Bayesian Quantile Regression with Lasso and Adaptive Lasso

Markov chain Monte Carlo samplers for Bayesian quantile regression, based on the asymmetric Laplace distribution and the location-scale mixture representation of Kozumi and Kobayashi (2011) . A binary response and an observed continuous response are both supported, each with three penalty layers behind one interface: no penalty, following Benoit and Van den Poel (2012) ; the Bayesian lasso, following Benoit, Al-Hamzawi and Yu (2013) ; and the Bayesian adaptive lasso of Rubio Garcia (2023) < https://soar.wichita.edu/entities/publication/a2f86232-4704-4ec2-b685-751e7b04ec42>. In the binary family each is available as published and in a corrected form, the default, in which every improper prior component is replaced by a proper one so that the posterior exists unconditionally; the continuous family ships the corrected form only. The continuous adaptive-lasso layer at its default reproduces the penalty of Alhamzawi, Yu and Benoit (2012) . A binary threshold model identifies the coefficient vector only up to a positive scale, so the binary samplers expose the identification anchor as an explicit argument, allowing fixing the scale of the error distribution, fixing a single coefficient, and constraining the norm of the coefficient vector to be compared directly; an observed response identifies the scale, so the continuous samplers have no anchor and draw it every sweep. The MCMC cores are written in Fortran and called from R.