworks Huygens's On Reckoning in Games of Chance. Part II offers a thorough treatment of the mathematics of combinations and permutations, including the numbers since known as "Bernoulli numbers." In Part III, Bernoulli solves more complicated problems of games of chance using that mathematics. In the final part, Bernoulli's crowning achievement in mathematical probability becomes manifest he applies the mathematics of games of chance to the problems of epistemic probability in civil, moral, and economic matters, proving what we now know as the weak law of large numbers."
Author: John Allen Paulos
Publisher: Basic Books
ISBN: 0465050670
Category : Mathematics
Languages : en
Pages : 240
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Book Description
John Allen Paulos is a master at shedding mathematical lights on our everyday world:What exactly did Lani Guinier say about quotas?What is the probability of identifying a murderer through DNA testing?Which are the real risks to our health and which the phony ones?Employing the same fun-filled, user-friendly, and quirkily insightful approach that put Innumeracy on best-seller lists, Paulos now leads us through the pages of the daily newspaper, revealing the hidden mathematical angles of countless articles. From the Senate, the SATs, and sex to crime, celebrities, and cults, Paulos takes stories that may not seem to involve mathematics at all and demonstrates how mathematical naïtéan put readers at a distinct disadvantage.Whether he's using chaos theory to puncture economic and environmental predictions, applying logic and self-reference to clarify the hazards of spin doctoring and news compression, or employing arithmetic and common sense to give us a novel perspective on greed and relationships, Paulos never fails to entertain and enlighten.Even if you hated math in school, you'll love the numerical vignettes in this book.
Author: Harold Jeffreys
Publisher: OUP Oxford
ISBN: 0191589675
Category : Science
Languages : en
Pages : 474
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Book Description
Another title in the reissued Oxford Classic Texts in the Physical Sciences series, Jeffrey's Theory of Probability, first published in 1939, was the first to develop a fundamental theory of scientific inference based on the ideas of Bayesian statistics. His ideas were way ahead of their time and it is only in the past ten years that the subject of Bayes' factors has been significantly developed and extended. Until recently the two schools of statistics (Bayesian and Frequentist) were distinctly different and set apart. Recent work (aided by increased computer power and availability) has changed all that and today's graduate students and researchers all require an understanding of Bayesian ideas. This book is their starting point.
Author: David Sumpter
Publisher: Flatiron Books
ISBN: 1250246970
Category : Business & Economics
Languages : en
Pages : 336
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Book Description
Is there a secret formula for getting rich? For going viral? For deciding how long to stick with your current job, Netflix series, or even relationship? This book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthfully, and see through scaremongering. They are known by only the privileged few - until now. With wit and clarity, mathematician David Sumpter shows that it isn't the technical details that make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle - a way of seeing the world that anyone can learn. Empowering and illuminating, The Ten Equations shows how math really can change your life.
Author: Paul Meehl
Publisher: Echo Point Books & Media
ISBN: 9781626542303
Category : Medical
Languages : en
Pages : 164
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Book Description
"Clinical versus Statistical Prediction" is Paul Meehl's famous examination of benefits and disutilities related to the different ways of combining information to make predictions. It is a clarifying analysis as relevant today as when it first appeared. A major methodological problem for clinical psychology concerns the relation between clinical and actuarial methods of arriving at diagnoses and predicting behavior. Without prejudging the question as to whether these methods are fundamentally different, we can at least set forth the obvious distinctions between them in practical applications. The problem is to predict how a person is going to behave: What is the most accurate way to go about this task? "Clinical versus Statistical Prediction" offers a penetrating and thorough look at the pros and cons of human judgment versus actuarial integration of information as applied to the prediction problem. Widely considered the leading text on the subject, Paul Meehl's landmark analysis is reprinted here in its entirety, including his updated preface written forty-two years after the first publication of the book. This classic work is a must-have for students and practitioners interested in better understanding human behavior, for anyone wanting to make the most accurate decisions from all sorts of data, and for those interested in the ethics and intricacies of prediction. As Meehl puts it, " "When one is dealing with human lives and life opportunities, it is immoral to adopt a mode of decision-making which has been demonstrated repeatedly to be either inferior in success rate or, when equal, costlier to the client or the taxpayer.""
Author: Will Kurt
Publisher: No Starch Press
ISBN: 1593279566
Category : Mathematics
Languages : en
Pages : 258
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Book Description
Fun guide to learning Bayesian statistics and probability through unusual and illustrative examples. Probability and statistics are increasingly important in a huge range of professions. But many people use data in ways they don't even understand, meaning they aren't getting the most from it. Bayesian Statistics the Fun Way will change that. This book will give you a complete understanding of Bayesian statistics through simple explanations and un-boring examples. Find out the probability of UFOs landing in your garden, how likely Han Solo is to survive a flight through an asteroid shower, how to win an argument about conspiracy theories, and whether a burglary really was a burglary, to name a few examples. By using these off-the-beaten-track examples, the author actually makes learning statistics fun. And you'll learn real skills, like how to: - How to measure your own level of uncertainty in a conclusion or belief - Calculate Bayes theorem and understand what it's useful for - Find the posterior, likelihood, and prior to check the accuracy of your conclusions - Calculate distributions to see the range of your data - Compare hypotheses and draw reliable conclusions from them Next time you find yourself with a sheaf of survey results and no idea what to do with them, turn to Bayesian Statistics the Fun Way to get the most value from your data.
Author: Nikolai Dokuchaev
Publisher: World Scientific Publishing Company
ISBN: 9814678058
Category : Business & Economics
Languages : en
Pages : 224
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Book Description
This book provides a systematic, self-sufficient and yet short presentation of the mainstream topics on introductory Probability Theory with some selected topics from Mathematical Statistics. It is suitable for a 10- to 14-week course for second- or third-year undergraduate students in Science, Mathematics, Statistics, Finance, or Economics, who have completed some introductory course in Calculus. There is a sufficient number of problems and solutions to cover weekly tutorials.
