Bayesian Multiple Quantile Regression for Linear Models Using a Score Likelihood*

Research output: Contribution to journalArticlepeer-review


We propose the use of a score based working likelihood function for quantile regression which can perform inference for multiple conditional quantiles of an arbitrary number. We show that the proposed likelihood can be used in a Bayesian framework leading to valid frequentist inference, whereas the commonly used asymmetric Laplace working likelihood leads to invalid interval estimations and requires further correction. For computation, we propose a novel adaptive importance sampling algorithm to compute important posterior summaries such as the posterior mean and the covariance matrix. Our proposed approach makes it feasible to perform valid inference for parameters such as the slope differences at different quantile levels, which is either not possible or cumbersome using existing Bayesian approaches. Empirical results demonstrate that the proposed likelihood has good estimation and inferential properties and that the proposed computational algorithm is more efficient than its competitors.

Original languageEnglish (US)
Pages (from-to)875-903
Number of pages29
JournalBayesian Analysis
Issue number3
StatePublished - 2021


  • adaptive importance sampling
  • Bayesian quantile regression
  • multiple quantile regression
  • working likelihood

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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