<Dl> <Dd> x i ∼ N (θ i, σ 2), (\ displaystyle x_ (i) \ sim N (\ theta _ (i), \ sigma ^ (2)),) </Dd> <Dd> θ i ∼ N (φ, τ 2) (\ displaystyle \ theta _ (i) \ sim N (\ varphi, \ tau ^ (2))) </Dd> </Dl> <Dd> x i ∼ N (θ i, σ 2), (\ displaystyle x_ (i) \ sim N (\ theta _ (i), \ sigma ^ (2)),) </Dd> <Dd> θ i ∼ N (φ, τ 2) (\ displaystyle \ theta _ (i) \ sim N (\ varphi, \ tau ^ (2))) </Dd> <P> with improper priors φ ∼ (\ displaystyle \ varphi \ sim) flat, τ ∼ (\ displaystyle \ tau \ sim) flat ∈ (0, ∞) (\ displaystyle \ in (0, \ infty)). When n ≥ 3 (\ displaystyle n \ geq 3), this is an identified model (i.e. there exists a unique solution for the model's parameters), and the posterior distributions of the individual θ i (\ displaystyle \ theta _ (i)) will tend to move, or shrink away from the maximum likelihood estimates towards their common mean . This shrinkage is a typical behavior in hierarchical Bayes models . </P>

Where does the bayesian rule can be used