All simulators
Beta–Binomial Updating
Prior × likelihood = posterior. Change prior strength and data and watch the posterior move.
Day 13: Bayesian Inferenceprior Beta(5, 5)likelihood (normalised)posterior Beta(13, 17)
Posterior mean
0.433
MAP (mode)
0.429
MLE k/n
0.400
Prior weight
33%
prior mean 0.50
95% credible interval
0.264 – 0.611
Prior (dashed) × likelihood (normalised, thin) ∝ posterior (filled). The posterior mean is a weighted average of the prior mean and the MLE, with the prior's weight (α+β)/(α+β+n).