Complete pooling, no pooling, and partial pooling
Section of Hierarchical Bayes, part of Bayesian statistics
Complete pooling, no pooling, and partial pooling
| Type | Section |
| Taught in | Hierarchical Bayes |
| Part | Bayesian statistics |
| Questions using it | 4 |
The modelling choice can be organised into three cases.
| Approach | Assumption and consequence |
|---|---|
| Complete pooling | Set \theta_1=\cdots=\theta_J=\theta and analyse all students as though every class has exactly the same mean. |
| No pooling | Estimate each \theta_j from class j alone; information from the other classes is discarded. |
| Partial pooling | Retain distinct \theta_j’s but connect them through the shared distribution in Equation (2) in Hierarchical Bayes. |
Hierarchical Bayes produces partial pooling. A large class can speak mostly for itself. A small class has a noisy sample mean, so its estimate is pulled more strongly toward the population centre. This movement is called shrinkage or borrowing strength.
Used in
- Taught in Hierarchical Bayes
- Questions that use it (4) — Pooling · Q23 (answer) · Question 17 (answer) · C9
- All 9 questions on Hierarchical Bayes
See also
Hierarchical Bayesian model · Hyperparameter · Normal hierarchical shrinkage · Exchangeability · Empirical Bayes · Study-rate full conditional · Marginal hyperposterior · Uniformity depends on a domain