A Note on Bayesian Nonparametric Inference for Spherically Symmetric Distribution

TL;DR

This paper introduces a Bayesian nonparametric method using Dirichlet invariant processes to infer bivariate spherically symmetric distributions, extending previous work to higher dimensions and infinite groups.

Contribution

It develops a novel Bayesian nonparametric framework for spherically symmetric distributions using Dirichlet invariant processes, including the infinite group case.

Findings

Derived the Dirichlet invariant process posterior for finite rotation groups.

Extended the approach to infinite transformation groups, showing convergence to Dirichlet process.

Provided theoretical proofs for the properties of the proposed posterior.

Abstract

In this paper, we describe a Bayesian nonparametric approach to make inference for a bivariate spherically symmetric distribution. We consider a Dirichlet invariant process prior on the set of all bivariate spherically symmetric distributions and we derive the Dirichlet invariant process posterior. Indeed, our approach is an extension of Dirichlet invariant process for the symmetric distributions on the real line to a bivariate spherically symmetric distribution where the underlying distribution is invariant under a finite group of rotations. Moreover, we obtain the Dirichlet invariant process posterior for the infinite transformation group and we prove that it approaches to Dirichlet process.