Modern Directional Statistics

Ley, Christophe; Verdebout, Thomas

doi:10.1201/9781315119472

Cited by 165 publications

(102 citation statements)

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“…Many texts have been dedicated to describing statistical treatment of circular data: e.g. Batschelet (1981), Fisher (1995), Jammalamadaka and SenGupta (2001), Ley and Verdebout (2017), Mardia and Jupp (2000), Pewsey et al (2013), and some commonly used general statistics texts aimed at biologists also cover this (e.g. Zar 2013).…”

Section: Introductionmentioning

confidence: 99%

Circular data in biology: advice for effectively implementing statistical procedures

Landler

Ruxton

Malkemper

2018

Behav Ecol Sociobiol

134

120

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Circular data are common in biological studies. The most fundamental question that can be asked of a sample of circular data is whether it suggests that the underlying population is uniformly distributed around the circle, or whether it is concentrated around at least one preferred direction (e.g. a migratory goal or activity phase). We compared the statistical power of five commonly used tests (the Rayleigh test, the V-test, Watson’s test, Kuiper’s test and Rao’s spacing test) across a range of different unimodal scenarios. The V-test showed higher power for symmetrical distributions, Rao’s spacing performed worst for all explored unimodal distributions tested and the remaining three tests showed very similar performance. However, the V-test only applies if the hypothesis is restricted to one (pre-specified) direction of interest. In all other unimodal cases, we recommend using the Rayleigh test. Much less explored is the multimodal case with data concentrated around several directions. We performed power simulations for a variety of multimodal situations, testing the performance of the widely used Rayleigh, Rao’s, Watson, and Kuiper’s tests as well as the more recent Bogdan and Hermans-Rasson tests. Our analyses of alternative statistical methods show that the commonly used tests lack statistical power in many of multimodal cases. Transformation of the raw data (e.g. doubling the angles) can overcome some of the issues, but only in the case of perfect f-fold symmetry. However, the Hermans-Rasson method, which is not yet implemented in any software package, outcompetes the alternative tests (often by substantial margins) in most of the multimodal situations explored. We recommend the wider uptake of the powerful but hitherto neglected Hermans-Rasson method. In summary, we provide guidance for biologists helping them to make decisions when testing circular data for single or multiple departures from uniformity.Electronic supplementary materialThe online version of this article (10.1007/s00265-018-2538-y) contains supplementary material, which is available to authorized users.

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Section: Introductionmentioning

confidence: 99%

Circular data in biology: advice for effectively implementing statistical procedures

Landler

Ruxton

Malkemper

2018

Behav Ecol Sociobiol

134

120

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“…In this publication we restrict our consideration only to star-shaped data. More details on other models and methods in statistical directional and shape analysis can be found in [13] and [15].…”

Section: Directional Datamentioning

confidence: 99%

Spherical Data Handling and Analysis with R package rcosmo

Fryer

Olenko

2019

Communications in Computer and Information Science

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The R package rcosmo was developed for handling and analysing Hierarchical Equal Area isoLatitude Pixelation(HEALPix) and Cosmic Microwave Background(CMB) radiation data. It has more than 100 functions. rcosmo was initially developed for CMB, but also can be used for other spherical data. This paper discusses transformations into rcosmo formats and handling of three types of non-CMB data: continuous geographic, point pattern and star-shaped. For each type of data we provide a brief description of the corresponding statistical model, data example and ready-to-use R code. Some statistical functionality of rcosmo is demonstrated for the example data converted into the HEALPix format. The paper can serve as the first practical guideline to transforming data into the HEALPix format and statistical analysis with rcosmo for geo-statisticians, GIS and R users and researches dealing with spherical data in non-HEALPix formats.

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“…In directional statistics, the sample space is the unit sphere S p−1 = {x ∈ R p : x 2 = x x = 1} in R p . By far the most classical distributions on S p−1 are the Fisher-von Mises-Langevin (FvML) ones; see, e.g., [27] or [28]. We say that the random vector X with values in S p−1 has an FvML p (θ θ θ, κ) distribution, with θ θ θ ∈ S p−1 and κ ∈ (0, ∞), if it admits the density (throughout, densities on the unit sphere are with respect to the surface area measure)…”

Section: Introductionmentioning

confidence: 99%

Detecting the direction of a signal on high-dimensional spheres: non-null and Le Cam optimality results

Paindaveine

Verdebout

2019

Probab. Theory Relat. Fields

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We consider one of the most important problems in directional statistics, namely the problem of testing the null hypothesis that the spike direction θ θ θ of a Fisher-von Mises-Langevin distribution on the p-dimensional unit hypersphere is equal to a given direction θ θ θ 0 . After a reduction through invariance arguments, we derive local asymptotic normality (LAN) results in a general high-dimensional framework where the dimension p n goes to infinity at an arbitrary rate with the sample size n, and where the concentration κ n behaves in a completely free way with n, which offers a spectrum of problems ranging from arbitrarily easy to arbitrarily challenging ones. We identify various asymptotic regimes, depending on the convergence/divergence properties of (κ n ), that yield different contiguity rates and different limiting experiments. In each regime, we derive Le Cam optimal tests under specified κ n and we compute, from the Le Cam third lemma, asymptotic powers of the classical Watson test under contiguous alternatives. We further establish LAN results with respect to both spike direction and concentration, which allows us to discuss optimality also under unspecified κ n . To investigate the non-null behavior of the Watson test outside the parametric framework above, we derive its local

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Modern Directional Statistics

Cited by 165 publications

References 0 publications

Circular data in biology: advice for effectively implementing statistical procedures

Circular data in biology: advice for effectively implementing statistical procedures

Spherical Data Handling and Analysis with R package rcosmo

Detecting the direction of a signal on high-dimensional spheres: non-null and Le Cam optimality results

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