Bayesian multivariate quantile regression using Dependent Dirichlet Process prior

Indrabati Bhattacharya and Subhashis Ghosal

Journal of Multivariate Analysis, 2021, vol. 185, issue C

Abstract: In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The proposed approach involves modeling of related conditional distributions of a response vector given the covariates using a Dependent Dirichlet Process (DDP) prior. The DDP is used to introduce dependence across covariates. The flexible covariate-dependent mixture of multivariate Gaussian kernels gives rise to an induced posterior for the desired multivariate quantile. For posterior computations, we use a truncated stick-breaking representation of the DDP, and use a block Gibbs sampler for estimating the model parameters. We illustrate our method with simulation studies, and a data containing blood pressures of 40 women. Finally, we provide a theoretical justification for the proposed method through posterior consistency and support properties of the prior.

Keywords: Bayesian quantile regression; Dependent Dirichlet Process; Posterior consistency; Stick-breaking (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.jmva.2021.104763

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