What is a hierarchical Bayesian model?

hard

Answer

${\theta}_{j}$
$Partial pooling: group estimates borrow strength from each other via the shared prior — automatic shrinkage.$
$Uses: hospital effects, per-user models, radon by county (Gelman's classic example).$
$Solves the 'estimate 10,000 individual users' problem: no-pool overfits, full-pool ignores individuality, partial-pool balances them.$

Check yourself — multiple choice

Only fixed effects
Multi-level: ${\theta}_{j}$ ~ shared population $({\theta}_{j}\; \sim \;N({\mu}, \;{\tau}^{2}))$ ; partial pooling → shrinkage; solves 'no-pool overfits vs full-pool ignores individuality'
Same as OLS
Random

Hierarchical: partial pooling via shared prior; balances no-pool / full-pool.

#bayesian#mixed-effects

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