tion, the concept has gained considerable attention from researchers worldwide and across ideologies. In classical statistics/econometrics, the advantages of quantile regression es- timators have been well studied and the computational challenges pertaining to optimiz- ing a non-differentiable loss/objective function have also been adequately dealt (Koenker, 2005). The impediment to the development of Bayesian quantile regression was that the errors in a quantile regression model did not or was not assumed to follow any distribu- tion. About two decades later, Koenker and Machado (1999) noted that the quantile loss function appears in the exponent of an asymmetric Laplace (AL) distribution (Kotz et al., 2001; Yu and Zhang, 2005), thus facilitating the construction of a parametric likelihood. This was utilized by Yu and Moyeed (2001) to propose a Bayesian method for estimating quantile regression in linear models. The estimation algorithm for Bayesian quantile re- gression was further refined in Tsionas (2003) and Reed and Yu (2009). However, a Gibbs sampling algorithm was proposed in Kozumi and Kobayashi (2011), where they utilize the normal-exponential mixture representation of the AL distribution. The AL likelihood has been further exploited and utilized with/without the normal-exponential mixture to develop algorithms for Bayesian estimation of quantile regression in Tobit models (Yu and Stander, 2007; Kozumi and Kobayashi, 2011), Tobit models with endogenous covariates (Kobayashi, 2017), censored models (Reich and Smith, 2013), count data models (Lee and Neocleous, 2010), binary models (Benoit and Poel, 2010), ordinal models (Rahman, 2016), censored dynamic panel data models (Kozumi and Kobayashi, 2012) and mixed-effect or longitudinal data models (Geraci and Bottai, 2007; Luo et al., 2012). The AL likelihood has also been employed for Bayesian variable selection in quantile regression and some recent work on this topic includes Alhamzawi (2012), Ji et al. (2012) Yu et al. (2013), Alhamzawi and Yu (2013) and Alhamzawi (2016). The above set of papers is an incomplete list of works on Bayesian quantile regression, but they clearly affirm that the AL distribution has played a crucial role in the development of Bayesian quantile regression. However, the AL distribution poses a critical limitation since a 2