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Activity Number: 403 - SPAAC Poster Competition
Type: Topic Contributed
Date/Time: Tuesday, July 30, 2019 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #304150
Title: Bayesian Inference on Multivariate Medians and Quantiles
Author(s): Indrabati Bhattacharya* and Subhashis Ghosal
Companies: North Carolina State University and North Carolina State University
Keywords: Affine equivariance; Bayesian bootstrap; Dirichlet process; Empirical process; Multivariate median; Multivariate quantile

We consider Bayesian inference on a class of multivariate median and multivariate quantile functionals using a Dirichlet process prior. We derive a Bernstein-von Mises theorem for the multivariate L1-median functional, which in particular shows that its posterior concentrates around its true value at the parametric rate and the posterior credible sets have asymptotically correct frequentist coverage. The technique involves approximating the posterior Dirichlet process by a Bayesian bootstrap process and deriving a conditional Donsker theorem. We also obtain analogous results for an affine equivariant version of the multivariate L1-median based on an adaptive transformation and re-transformation technique. We further derive a multidimensional Bernstein-von Mises theorem for a vector of multivariate quantiles. A simulation study on coverage probabilities of the multivariate L1-median supports the limiting results for finite sample situations. We apply the technique to analyze Fisher's iris dataset.

Authors who are presenting talks have a * after their name.

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