Bayesian analysis of multivariate stable distributions using one-dimensional projections

TL;DR

This paper develops Bayesian inference methods for multivariate stable distributions using one-dimensional projections, spectral measures, and efficient MCMC algorithms with novel computational schemes.

Contribution

It introduces new Bayesian MCMC techniques for multivariate stable distributions, utilizing spectral measure approximations and characteristic function-based computations.

Findings

Efficient MCMC schemes for spectral measure approximation.

Novel computational methods using characteristic functions.

Successful application to multivariate stable distribution inference.

Abstract

In this paper we take up Bayesian inference in general multivariate stable distributions. We exploit the representation of Matsui and Takemura (2009) for univariate projections, and the representation of the distributions in terms of their spectral measure. We present efficient MCMC schemes to perform the computations when the spectral measure is approximated discretely or, as we propose, by a normal distribution. Appropriate latent variables are introduced to implement MCMC. In relation to the discrete approximation, we propose efficient computational schemes based on the characteristic function.