Bayesian Quantile Regression. Elliott1 and Xi Xia2 Standard randomization-based inference conditions on the data in the population and makes inference with respect to the repeating sampling properties of the sampling indicators. However quantile regression is not equipped with a parametric likelihood and therefore Bayesian inference for quantile regression demands careful investigation.
In Bayesian statistics we deal with distribution. For Linear and Quantile Regression Michael R. Jun 12 2013 While frequentist treatments of quantile regression are typically completely nonparametric a Bayesian formulation relies on assuming the asymmetric Laplace distribution as auxiliary error distribution that yields posterior modes equivalent to frequentist estimates.
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For a Bayesian approach to quantile regression you form the likelihood function based on the asymmetric Laplace distribution regardless of the actual distribution of the data. However the tails of the response distribution are as important as the center in many subs Bayesian quantile nonhomogeneous hidden Markov models Stat Methods Med Res. For example Bayesian quantile regression methods make use of Markov chain Monte Carlo MCMC algorithms to sample the parameter values from the posterior distribution and the resultant estimator is as e cient as the classical estimator. Jun 23 2020 Bayesian methods using Markov chain Monte Carlo MCMC algorithms for estimating quantile regression was introduced in Yu and Moyeed 2001 and refined among others in Kozumi and Kobayashi 2011.
