Bayesian Updating
Beta-Binomial conjugate family
Start with a Beta(α, β) prior over a coin's bias θ. Flip coins to observe heads and tails. Watch the posterior distribution sharpen around the true probability as evidence accumulates.
Observations
Heads: 0 | Tails: 0 | Total: 0
Posterior: Beta(2.0, 2.0)
Post. mean: 0.500 | mode: 0.500
Prior Beta(2.0, 2.0)Posterior Beta(2.0, 2.0)
Prior Beta(α, β) updated by 0 heads + 0 tails → Posterior Beta(α+H, β+T). The Beta-Binomial model is a conjugate pair.