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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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Enter MCMC – stage left

As mentioned earlier, we started with the coin flip examples because of the ease of determining the posterior distribution analytically—primarily because of the beta distribution's self-conjugacy with respect to the binomial likelihood function.

It turns out that most real-world Bayesian analyses require a more complicated solution. In particular, the hyper-parameters that define the posterior distribution are rarely known. What can be determined is the probability density in the posterior distribution for each parameter value. The easiest way to get a sense of the shape of the posterior is to sample from it many thousands of times. More specifically, we sample from all possible parameter values and record the probability ...

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