space and games

March 31, 2007

Laplace’s Rule of Succession

Filed under: Useful Statistics — Peter de Blanc @ 1:08 am

Laplace’s Rule of Succession is really easy.

Say we have a 2-sided coin that comes up heads with some frequency f, and we have a uniform distribution on [0, 1] for the value of f. Then after n coin-flips, k of which are heads, the Rule of Succession gives:

P(heads | k, n) = (k + 1) / (n + 2)

as our probability for a heads on the next flip.

I decided to bring this up because I see people using Maximum Likelihood for this sort of thing all the time, which is pretty silly given how easy it is to do it the Bayesian way.

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