Modern Science

Modern Science - MODERN SCIENCE AND THE...

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MODERN SCIENCE AND THE BAYESIAN-FREQUENTIST CONTROVERSY Bradley Efron Abstract The 250-year debate between Bayesians and frequentists is unusual among philo- sophical arguments in actually having important practical consequences. Whenever noisy data is a major concern, scientists depend on statistical inference to pursue na- ture’s mysteries. 19th Century science was broadly Bayesian in its statistical method- ology, while frequentism dominated 20th Century scientiFc practice. This brings up a pointed question: which philosophy will predominate in the 21st Century? One thing is already clear – statistical inference will pay an increased role in scientiFc progress as scientists attack bigger, messier problems in biology, medicine, neuroscience, the en- vironment, and other Felds that have resisted traditional deterministic analyses. This talk argues that a combination of frequentist and Bayesian thinking will be needed to deal with the massive data sets scientists are now bringing us. Three examples are given to suggest how such combinations might look in practice. A large portion of the talk is based on my presidential address to the American Statistical Association and a related column in Amstat News.
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Autumn in Stanford brings with it two notable natural phenomena: the days get short and it starts to rain a lot. These are both “scientiFc facts” but they involve quite di±erent kinds of science. Shorter days exemplify hard-edged science, precise and so predictable that you can sell an almanac saying exactly how short each day will be, down to the nearest second. The almanacs try to predict rainfall too but they’re not nearly so successful. Rainfall is a famously random phenomenon, as centuries of unhappy farmers can testify. (My father’s almanac went further, predicting good or bad Fshing weather for each day, indicated by a full Fsh icon, an empty Fsh, or a half Fsh for borderline days.) Hard-edged science still dominates public perceptions, but the attention of modern sci- entists has swung heavily toward rainfall-like subjects, the kind where random behavior plays a major role. A cartoon history of western thought might recognize three eras: an unpre- dictable pre-scientiFc world ruled by willful gods and magic; the precise clockwork universe of Newton and Laplace; and the modern scientiFc perspective of an understandable world, but one where predictability is tempered by a heavy dose of randomness. Deterministic Newtonian science is majestic, and the basis of modern science too, but a few hundred years of it pretty much exhausted nature’s storehouse of precisely predictable events. Subjects like biology, medicine, and economics require a more flexible scientiFc world view, the kind we statisticians are trained to understand.
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Modern Science - MODERN SCIENCE AND THE...

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