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The score‐driven approach to time series modelling is able to handle circular data and switching regimes with intra‐regime dynamics. Furthermore it enables a dynamic model to be fitted to a linear and a circular variable when their joint distribution is a cylinder. The viability of the new method is illustrated by estimating models for hourly data on wind direction and speed in Galicia, north‐west Spain. The modelling of intra‐regime dynamics is shown to be of critical importance. [ABSTRACT FROM AUTHOR]

Regular changes in the environment and biological responses generate seasonal patterns in the reproduction in small ruminants. Breeding seasonality is a significant constraint impacting efficiency of lamb production. However, seasonality‐related traits present a special peculiarity from a statistical point of view being circular data (day of year running 1:365). Recently, circular mixed models have been developed on the basis of the von Mises distribution and were applied to analyse lambing day distribution recorded from five major Canadian sheep breeds (Rideau Arcott, Romanov, Dorset, Suffolk and Polypay). In a simulation study, the linear model was not able to capture the variance components simulated under the circular paradigm; however, the von Mises model evidenced its ability to infer the variance components of simulated circular records. Using real data of sheep, mostly negligible variances were observed for additive genetic effect when using a linear model on circular data values. In contrast, when using the von Mises model, genetic variances were different across breeds, and it raises the possibility to delay the peak of reproduction and to change the seasonality of the ewes. However, a large variance was captured by flock‐year effects emphasizing the strong influence of management in lambing seasons for Canadian sheep populations. Finally, the results suggest the potential of using the von Mises model to analyse circular data, and further research is needed for better understand the complexity of this trait and the von Mises models. [ABSTRACT FROM AUTHOR]

This paper proposes a new Shewhart‐type control chart for circular or directional data. This type of data is found in several fields and applications, such as wind direction, the arrival time of a patient in a hospital, and the route of animals. The proposal is based on the Jones–Pewsey distribution, which is a very flexible three‐parameter distribution for modeling processes that can be represented as points on the circumference of the unit circle. We conduct an extensive Monte Carlo simulation study to evaluate and compare the performance of the proposed control chart with some competitors considering individual measurements and the mean direction (nonindividual observations). The results show that the Jones–Pewsey control chart outperforms the competitors in terms of run length distribution analysis. Finally, we present and discuss two applications based on actual datasets to show the applicability of the proposed control chart. [ABSTRACT FROM AUTHOR]

This paper is motivated by applications in oscillatory systems where researchers are typically interested in discovering components of those systems that display rhythmic temporal patterns. The contributions of this paper are twofold. First, a methodology is developed based on a circular signal plus error model that is defined using order restrictions. This mathematical formulation of rhythmicity is simple, easily interpretable and very flexible, with the latter property derived from the nonparametric formulation of the signal. Second, we address various commonly encountered problems in the analysis of oscillatory systems data. Specifically, we propose a methodology for (a) detecting rhythmic signals in an oscillatory system and (b) estimating the unknown sampling time that occurs when tissues are obtained from subjects whose time of death is unknown. The proposed methodology is computationally efficient, outperforms the existing methods, and is broadly applicable to address a wide range of questions related to oscillatory systems. [ABSTRACT FROM AUTHOR]

We present a likelihood-based test for clustering among sub-population mean directions for circular data. The test is based on a two-level hierarchical model with von Mises distributed variation on each level. The properties of the tests are investigated and compared to the commonly applied techniques of second-order analysis and pseudo-pooling of directions for the situation at hand. Finally we apply the technique to some previously published data sets, to determine the presence of directional clustering among the sub-populations. The Canadian Journal of Statistics 45: 461-478; 2017 © 2017 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

Objectives The fibula transmits loads within the lower limb of hominids. The few studies of variation in the cross-sectional geometric (CSG) properties of the fibula have established differences in its rigidity among groups engaged in distinct habitual loading activities. This study adds to this research by considering the relationship between CSG properties and the anatomical position of the fibula relative to the tibia among groups with differences in documented activity patterns. Material and methods We used pQCT scans taken at 50% of the length of the lower leg in 83 healthy young adult collegiate-aged individuals divided into five activity groups: runners, swimmers, cricketers, field hockey players, and non-athletes. We compared variation in calculated CSG properties against the distance between fibular and tibial centroids, as well as the angle of that plane relative to the plane of tibial Imax. Results Tibial and fibular CSG properties vary with respect to the relative position of the two bones. Tibial CSG properties differ in concert with the relative angle of the fibula to tibial Imax, while fibular CSG properties differ with the distance between the elements. Fibulae are more posterior-medially positioned in groups engaged in terrestrial athletics than among swimmers. Discussion The tibia and fibula experience different loads. The relative position of the two bones leads to compensatory differences in their CSG properties, perhaps due to increased resistance to bending in fibulae with greater distances from the tibia. Examinations of tibial CSG properties without considering the fibula limits interpretations about activity. [ABSTRACT FROM AUTHOR]

