Recent advances in directional statistics

Abstract

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere, and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper, we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (Wiley 1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, space situational awareness, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. AnWe are most grateful to three anonymous referees and, in alphabetical order, to

Detecting (non)parallel evolution in multidimensional spaces: angles, correlations and eigenanalysis

“…In this regard, the literature of directional statistics (e.g. [71,85,86]) may potentially provide useful directions for future methodological developments.…”

Detecting (non)parallel evolution in multidimensional spaces: angles, correlations, and eigenanalysis

“…Robustness of resampling-based tests against such cases needs to be critically assessed. The literature of directional statistics (e.g., Mardia & Jupp, 1999;Ley & Verdebout, 2017;Pewsey & García-Portugués, 2021) may potentially provide useful directions for alternatives.…”

“…Examples include balanced multimodal concentration (e.g., equal parallel and antiparallel signals) and uniform distribution on a large circle. There exist several other tests of concentration for those cases(Mardia & Jupp, 1999;Cai et al, 2013;Pewsey & García-Portugués, 2021), among whichSchott's (2005) test described above could be placed as well.3 Example analysisStuart et al's (2017) dataset of lake-stream divergence in the threespine stickleback (Gasterosteus aculeatus) is re-analysed here for demonstration. The original data were pre-processed as described in Appendix B.…”

Coming Together of Bayesian Inference and Skew Spherical Data

“…From 2017 and onwards the following contributions can be highlighted: Straub ( 2017 ) presented Bayesian analysis for the FvML distribution in 3D; Røge et al ( 2017 ) presented Bayesian inference in the case of infinite FvML mixture model assumption; Mulder et al ( 2020 ) provided Bayesian inference for mixtures of von Mises distributions using a reversible jump MCMC sampler and focused on non-informative priors. Lastly, the interested reader is referred to Pewsey and García-Portugués ( 2021 ) for Bayesian inference of other directional distributions.…”