where the posterior variance ˜ B and the posterior mean ˜ β are defined as follows: ˜ B − 1 = ( n ∑ i =1 x$_{i}$x ′ i σBν$_{i}$ + B − 1 0 ) and ˜ β = ˜ B ( n ∑ i =1 x$_{i}$ ( z$_{i}$ − Aν$_{i}$ − C | γ | h$_{i}$ ) σBν$_{i}$ + B − 1 0 β$_{0}$ ) . Hence, the conditional posterior is a normal distribution and β | z, ν, h, σ, γ ∼ N ( ˜ β, ˜ B ). (2) The parameters ( σ, γ ) are jointly sampled marginally of ( z, ν, h ) to reduce autocor- relation in the MCMC draws. Collecting terms involving ( σ, γ ) from the joint posterior (14) does not yield a tractable distribution, hence ( σ, γ ) are sampled using a joint random-walk MH algorithm. The proposed values are generated from a truncated bivariate normal distri- bution BT N$_{(0}$$_{,}$$_{∞}$$_{)}$$_{×}$$_{(}$$_{L,U}$$_{)}$ ( σ$_{c}$, γ$_{c}$, ι 2 1 ˆ D$_{1}$ ) ) , where ( σ$_{c}$, γ$_{c}$ ) represent the current values, ι$_{1}$ denotes the tuning factor and ˆ D$_{1}$ is the negative inverse of the Hessian obtained by maximizing the log-likelihood (9) with respect to ( σ, γ ). This maximization process to obtain ˆ D$_{1}$ is compu- tationally expensive and so may be done only once at the beginning of the algorithm with β values fixed at the BQROR or OLS estimates. The proposed draws are accepted with MH probability, otherwise, ( σ$_{c}$, γ$_{c}$ ) is repeated in the next MCMC iteration. Here, f ( · ) represents the full likelihood (9), π ( β, σ, δ, γ ) denotes the prior distributions (13), 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 ˆ D$_{1}$ . The expression π ( σ $^{′}$, γ $^{′}$| ( σ$_{c}$, γ$_{c}$ ) , ι 2 1 ˆ D$_{1}$ ) has an analogous interpretation. Note that the tuning pa- rameter ι can be adjusted for appropriate step-size and acceptance rate and the parameters ( A, B, C ) depend on p which is turn is a function of p$_{0}$ and γ . (3) The conditional posterior of ν is obtained from the joint posterior density by collecting terms involving ν . This is done element-wise as follows: 38 π ( ν$_{i}$ | z, β, h, σ, γ ) ∝ ν − 1 2 i exp { − 1 2 [ ( z$_{i}$ − x ′ $_{i}$β − Aν$_{i}$ − C | γ | h$_{i}$ ) 2 σBν$_{i}$ ] − ν$_{i}$ σ } 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$_{1}$ $_{)}$]} ,