Bayesian Updating

Learning a coin’s bias from data

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Posterior ∝ likelihood × prior.
• Flat prior: after $h$ heads in $n$ flips, $P(\text{next head}) = \frac{h+1}{n+2}$.
• Priors act like imaginary data; enough real data overwhelms them.

Steps

1. Beliefs as distributions
2. Watch the belief sharpen
3. Rule of succession
4. Will the sun rise?
5. No successes yet
6. A confident sceptic