We consider small area estimation for the departure times of recreational anglers along the Atlantic and Gulf coasts of the United States. A Bayesian area-level Fay-Herriot model is considered to obtain estimates of the departure time distribution functions. The departure distribution functions are modelled as circular distributions plus area-specific errors. The circular distributions are modelled as projected normal, and a regression model is specified to borrow information across domains. Estimation is conducted through the use of a Hamiltonian Monte Carlo sampler and a projective approach onto the probability simplex. The Canadian Journal of Statistics 44: 416-430; 2016 © 2016 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

Among the diverse frameworks that have been proposed for regression analysis of angular data, the projected multivariate linear model provides a particularly appealing and tractable methodology. In this model, the observed directional responses are assumed to correspond to the angles formed by latent bivariate normal random vectors that are assumed to depend upon covariates through a linear model. This implies an angular normal distribution for the observed angles, and incorporates a regression structure through a familiar and convenient relationship. In this paper we extend this methodology to accommodate clustered data ( e.g., longitudinal or repeated measures data) by formulating a marginal version of the model and basing estimation on an EM-like algorithm in which correlation among within-cluster responses is taken into account by incorporating a working correlation matrix into the M step. A sandwich estimator is used for the parameter estimates' covariance matrix. The methodology is motivated and illustrated using an example involving clustered measurements of microbril angle on loblolly pine ( Pinus taeda L.) Simulation studies are presented that evaluate the finite sample properties of the proposed fitting method. In addition, the relationship between within-cluster correlation on the latent Euclidean vectors and the corresponding correlation structure for the observed angles is explored. [ABSTRACT FROM AUTHOR]

In this paper, we study an unsupervised clustering problem. The originality of this problem lies in the data, which consist of the positions of five separate X-ray beams on a circle. Radiation therapists positioned the five X-ray beam 'projectors' around each patient on a predefined circle. However, similarities exist in positioning for certain groups of patients, and we aim to describe these similarities with the goal of creating pre-adjustment settings that could help save time during X-ray positioning. We therefore performed unsupervised clustering of observed X-ray positions. Because the data for each patient consist of five angle measurements, Euclidean distances are not appropriated. Furthermore, we cannot perform k-means algorithm, usually used for minimizing corresponding distortion because we cannot calculate centers of clusters. We present here solutions to these problems. First, we define a suitable distance on the circle. Then, we adapt an algorithm based on simulated annealing to minimize distortion. This algorithm is shown to be theoretically convergent. Finally, we present simulations on simulated and real data. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Because of its role in many ecological processes, movement of animals in response to landscape features is an important subject in ecology and conservation biology. In this paper, we develop models of animal movement in relation to objects or fields in a landscape. We took a finite mixture modeling approach in which the component densities are conceptually related to different choices for movement in response to a landscape feature, and the mixing proportions are related to the probability of selecting each response as a function of one or more covariates. We combined particle swarm optimization and an expectation‐maximization (EM) algorithm to obtain maximum‐likelihood estimates of the model parameters. We used this approach to analyze data for movement of three bobcats in relation to urban areas in southern California, USA. A behavioral interpretation of the models revealed similarities and differences in bobcat movement response to urbanization. All three bobcats avoided urbanization by moving either parallel to urban boundaries or toward less urban areas as the proportion of urban land cover in the surrounding area increased. However, one bobcat, a male with a dispersal‐like large‐scale movement pattern, avoided urbanization at lower densities and responded strictly by moving parallel to the urban edge. The other two bobcats, which were both residents and occupied similar geographic areas, avoided urban areas using a combination of movements parallel to the urban edge and movement toward areas of less urbanization. However, the resident female appeared to exhibit greater repulsion at lower levels of urbanization than the resident male, consistent with empirical observations of bobcats in southern California. Using the parameterized finite mixture models, we mapped behavioral states to geographic space, creating a representation of a behavioral landscape. This approach can provide guidance for conservation planning based on analysis of animal movement data using statistical models, thereby linking connectivity evaluations to empirical data. [ABSTRACT FROM AUTHOR]

