Extending Bayesian analysis of circular data to comparison of multiple groups

TL;DR

This paper extends Bayesian MCMC methods for circular data to compare multiple groups, evaluating their performance and identifying the rejection sampler as the most effective approach.

Contribution

It introduces a novel procedure for comparing multiple groups of circular data using extended Bayesian MCMC methods.

Findings

All methods overestimate the concentration parameter.

Coverage probabilities were reasonable across methods.

Rejection sampler performed best in simulations.

Abstract

Circular data are data measured in angles and occur in a variety of scientific disciplines. Bayesian methods promise to allow for flexible analysis of circular data. Three existing MCMC methods (Gibbs, Metropolis-Hastings, and Rejection) for a single group of circular data were extended to be used in a between-subjects design, providing a novel procedure to compare groups of circular data. Investigating the performance of the methods by simulation study, all methods were found to overestimate the concentration parameter of the posterior, while coverage was reasonable. The rejection sampler performed best. In future research, the MCMC method may be extended to include covariates, or a within-subjects design.