Sequential Bayesian Updating

Belief Update P(θ|x) ∝ P(x|θ)P(θ) as Data Arrives

Observations: 0
α (successes+prior): —
β (failures+prior): —
Posterior mean: —
No observations yet.
Beta distribution is conjugate prior for Bernoulli likelihood. After n obs with s successes: Beta(α+s, β+n−s). Posterior narrows as evidence accumulates.