# Gibbs posterior inference on multivariate quantiles

arXiv: https://arxiv.org/abs/2002.01052 · HTML: https://mlsanity.com/paper/2002.01052/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2020.

## Built on by (most cited first, 3 of 3)

- [Valid Inference for Machine Learning Model Parameters](https://mlsanity.com/paper/2302.10840/) (2023)
- [Sequential Gibbs Posteriors with Applications to Principal Component Analysis](https://mlsanity.com/paper/2310.12882/) (2023)
- [PAC-Bayes Bounds for Gibbs Posteriors via Singular Learning Theory](https://mlsanity.com/paper/2604.17219/) (2026)

## Abstract (arXiv)

Bayesian and other likelihood-based methods require specification of a statistical model and may not be fully satisfactory for inference on quantities, such as quantiles, that are not naturally defined as model parameters. In this paper, we construct a direct and model-free Gibbs posterior distribution for multivariate quantiles. Being model-free means that inferences drawn from the Gibbs posterior are not subject to model misspecification bias, and being direct means that no priors for or marginalization over nuisance parameters are required. We show here that the Gibbs posterior enjoys a root-n convergence rate and a Bernstein--von Mises property, i.e., for large n, the Gibbs posterior distribution can be approximated by a Gaussian. Moreover, we present numerical results showing the validity and efficiency of credible sets derived from a suitably scaled Gibbs posterior.