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where N , IG and SB denote normal, inverse-gamma and scaled-Beta distributions, respec- tively. The lower and upper bounds of the scaled-Beta distribution are obtained as men- tioned in Section 2. Combining the likelihood and the prior distributions, the augmented joint posterior density can be written as, 

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where the likelihood, based on GAL (0 , σ, γ ), uses the fact that given z and δ , the observed y is independent of the remaining parameters, because (8) determines y$_{i}$ given ( z, δ ) with probability 1. The conditional density of latent data z can be obtained from (11) and is given by π ( z | β, σ, ν, h, γ ) = ∏ n i =1 N ( z$_{i}$ | x ′ $_{i}$β + Aν$_{i}$ + C | γ | h$_{i}$, σBν$_{i}$ ). Additionally, the prior distributions for ( β, σ, γ, δ ) are assumed to be independent in equation (14). Using the preceding explanations, the “complete data posterior” in equation (14) can be expressed as, 

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The objects of interest i.e., ( z, β, ν, h, σ, γ, δ ) can be sampled by deriving the conditional pos- terior densities from the complete data posterior (15) and judiciously using the full likelihood (9) as presented in Algorithm 1. 

