What is Bayesian shrinkage?
hardAnswer
- Posterior estimates are pulled ('shrunk') from noisy per-group MLEs toward the prior / group mean.
- Effect: reduces variance at the cost of small bias — Stein's paradox shows shrinkage dominates MLE in ≥ 3 dimensions.
- Uses: multi-arm bandits, small-sample rate estimation (individual player batting averages, per-store conversion), empirical Bayes hierarchical models.
- Frequentist equivalents: ridge regression, James-Stein estimator, empirical Bayes.
Check yourself — multiple choice
- Not real
- Posterior pulled toward prior / group mean → lower variance at slight bias; dominates MLE in ≥ 3 dims (Stein); ~ ridge / James-Stein / empirical Bayes
- Random
- Only for regression
Shrinkage: posterior toward prior/global; dominates MLE in ≥ 3 dims (Stein).
#bayesian#estimation
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