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Statistics Fundamentals · section 12 of 15

Mixed effects & clustering

1 interview question on mixed effects & clustering, each answered in full. Free to read, no account needed.

What is a hierarchical Bayesian model?

hard
  • Multi-level model: parameters θj{\theta}_{j} vary across groups j and are themselves drawn from a shared 'population' distribution θj{\theta}_{j} ~ N(μ,  τ2)N({\mu}, \;{\tau}^{2}).
  • 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.
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