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Journal articles on the topic 'Directional statistics'

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Published: 4 June 2021
Last updated: 25 May 2024

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1

Pewsey, Arthur, and Eduardo García-Portugués. "Recent advances in directional statistics." TEST 30, no. 1 (March 2021): 1–58. http://dx.doi.org/10.1007/s11749-021-00759-x.

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2

Binette, Olivier, and Simon Guillotte. "Bayesian nonparametrics for directional statistics." Journal of Statistical Planning and Inference 216 (January 2022): 118–34. http://dx.doi.org/10.1016/j.jspi.2021.05.007.

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3

Mardia, K. V. "Directional statistics and shape analysis." Journal of Applied Statistics 26, no. 8 (December 1999): 949–57. http://dx.doi.org/10.1080/02664769921954.

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4

Ehler, Martin, and Jennifer Galanis. "Frame theory in directional statistics." Statistics & Probability Letters 81, no. 8 (August 2011): 1046–51. http://dx.doi.org/10.1016/j.spl.2011.02.027.

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5

El Khattabi, Sana, and Franz Streit. "Identification analysis in directional statistics." Computational Statistics & Data Analysis 23, no. 1 (November 1996): 45–63. http://dx.doi.org/10.1016/s0167-9473(96)00020-5.

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6

Craven, B. D. "On quasidifferentiable optimization." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, no. 1 (August 1986): 64–78. http://dx.doi.org/10.1017/s1446788700028081.

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AbstractLagrangian necessary conditions for optimality, of both Fritz John and Kuhn Tucker types, are obtained for a constrained minimization problem, where the functions are locally Lipschitz and have directional derivatives, but need not have linear Gâteaux derivatives; the variable may be constrained to lie in a nonconvex set. The directional derivatives are assumed to have some convexity properties as functions of direction; this generalizes the concept of quasidifferentiable function. The convexity is not required when directional derivatives are replaced by Clarke generalized derivatives. Sufficient Kuhn Tucker conditions, and a criterion for the locally solvable constraint qualification, are obtained for directionally differentiable functions.
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7

Cipolloni, Giorgio, László Erdős, Dominik Schröder, and Yuanyuan Xu. "Directional extremal statistics for Ginibre eigenvalues." Journal of Mathematical Physics 63, no. 10 (October 1, 2022): 103303. http://dx.doi.org/10.1063/5.0104290.

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We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)].
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8

Goda, Y. "Statistics of Wave Crest Lengths Based on Directional Wave Simulations." Journal of Offshore Mechanics and Arctic Engineering 116, no. 4 (November 1, 1994): 239–45. http://dx.doi.org/10.1115/1.2920158.

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Spatial surface elevations of directional random waves have numerically been simulated for various directional spectral conditions in deep water and finite uniform depth water. Individual wave crests are defined on the simulated surface data and the statistics of crest lengths are examined. The ratio of the mean crest length to the local wavelength is found to be governed by the directional spreading parameter. The average longitudinal profiles of high wave crests are presented for three typical values of directional spreading parameters.
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9

YAMAKI, Shunsuke, Masahide ABE, and Masayuki KAWAMATA. "Statistical Analysis of Phase-Only Correlation Functions Based on Directional Statistics." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E97.A, no. 12 (2014): 2601–10. http://dx.doi.org/10.1587/transfun.e97.a.2601.

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10

Scott, Nicholas, Tetsu Hara, Paul A. Hwang, and Edward J. Walsh. "Directionality and Crest Length Statistics of Steep Waves in Open Ocean Waters." Journal of Atmospheric and Oceanic Technology 22, no. 3 (March 1, 2005): 272–81. http://dx.doi.org/10.1175/jtech1703.1.

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Abstract A new wavelet analysis methodology is applied to open ocean wave height data from the Southern Ocean Waves Experiment (1992) and from a field experiment conducted at Duck, North Carolina, in 1997 with the aim of estimating the directionality and crest lengths of steep waves. The crest directionality statistic shows that most of the steep wave crests are normal to the direction of the mean wind. This is inconsistent with the Fourier wavenumber spectrum that shows a broad bimodal directional spreading at high wavenumbers. The crest length statistics demonstrate that the wave field is dominated by short-crested waves with small crest length/wavelength ratios. The one-dimensional steep wave statistic obtained from the integration of the directional (two dimensional) steep wave statistic is consistent with the one-dimensional steep wave statistic obtained from the one-dimensional analysis at high wave slope thresholds.
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11

Chung, Hun, and John Duggan. "Directional equilibria." Journal of Theoretical Politics 30, no. 3 (July 2018): 272–305. http://dx.doi.org/10.1177/0951629818775515.

