frequentism

Example Sentences

• "Galavotti regards this as an open problem, as some passages from his Philosophical Papers seem to suggest that Ramsey, like Carnap, admitted two notions of probability: one epistemic and subjective, and one empirical and close to frequentism."
• "Laplace continued his research throughout France’s political upheavals. In 1810 he announced the central limit theorem, one of the great scientific and statistical discoveries of all time. It asserts that, with some exceptions, any average of a large number of similar terms will have a normal, bell-shaped distribution. Suddenly, the easy-to-use bell curve was a real mathematical construct. Laplace’s probability of causes had limited him to binomial problems, but his final proof of the central limit theorem let him deal with almost any kind of data. In providing the mathematical justification for taking the mean of many data points, the central limit theorem had a profound effect on the future of Bayes' rule. At the age of 62, Laplace, its chief creator and proponent, made a remarkable about-face. He switched allegiances to an alternate, frequency-based approach he had also developed. From 1811 until his death 16 years later Laplace relied primarily on this approach, which twentieth-century theoreticians would use to almost obliterate Bayes’ rule. Laplace made the change because he realized that where large amounts of data were concerned, both approaches generally produce much the same results. The probability of causes was still useful in particularly uncertain cases because it was more powerful than frequentism. But science matured during Laplace’s lifetime. By the 1800s mathematicians had much more reliable data than they had had in his youth and dealing with trustworthy data was easier with frequentism. Mathematicians did not learn until the midtwentieth century that, even with great amounts of data, the two methods can sometimes seriously disagree."