10 (1) Sample β | z, ν, h, σ, γ ∼ N ( ˜ β, ˜ B ), where ˜ B − 1 = ( B − 1 0 + n ∑ i =1 x$_{i}$x ′ i σBν$_{i}$ ) and ˜ β = ˜ B ( n ∑ i =1 x$_{i}$ ( z$_{i}$ − Aν$_{i}$ − C | γ | h$_{i}$ ) σBν$_{i}$ + B − 1 0 β$_{0}$ ) . (2) Sample ( σ, γ ) marginally of ( z, ν, h ) using a joint random-walk MH algorithm. The proposed values ( σ $^{′}$, γ $^{′}$) are generated from a truncated bivariate normal distribution BT N$_{(0}$$_{,}$$_{∞}$$_{)}$$_{×}$$_{(}$$_{L,U}$$_{)}$ ( σ$_{c}$, γ$_{c}$ ) , ι 2 1 ˆ D$_{1}$ ) , where ( σ$_{c}$, γ$_{c}$ ) denote the current values, ι denotes the tun- ing factor and ˆ D$_{1}$ is the negative inverse of the Hessian obtained by maximizing the log- likelihood (9) with respect to ( σ, γ ). The proposed draws are accepted with MH probability, α$_{MH}$ ( σ$_{c}$, γ$_{c}$ ; σ $^{′}$, γ $^{′}$) = min { 0 , ln [ f ( y | β, σ $^{′}$, γ $^{′}$, δ ) π ( β, σ $^{′}$, γ $^{′}$, δ ) f ( y β, σ$_{c}$, γ$_{c}$, δ ) π ( β, σ$_{c}$, γ$_{c}$, δ ) π ( σ$_{c}$, γ$_{c}$ | ( σ $^{′}$, γ $^{′}$) , ι 2 1 ˆ D$_{1}$ ) π ( σ $^{′}$, γ $^{′}$| ( σ$_{c}$, γ$_{c}$ ) , ι 2 1 ˆ D$_{1}$ ) ]} , else, repeat ( σ$_{c}$, γ$_{c}$ ) in the next MCMC iteration. Here, f ( · ) represents the full likelihood (9) obtained as the difference of cdf , π ( β, σ, δ, γ ) denotes the prior distributions (13), and π ( σ$_{c}$, γ$_{c}$ | ( σ $^{′}$, γ $^{′}$) , ι 2 1 ˆ D$_{1}$ ) stands for the bivariate truncated normal probability with mean ( σ $^{′}$, γ $^{′}$) and covariance ι 2 1 ˆ D$_{1}$ . The term π ( σ $^{′}$, γ $^{′}$| ( σ$_{c}$, γ$_{c}$ ) , ι 2 1 ˆ D$_{1}$ ) has an analogous interpretation. (3) Sample ν$_{i}$ | z$_{i}$, β, h, σ, γ ∼ GIG (0 . 5 , a$_{i}$, b ), for i = 1 , . . . , n , where a$_{i}$ = ( z$_{i}$ − x ′ $_{i}$β − C | γ | h$_{i}$ ) 2 σB and b = ( A 2 σB + 2 σ ) . (4) Sample h$_{i}$ | z$_{i}$, β, ν$_{i}$, σ, γ ∼ N $^{+}$( µ$_{h}$$_{i}$, σ 2 $_{h$_{i}$}$) for i = 1 , . . . , n , where ( σ 2 $_{h$_{i}$}$) − 1 = ( 1 σ 2 + C $^{2}$γ2 σBν$_{i}$ ) and µ$_{h}$$_{i}$ = σ 2 h$_{i}$ ( C | γ | ( z$_{i}$ − x ′ $_{i}$β − Aν$_{i}$ ) σBν$_{i}$ ) . (5) Sample δ | β, σ, γ, y marginally of ( z, ν, h ) using a random-walk MH step. The proposed value δ ′ is generated as δ ′ = δ$_{c}$ + u , where u ∼ N (0$_{J}$$_{−}$$_{3}$ , ι 2 ˆ D$_{2}$ ), ι$_{2}$ is a tuning parameter and ˆ D$_{2}$ is analogous to ˆ D$_{1}$ . Accept δ ′ with MH probability, α$_{MH}$ ( δ$_{c}$, δ $^{′}$) = min { 0 , ln [ f ( y | β, σ, γ, δ $^{′}$) π ( β, σ, γ, δ $^{′}$) f ( y β, σ, γ, δ$_{c}$ ) π ( β, σ, γ, δ$_{c}$ ) ]} , else, repeat δ$_{c}$ . Again f ( · ) denotes the full likelihood (9) and π ( β, σ, δ, γ ) denotes the priors. (6) Sample z$_{i}$ | y, β, ν$_{i}$, h$_{i}$, σ, γ, δ ∼ T N$_{(}$$_{ξ}$$_{j}$$_{−}$$_{1}$$_{, ξ}$$_{j}$$_{)}$ ( x ′ $_{i}$β + Aν$_{i}$ + C | γ | h$_{i}$, σBν$_{i}$ ) for i = 1 , 2 , . . . , n , where ξ is obtained from δ by one-to-one mapping using equation (12). Algorithm 1 (Sampling in FBQROR Model)