advanced practice · coding problem
Beta-Binomial posterior update
Prior: Beta(1,1) (uniform) on conversion rate θ. Observe 8 successes in 100 trials. Compute the posterior Beta(9,93). Give the posterior mean and a 95% credible interval (approximate with Normal: mean ± 1.96√(pq/(n+2))).
The mechanism
Frequentist stats ask how surprising the data is under a null. Bayesian stats start with a prior belief, observe data, and land on a posterior — a direct distribution over what you care about. Credible intervals are 'where the parameter probably lives' given data and prior.
Expected evidence
Posterior mean = 9/102 ≈ 0.088; CI roughly [0.035, 0.141] — direct 'where θ probably lives' statement.
Try this drill in the practice workspace →
Hints when you need them
- Beta(a,b) + s successes, f failures → Beta(a+s, b+f).
- Posterior mean = α/(α+β).
Watch for these mistakes
- Treating the prior as truth instead of a starting opinion
- Confusing credible intervals with confidence intervals
- Using flat priors and expecting magic objectivity