Bayesian Analysis of Least Absolute Relative Error Regression

In an important article by Chen et al. (2010) introduced a new distribution compatible with maximum likelihood estimation in a Least Absolute Relative Error (LARE) setting. In this article, we show first that the posterior of the model is log - concave and thus specialized and highly efficient techniques can be used to perform Bayesian inference without the use of MCMC since they provide independent draws from the posterior. Second, we approximate the distribution using a finite mixture of normals. Surprisingly, the log-LARE distribution can be approximated using a finite scale mixture of normals with few components.