Talk by Prof. Havard Rue (KAUST): Bayesian quantile regression for discrete observations

Prof. Havard Rue from KAUST (and one of the main authors of the famous INLA package for spatial statistics) will visit us next week and give a talk.

Title: Bayesian quantile regression for discrete observations
Affiliation: King Abdullah University of Science and Technology, Saudi Arabia
Abstract:

Quantile regression, i.e. modeling conditional quantiles of some
covariates and other effects through the linear predictor, has
typically been carried out exploiting the asymmetric Laplace
distribution (ALD) as a working "likelihood''. In the Bayesian
framework, this is highly questionable as the posterior variance
is affected by the artificial ALD "likelihood''. With continuous
responses, we can reparameterize the likelihood in terms of a
$\alpha$-quantile, and let the $alpha$-quantile depend on the
linear predictor. We can then do model based quantile regression
with little effort using the R-INLA package doing approximate Bayesian inference for
latent Gaussian models, and trust the quantile regression
posterior in the same way as when doing parametric mean
regression.

For discrete variables, like Poisson and (negative) Binomial,
there is no continuous relationship between quantiles and
distribution’s parameters, hence model based quantile regression
seems no longer possible. In this talk I will discuss how to
resolve this issue, so that we can do model based quantile
regression also for discrete responses. I will present some
examples that also demonstrate how the parametric approach almost
resolves the quantile crossing problem.

This is joint work with Tullia Padellini, Sapienza University of
Rome, Italy.