Bayesian updating: a coin and a Beta prior

Flip a coin with a hidden bias and watch the posterior over μ sharpen. Compare the MLE, the MAP estimate and the posterior.

Learn a coin's bias μ from flips

true μ (hidden) prior αprior β

Try thisUse a strong wrong prior (α = 20, β = 2, while the true μ is 0.3). Flip 10 at a time and watch the data pull the posterior over. With few flips, MAP and MLE disagree a lot; with many, they meet.