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R: Data Analysis and Visualization by Ágnes Vidovics-Dancs, Kata Váradi, Tamás Vadász, Ágnes Tuza, Balázs Árpád Szucs, Julia Molnár, Péter Medvegyev, Balázs Márkus, István Margitai, Péter Juhász, Dániel Havran, Gergely Gabler, Barbara Dömötör, Gergely Daróczi, Ádám Banai, Milán Badics, Ferenc Illés, Edina Berlinger, Bater Makhabel, Hrishi V. Mittal, Jaynal Abedin, Brett Lantz, Tony Fischetti

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Chapter 7. Bayesian Methods

Suppose I claim that I have a pair of magic rainbow socks. I allege that whenever I wear these special socks, I gain the ability to predict the outcome of coin tosses, using fair coins, better than chance would dictate. Putting my claim to the test, you toss a coin 30 times, and I correctly predict the outcome 20 times. Using a directional hypothesis with the binomial test, the null hypothesis would be rejected at alpha-level 0.05. Would you invest in my special socks?

Why not? If it's because you require a larger burden of proof on absurd claims, I don't blame you. As a grandparent of Bayesian analysis Pierre-Simon Laplace (who independently discovered the theorem that bears Thomas Bayes' name) once said: The weight ...

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