Study-rate full conditional
Proposition taught in Hierarchical Bayes, part of Bayesian statistics
Study-rate full conditional
| Type | Proposition |
| Taught in | Hierarchical Bayes |
| Part | Bayesian statistics |
Normalising gives \boxed{ \theta_j\mid\alpha,\beta,{\boldsymbol{y}} \sim\operatorname{Beta}(y_j+\alpha,n_j-y_j+\beta)}. Conditional on the hyperparameters, the study rates are independent, so the joint conditional is the product of these J Beta densities.
Used in
- Taught in Hierarchical Bayes, where the derivation and examples are.
- All 9 questions on Hierarchical Bayes
See also
Hyperparameter · Hierarchical Bayesian model · Normal hierarchical shrinkage · Exchangeability · Empirical Bayes · Marginal hyperposterior · Uniformity depends on a domain · Grid Monte Carlo approximation