Coming Together of Bayesian Inference and Skew Spherical Data

Najmeh Nakhaei Rad; Andriette Bekker; Mohammad Arashi; Christophe Ley

doi:10.3389/fdata.2021.769726

Coming Together of Bayesian Inference and Skew Spherical Data

Front Big Data. 2022 Feb 8:4:769726. doi: 10.3389/fdata.2021.769726. eCollection 2021.

Authors

Najmeh Nakhaei Rad^{1

2

3}, Andriette Bekker³, Mohammad Arashi^{3

4}, Christophe Ley⁵

Affiliations

¹ Department of Mathematics and Statistics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.
² DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg, South Africa.
³ Department of Statistics, University of Pretoria, Pretoria, South Africa.
⁴ Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.
⁵ Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Ghent, Belgium.

Abstract

This paper presents Bayesian directional data modeling via the skew-rotationally-symmetric Fisher-von Mises-Langevin (FvML) distribution. The prior distributions for the parameters are a pivotal building block in Bayesian analysis, therefore, the impact of the proposed priors will be quantified using the Wasserstein Impact Measure (WIM) to guide the practitioner in the implementation process. For the computation of the posterior, modifications of Gibbs and slice samplings are applied for generating samples. We demonstrate the applicability of our contribution via synthetic and real data analyses. Our investigation paves the way for Bayesian analysis of skew circular and spherical data.

Keywords: Fisher-von Mises-Langevin distribution; Gibbs sampling; MCMC method; Wasserstein Impact Measure; skew-rotationally-symmetric distributions; slice sampler; spherical data.