Psychological researchers in different fields sometimes encounter circular or directional data. Circular data are data measured in the form of angles or two-dimensional orientations. As an example, experiments investigating the development of spatial memory and the influence of visual experience on haptic orientation perception are presented. Three permutation tests are proposed for the evaluation of ordered hypotheses. The quality of the permutation tests is investigated by means of several simulation studies. The results of these studies show the expected increase in power when the permutation tests for ordered hypotheses are compared to a common non-directional test for circular data. The differences in power between the three tests for ordered alternatives are small. [ABSTRACT FROM AUTHOR]

When ecological traits differ seasonally among biological groups, environmental adaptation is expected. However, current analytical methods for such seasonal data ignore the circular nature of data and therefore are likely to be flawed. We propose a simple bootstrap hypothesis test which statistically quantifies the presence/absence of differences in peak months for multiple groups taking the circular nature of the data into account. The test is based on a robust distribution-free method. Simulations showed that the test gives a satisfactory performance. The test is illustrated using data for anchovy and sardine egg abundances in the western North Pacific. [ABSTRACT FROM AUTHOR]

Two contributions to the statistical analysis of circular data are given. First we construct data-driven smooth goodness-of-fit tests for the circular von Mises assumption. As a second method, we propose a new graphical diagnostic tool for the detection of lack-of-fit for circular distributions. We illustrate our methods on two real datasets. [ABSTRACT FROM AUTHOR]

A U-statistic is not easy to apply or cannot be applied in hypothesis testing when it is degenerate or has an indeterminate degeneracy under the null hypothesis. A class of two-stage U-statistics (TU-statistics) is proposed to remedy these drawbacks. Both the asymptotic distributions under the null and the alternative of TU-statistics are shown to have simple forms. When the degeneracy is indeterminate, the Pitman asymptotic relative efficiency of a TU-statistic dominates that of the incomplete U-statistics. If the kernel is degenerate under the null hypothesis but non-degenerate under the alternative, a TU-statistic is proved to be more powerful than its corresponding U-statistic. Applications to testing independence of paired angles in ecology and marine biology are given. Finally, a simulation study shows that a TU-statistic is more powerful than its corresponding incomplete U-statistic in almost all cases under two settings. [ABSTRACT FROM AUTHOR]

L'auteur s'inte'resse à la façon de tester si une loi circulaire est syme'trique par rapport à une direction centrale inconnue; il propose un test omnibus simple fondé sur la valeur observéd du deuxiéme moment sinusoidal centré par rapport à une estimation de cette direction. Sous des conditions trés générales, il montre que la statistique du test obéit asymptotiquement à une loi normale centrée réduite lorsque la distribution des observations est effectivement symeérique. II a recours à des simulations pour étudier le comportement de différentes versions de son test, dont des variantes randomiséd et bootstrap. Les versions asymptotique et bootstrap du test sont illustrées au moyen de deux jeux de données circulaires issus de la littérature sur le sujet. [ABSTRACT FROM AUTHOR]

This paper discusses deviance residual approximations in von Mises regression models. By using a relationship between the von Mises and the wrapped normal distributions, the paper shows that the deviance component of the von Mises distribution is approximately a linear function of the standard normal distribution. Two standardized forms are proposed for the deviance residual, and a simulation study is performed to compare the approximation of the proposed residuals to the standard normal distribution. An illustrative example is given. [ABSTRACT FROM AUTHOR]

Summary This paper derives estimating equations for modelling circular data with longitudinal structure for a family of circular distributions with two parameters. Estimating equations for modelling the circular mean and the resultant length are given separately. Estimating equations are then derived for a mixed model. This paper shows that the estimators that follow from these equations are consistent and asymptotically normal. The results are illustrated by an example about the direction taken by homing pigeons. [ABSTRACT FROM AUTHOR]

Les auteurs montrent comment analyser des données circulates de facon bayésienne, notamment au moyen de la loi de von Mises. Us montrent comment exploiter l'échantillonneur de Gibbs pour obtenir des observations de la loi a posteriori, laquelle peut avoir des lois conditionnelles de tous les types connus, une fois prises en compte certaines variables latentes. [ABSTRACT FROM AUTHOR]