simulated data, the number of observations corresponding to the four categories of y are 42 (14%) , 81 (27%), 99 (33%) and 78 (26%), respectively. The posterior estimates of the model parameters are obtained based on the simulated data and the following moderately diffused priors: β ∼ N (0$_{3}$ , 10 I$_{3}$ ), σ ∼ IG (5 / 2 , 8 / 2), γ ∼ SB ( L, U, 4 , 4) and δ ∼ N (0$_{J}$$_{−}$$_{3}$ , I$_{J}$$_{−}$$_{3}$ ) for p$_{0}$ = (0 . 25 , 0 . 5 , 0 . 75), where ( L, U ) de- pends on the value of p$_{0}$ as mentioned in Section 2. Table 1 reports the MCMC results obtained from 15,000 iterations, after a burn-in of 5,000 iterations, along with the ineffi- ciency factors calculated using the batch-means method (Greenberg, 2012). The param- eters ( σ, γ ) is jointly sampled using random-walk MH algorithm with tuning parameters ι$_{1}$ $_{= (}$√$_{1}$$_{.}$$_{7}$$_{,}$ √$_{2}$$_{.}$$_{25}$$_{,}$ √$_{2}$$_{.}$$_{0) to achieve an acceptance rate of approximately 33 percent for the}$ three considered quantiles. Similarly, δ is sampled using a random-walk MH algorithm with tuning factor ι$_{2}$ $_{= (}$√$_{4}$$_{.}$$_{0}$$_{,}$ √$_{3}$$_{.}$$_{2}$$_{,}$ √$_{2}$$_{.}$$_{5) to obtain an acceptance rate of around 33 percent.}$ Figure 2: Trace plots of the MCMC draws at the 25th quantile for Simulation Study 1. 13 0 5000 10000 15000 −2 0 2 4 Trace of  1 0 5000 10000 15000 −5 0 Trace of  2 0 5000 10000 15000 0 5 10 Trace of  3 0 5000 10000 15000 0 0.5 1 1.5 Trace of  0 5000 10000 15000 0 1 2 3 Trace of  0 5000 10000 15000 0 1 2 Trace of 