Bayes' theorem 是概率论中的一个基本定理,帮助「概率」这一学科建立起了和「数学」之间的关联,在实际运用中也可以用来描述人的直觉,Harold Jeffreys 把 Bayes' theorem 类比为几何学中的毕达哥拉斯定理
Bayes’ theorem is named after Reverend Thomas Bayes (1701–1761), who first provided an equation that allows new evidence to update beliefs in his An Essay towards solving a Problem in the Doctrine of Chances (1763). It was further developed by Pierre-Simon Laplace, who first published the modern formulation in his 1812 "Théorie analytique des probabilités". Sir Harold Jeffreys put Bayes’ algorithm and Laplace's formulation on an axiomatic basis. Jeffreys wrote that Bayes' theorem "is to the theory of probability what the Pythagorean theorem is to geometry".
Bayes 没有觉得这个定理有那么重要,他死后亲戚们找他的朋友 Richard Price 看看在遗物里面有没有什么可以发表的东西,才不小心找到了这个定理~
Julia Galef 的一个简单介绍,关于 Bayes' theorem 在生活中的运用:
https://www.youtube.com/watch?v=BrK7X_XlGB8
Ve先生的讲解里面融入了一些他自己的观点,确实,Bayes' theorem 虽然可以帮你逐渐的接近真相,但是无法解决根本性的「变革」问题:
https://www.youtube.com/watch?v=R13BD8qKeTg
对这个定理的讲解比较好的视频:
https://www.youtube.com/watch?v=OqmJhPQYRc8
P(A|B) = P(A ∩ B)/P(B) 的推导:
https://www.youtube.com/watch?v=cwADSMeiIoE