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We propose the solution concept of directional equilibrium for the multidimensional model of voting with general spatial preferences. This concept isolates alternatives that are stable with respect to forces applied by all voters in the directions of their gradients, and it extends a known concept from statistics for Euclidean preferences. We establish connections to the majority core, Pareto optimality, and existence and closed graph, and we provide non-cooperative foundations in terms of a local contest game played by voters.
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12

Scealy, Janice L. "Comments on: Recent advances in directional statistics." TEST 30, no. 1 (March 2021): 68–70. http://dx.doi.org/10.1007/s11749-021-00763-1.

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13

Crujeiras, Rosa M., and Paula Saavedra-Nieves. "Comments on: Recent advances in directional statistics." TEST 30, no. 1 (March 2021): 64–67. http://dx.doi.org/10.1007/s11749-021-00761-3.

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14

Huckemann, Stephan F. "Comments on: Recent advances in directional statistics." TEST 30, no. 1 (March 2021): 71–75. http://dx.doi.org/10.1007/s11749-021-00764-0.

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AbstractInspired by this felicitous, highly concentrated and rather exhaustive review of a rapidly growing field, many larger research areas that warrant further investigation come to mind. In this comment, three areas are selected: fully satisfactory PCA on tori and polyspheres, harnessing linearity through Lie algebras underlying homogeneous spaces such as those for directional data, and statistical analysis based on critical points (e.g. mode and antimodes) of Fréchet $$L^p$$ L p -functions.
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15

Mardia, Kanti V. "Comments on: Recent advances in directional statistics." TEST 30, no. 1 (March 2021): 59–63. http://dx.doi.org/10.1007/s11749-021-00760-4.

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16

Pewsey, Arthur, and Eduardo García-Portugués. "Rejoinder on: Recent advances in directional statistics." TEST 30, no. 1 (March 2021): 76–82. http://dx.doi.org/10.1007/s11749-021-00762-2.

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17

NAGASAKI, Kota, Wataru NAKANISHI, and Yasuo ASAKURA. "ANALYSING ROAD NETWORKS BY USING DIRECTIONAL STATISTICS." Journal of Japan Society of Civil Engineers, Ser. D3 (Infrastructure Planning and Management) 75, no. 6 (2020): I_199—I_205. http://dx.doi.org/10.2208/jscejipm.75.6_i_199.

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18

Bowers, J. A., I. D. Morton, and G. I. Mould. "Directional statistics of the wind and waves." Applied Ocean Research 22, no. 1 (February 2000): 13–30. http://dx.doi.org/10.1016/s0141-1187(99)00025-5.

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19

Nikolaidis, N., and I. Pitas. "Directional statistics in nonlinear vector field filtering." Signal Processing 38, no. 3 (August 1994): 299–316. http://dx.doi.org/10.1016/0165-1684(94)90151-1.

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20

Lehmann, E. L., and J. Rojo. "Invariant Directional Orderings." Annals of Statistics 20, no. 4 (December 1992): 2100–2110. http://dx.doi.org/10.1214/aos/1176348905.

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21

ALMUDEVAR, ANTHONY. "A NOTE ON THE CALCULATION OF N-STATISTICS." Journal of Bioinformatics and Computational Biology 07, no. 05 (October 2009): 895–903. http://dx.doi.org/10.1142/s0219720009004382.

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A class of statistics suitable for testing against equality of multivariate distributions is described by Klebanov and co-workers in 2007. Referred to as N-statistics, their discriminating ability is based on various forms of distance kernels in ℝd, the intention being to capture distinct forms of deviation from equality. This makes them particularly suitable for large-scale genomic screening applications, in which such variety of alternatives can be anticipated. One of these kernels, denoted as L4, introduces weighting by directional densities, hence the evaluation of L4 requires integration on the unit sphere in ℝd. In this note we introduce a methodology for the evaluation of integrals related to L4. It is shown that for a class of directional densities including, but not limited to, the uniform density L4 reduces to Euclidean distance. For other cases, the methodology permits a direct interpretation of L4 in terms of the directional weighting.
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22

YAMAKI, Shunsuke. "Statistical Properties of the Phase-Only Correlation Functions Clarified through Directional Statistics." IEICE ESS Fundamentals Review 13, no. 2 (October 1, 2019): 108–17. http://dx.doi.org/10.1587/essfr.13.2_108.

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23

Boulerice, Bernard, and Gilles R. Ducharme. "Decentered directional data." Annals of the Institute of Statistical Mathematics 46, no. 3 (September 1994): 573–86. http://dx.doi.org/10.1007/bf00773518.

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24

Fraser, D. A. S. "Directional tests and statistical frames." Statistical Papers 34, no. 1 (December 1993): 213–36. http://dx.doi.org/10.1007/bf02925543.

