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Abstract Cylindrical data are bivariate data formed from the combination of circular and linear variables. Identifying outliers is a crucial step in any data analysis work. This paper proposes a new distribution-free procedure to detect outliers in cylindrical data using the Mahalanobis distance concept. The use of Mahalanobis distance incorporates the correlation between the components of the cylindrical distribution, which had not been accounted for in the earlier papers on outlier detection in cylindrical data. The threshold for declaring an observation to be an outlier can be obtained via parametric or non-parametric bootstrap, depending on whether the underlying distribution is known or unknown. The performance of the proposed method is examined via extensive simulations from the Johnson-Wehrly distribution. The proposed method is applied to two real datasets, and the outliers are identified in those datasets. [ABSTRACT FROM AUTHOR]

Cylindrical data are multivariate data which consist of a directional, in this paper circular, and a linear component. Examples of cylindrical data in psychology include human navigation (direction and distance of movement), eye-tracking research (direction and length of saccades) and data from an interpersonal circumplex (location and intensity on the IPC). In this paper we adapt four models for cylindrical data to include a regression of the circular and linear component onto a set of covariates. Subsequently, we illustrate how to fit these models and interpret their results on a dataset on the interpersonal behavior of teachers. [ABSTRACT FROM AUTHOR]

Cylindrical data are bivariate data from the combination of circular and linear variables. However, up to now no work has been done on the detection of outlier in cylindrical data. We introduce a definition of outlier for cylindrical data and present a new test of discordancy to detect outlier in this type of data, based on the k-nearest neighbor's distance. Cut-off points of the new test statistic based on the Johnson-Wehrly distribution are calculated and its performance is examined using simulation. A practical example is presented using wind speed and wind direction data obtained from the Malaysian Meteorological Department. [ABSTRACT FROM AUTHOR]

Highlights • A Bayesian method to estimate parameters of a cylindrical mixture distribution. • Application of cylindrical distributions to a new dataset with time-of-day as circular variable. • Estimation uncertainty is directly inferred in the proposed method without extra calculations. Abstract This paper proposes a Metropolis–Hastings algorithm based on Markov chain Monte Carlo sampling, to estimate the parameters of the Abe–Ley distribution, which is a recently proposed Weibull-Sine-Skewed-von Mises mixture model, for bivariate circular-linear data. Current literature estimates the parameters of these mixture models using the expectation-maximization method, but we will show that this exhibits a few shortcomings for the considered mixture model. First, standard expectation-maximization does not guarantee convergence to a global optimum, because the likelihood is multi-modal, which results from the high dimensionality of the mixture's likelihood. Second, given that expectation-maximization provides point estimates of the parameters only, the uncertainties of the estimates (e.g., confidence intervals) are not directly available in these methods. Hence, extra calculations are needed to quantify such uncertainty. We propose a Metropolis–Hastings based algorithm that avoids both shortcomings of expectation-maximization. Indeed, Metropolis–Hastings provides an approximation to the complete (posterior) distribution, given that it samples from the joint posterior of the mixture parameters. This facilitates direct inference (e.g., about uncertainty, multi-modality) from the estimation. In developing the algorithm, we tackle various challenges including convergence speed, label switching and selecting the optimum number of mixture components. We then (i) verify the effectiveness of the proposed algorithm on sample datasets with known true parameters, and further (ii) validate our methodology on an environmental dataset (a traditional application domain of Abe–Ley mixtures where measurements are function of direction). Finally, we (iii) demonstrate the usefulness of our approach in an application domain where the circular measurement is periodic in time. [ABSTRACT FROM AUTHOR]

A new hidden Markov random field model is proposed for the analysis of cylindrical spatial series, i.e. bivariate spatial series of intensities and angles. It allows us to segment cylindrical spatial series according to a finite number of latent classes that represent the conditional distributions of the data under specific environmental conditions. The model parsimoniously accommodates circular–linear correlation, multimodality, skewness and spatial autocorrelation. A numerically tractable expectation–maximization algorithm is provided to compute parameter estimates by exploiting a mean-field approximation of the complete-data log-likelihood function. These methods are illustrated on a case study of marine currents in the Adriatic sea. [ABSTRACT FROM AUTHOR]

A new hidden Markov model is proposed for the analysis of cylindrical time series, that is, bivariate time series of intensities and angles. It allows us to segment cylindrical time series according to a finite number of regimes that represent the conditional distributions of the data under specific environmental conditions. The model parsimoniously accommodates for circular-linear correlation, multimodality, skewness, and temporal autocorrelation. A computationally efficient expectation-maximization algorithm is described to estimate the parameters, and a parametric bootstrap routine is provided to compute confidence intervals. These methods are illustrated on cylindrical time series of wave heights and directions. [ABSTRACT FROM AUTHOR]

Abstract: Cylindrical models, although scarcely used, are helpful tools in atmospheric science applications such as siting wind machines or setting up atmospheric pollution monitors. In this paper, three simple models have been successfully compared. The first, a second-order model, is an addition of two harmonic functions and was obtained by a multiple linear regression. It may be expressed in closed form and for this reason was taken as the reference model. The second was a weighted local average of directional neighbours and the third a robust variant of the second model. These models were used with wind speed and temperature data obtained from a RASS sodar during April 2001. The measurements were 10-min averages calculated at 20m intervals from 40 to 500m. Two different analyses were considered, namely, daily evolution and directional behaviour. In the first, there was a good agreement between the three models. Major differences were observed in the transitions between day and night at intermediate levels, although they were smoother in the second-order model. The directional analyses showed that the prevailing directions were more poorly defined by the second-order model, although it may be considered a reasonable approximation. The weighted local average model presented oscillations, which is not desirable from a practical point of view; the third model was more robust. As a result, the second-order model was preferred in daily analyses of lower levels due to its closed form. The coefficients of this model for daily evolution were successfully parameterised as a function of height. Finally, the undesirable oscillations of the second model disappeared when the weighting interval widened, though prevailing directions were less well defined. [Copyright &y& Elsevier]

Spatial direction vector data can be represented cylindrically by linear magnitudes and circular angles. We analyze such data by using a hierarchical Markov random field model with latent discrete classes and conditionally independent cylindrical data given the classes. The structure of a Potts model segments the spatial domain, and each class defines a cylindrical density that represents a specific structure. We consider two types of cylindrical distributions; the Weibull sine-skewed von Mises distribution, which is skewed in the circular part, and the generalized Pareto-type wrapped Cauchy distribution, which is heavy-tailed in the linear part. In this setting, we develop a statistically efficient block composite likelihood method for parameter estimation. The method is shown to provide much faster convergence than an expectation–maximization approach. However, the convergence is less stable for the block composite likelihood method, and we suggest a hybrid estimation approach for practical use. We apply the approach to study ocean surface currents in the Norwegian Sea. The models are able to describe the currents in terms of interpretable local regimes of two–three classes. Scoring rules are used to measure predictive performance of the two cylindrical densities. Results indicate that there is clearly skew angular components, and possibly also some heavy tails in magnitude. [ABSTRACT FROM AUTHOR]