Sampling from the Fitting Posterior Distributions

For (2) and (4), the full conditional densities are given, respectively, as follows  

We can show that the full conditional distributions in (2.29) through (2.31) are log-concave in each of these parameters. Therefore, we can use the adaptive rejection algorithm of Gilks and Wild (1992) or the localized Metropolis algorithm discussed in Chen et al. (2000) to sample (y, 0, Oq). 

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