%0 Journal Article
%T Monte Carlo Experiments and a Few Observations on Bayesian Quantile Regression
%A Justin L. Tobias
%J Theoretical Economics Letters
%P 263-272
%@ 2162-2086
%D 2024
%I Scientific Research Publishing
%R 10.4236/tel.2024.141015
%X In many simulation-based Bayesian approaches to quantile regression,
Markov Chain Monte Carlo techniques are employed to generate draws from a
posterior distribution based on an asymmetric Laplace ˇ°workingˇ± likelihood.
Under flat improper priors, the mode of this posterior distribution is
coincident with the desired quantile function. However, simulation-based
approaches for estimation and inference commonly report a posterior mean as a
point estimate and interpret that mean synonymously with the quantile. In this
note, we analytically derive the exact posterior distribution of a quantile
regression parameter in a simple univariate setting free of covariates. We note
the non-uniqueness of the posterior mode in some cases and conduct a series of
Monte Carlo experiments to compare the sampling performances of posterior means
and modes. Interestingly, and perhaps surprisingly, the mean performs similarly
to, if not favorably to, the mode under several standard metrics, even in very
small samples.
%K Bayesian
%K Quantile Regression
%K Gibbs Sampling
%K Posterior Inference
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=131596