Gamma–Poisson hierarchical model
= Gamma–Poisson hierarchical model
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A <Gamma–Poisson hierarchical model> uses $Y_i\mid\theta_i\sim\operatorname{Poisson}(t_i\theta_i)$, $\theta_i\mid b\sim\operatorname{Gamma}(a,b)$, and $b\sim\operatorname{Gamma}(c,r)$, with <gamma distributions> in shape-rate convention. <Conditional independence> gives <full conditional distributions> $\theta_i\mid b,y\sim\operatorname{Gamma}(a+y_i,b+t_i)$ and $b\mid\theta,y\sim\operatorname{Gamma}(c+na,r+\sum_i\theta_i)$.