∝ ν − 1 2 i exp { − 1 2 [ ( z$_{i}$ − x ′ $_{i}$β − C | γ | h$_{i}$ ) 2 σB ν − 1 i + ( A 2 σB + 2 σ ) ν$_{i}$ ]} ∝ ν − 1 2 i exp { − 1 2 [ a$_{i}$ν − 1 i + bν$_{i}$ ]} , which is recognized as the kernel of a generalized inverse-Gaussian (GIG) distribution where, a$_{i}$ = ( z$_{i}$ − x ′ $_{i}$β − C | γ | h$_{i}$ ) 2 σB and b = ( A 2 σB + 2 σ ) . Hence, ν$_{i}$ | z, β, h, σ, γ ∼ GIG (0 . 5 , a$_{i}$, b ) for i = 1 , 2 , . . . , n . (4) The conditional posterior of h is obtained element-wise from the complete posterior density (15) conditional on γ and remaining parameters as follows: where the third line introduces the following notations: (5) Similar to Jeliazkov et al. (2008) and Rahman (2016), the transformed cut-point δ is sampled from the full likelihood (9), marginally of ( z, ν, h ). The proposed values are generated from a random-walk chain, δ ′ = δ$_{c}$ + u , where u ∼ N (0$_{J}$$_{−}$$_{3}$ , ι 2 ˆ D$_{2}$ ), ι$_{2}$ is a tuning pa- 39 ( σ 2 $_{h$_{i}$}$) − 1 = ( 1 σ 2 + C $^{2}$γ2 σBν$_{i}$ ) and µ$_{h}$$_{i}$ = σ 2 h$_{i}$ ( C | γ | ( z$_{i}$ − x ′ $_{i}$β − Aν$_{i}$ ) σBν$_{i}$ ) , π ( h$_{i}$ | z, β, ν, σ, γ ) ∝ exp { − 1 2 [ ( z$_{i}$ − x ′ $_{i}$β − Aν$_{i}$ − C | γ | h$_{i}$ ) 2 σBν$_{i}$ + h 2 i σ 2 ]} ∝ exp { − 1 2 [( 1 σ 2 + C $^{2}$γ2 σBν$_{i}$ ) h 2 i − 2 C | γ | ( z$_{i}$ − x ′ $_{i}$β − Aν$_{i}$ ) σBν$_{i}$ h$_{i}$ ]} ∝ exp { − 1 2 [ ( σ 2 $_{h$_{i}$}$) − $^{1}$h2 i − 2( σ 2 $_{h$_{i}$}$) − $^{1}$µ$_{h}$$_{i}$ h$_{i}$ ]} ∝ exp { − 1 2 ( σ 2 $_{h$_{i}$}$) − $^{1}$( h$_{i}$ − µ$_{h}$$_{i}$ ) 2 } , and the fourth line adds and subtracts ( σ 2 $_{h$_{i}$}$) − $^{1}$µ2 h$_{i}$ to complete the square. The last expres- sion is recognized as the kernel of a half-normal distribution and hence, h$_{i}$ | z, β, ν, σ, γ ∼ N $^{+}$( µ$_{h}$$_{i}$, σ 2 $_{h$_{i}$}$) for i = 1 , 2 , . . . , n .