Sequential Bayesian Updating
Belief Update P(θ|x) ∝ P(x|θ)P(θ) as Data Arrives
Prior Type
Beta (conjugate for Bernoulli)
Uniform (Beta(1,1))
Informed Beta(5,5)
Skewed Beta(2,8)
True θ (hidden):
0.65
Auto-stream speed:
3
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Observations: 0
α (successes+prior): —
β (failures+prior): —
Posterior mean: —
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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.