the interval where A$_{i}$ = { α : π α > u$_{i}$ } . [ max i : α $_{i}$= α { u$_{i}$ ∏ l< $_{α}$(1 − V$_{l}$ ) } , 1 − max i : α $_{i}$> α { u$_{i}$ V α ∏ l< α $^{,l}$̸ = $_{α}$(1 − V$_{l}$ ) } ] . P ( α i = α | ... ) = I ( α ∈ A$_{i}$ ) ∏ J j $_{=1}$p y$_{ij}$ j α ∑ $^{l}$∈A$_{i}$ J j $_{=1}$p y$_{ij}$ j α gamma(1 + M, 1 − M ∑ α =1 log(1 − V α )) . 5. Assuming a gamma(1 , 1) hyperprior for β , update β by its conditional posterior 42 4. Update each α i from the multinomial conditional distribution