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25

Latheef, M., and C. Swan. "A laboratory study of wave crest statistics and the role of directional spreading." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2152 (April 8, 2013): 20120696. http://dx.doi.org/10.1098/rspa.2012.0696.

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This paper concerns the crest height statistics arising in sea states that are broad banded in both frequency and direction. A new set of laboratory observations are presented and the results compared with the commonly applied statistical distributions. Taken as a whole, the data confirm that the crest-height distributions are critically dependent upon the directionality of the sea state. Although nonlinear effects arising at third order and above are most pronounced in uni-directional seas, the present data show that they are also important in directionally spread seas, provided the seas are sufficiently steep and not too short crested. The data also highlight the limiting effects of wave breaking. With individual breaking events dependent upon the local wave steepness, the directionality of the sea state again plays a significant role. Indeed, the present observations confirm that the two competing processes of nonlinear amplification and wave breaking can have a profound influence on the crest-height distributions leading to significant departures from established theory. In such cases, the key parameters are the sea state steepness and directional spread; the latter acting to counter the former in terms of nonlinear changes in the crest-height distributions.
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26

Zhao, Wen, and Larissa Santos. "The Weird Side of the Universe: Preferred Axis." International Journal of Modern Physics: Conference Series 45 (January 2017): 1760009. http://dx.doi.org/10.1142/s2010194517600096.

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In both WMAP and Planck observations on the temperature anisotropy of cosmic microwave background (CMB) radiation a number of large-scale anomalies were discovered in the past years, including the CMB parity asymmetry in the low multipoles. By defining a directional statistics, we find that the CMB parity asymmetry is directional dependent, and the preferred axis is stable, which means that it is independent of the chosen CMB map, the definition of the statistic, or the CMB masks. Meanwhile, we find that this preferred axis strongly aligns with those of the CMB quadrupole, octopole, as well as those of other large-scale observations. In addition, all of them aligns with the CMB kinematic dipole, which hints to the non-cosmological origin of these directional anomalies in cosmological observations.
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27

FIELD, A. S. "Principal Diffusion Direction in Peritumoral Fiber Tracts: Color Map Patterns and Directional Statistics." Annals of the New York Academy of Sciences 1064, no. 1 (December 1, 2005): 193–201. http://dx.doi.org/10.1196/annals.1340.037.

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28

Spydell, Matthew, and Falk Feddersen. "Lagrangian Drifter Dispersion in the Surf Zone: Directionally Spread, Normally Incident Waves." Journal of Physical Oceanography 39, no. 4 (April 1, 2009): 809–30. http://dx.doi.org/10.1175/2008jpo3892.1.

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Abstract Lagrangian drifter statistics in a surf zone wave and circulation model are examined and compared to single- and two-particle dispersion statistics observed on an alongshore uniform natural beach with small, normally incident, directionally spread waves. Drifter trajectories are modeled with a time-dependent Boussinesq wave model that resolves individual waves and parameterizes wave breaking. The model reproduces the cross-shore variation in wave statistics observed at three cross-shore locations. In addition, observed and modeled Eulerian binned (means and standard deviations) drifter velocities agree. Modeled surf zone Lagrangian statistics are similar to those observed. The single-particle (absolute) dispersion statistics are well predicted, including nondimensionalized displacement probability density functions (PDFs) and the growth of displacement variance with time. The modeled relative dispersion and scale-dependent diffusivity is consistent with the observed and indicates the presence of a 2D turbulent flow field. The model dispersion is due to the rotational components of the modeled velocity field, indicating the importance of vorticity in driving surf zone dispersion. Modeled irrotational velocities have little dispersive capacity. Surf zone vorticity is generated by finite crest-length wave breaking that results, on the alongshore uniform bathymetry, from a directionally spread wave field. The generated vorticity then cascades to other length scales as in 2D turbulence. Increasing the wave directional spread results in increased surf zone vorticity variability and surf zone dispersion. Eulerian and Lagrangian analysis of the flow indicate that the surf zone is 2D turbulent-like with an enstrophy cascade for length scales between approximately 5 and 10 m and an inverse-energy cascade for scales of 20 to 100 m. The vorticity injection length scale (the transition between enstrophy and inverse-energy cascade) is a function of the wave directional spread.
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29

Budavári, Tamás, and Thomas J. Loredo. "Probabilistic Record Linkage in Astronomy: Directional Cross-Identification and Beyond." Annual Review of Statistics and Its Application 2, no. 1 (April 10, 2015): 113–39. http://dx.doi.org/10.1146/annurev-statistics-010814-020231.

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30

Yu, Zhou, Yuexiao Dong, and Mian Huang. "General directional regression." Journal of Multivariate Analysis 124 (February 2014): 94–104. http://dx.doi.org/10.1016/j.jmva.2013.10.016.

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31

Gillard, Jonathan, and Anatoly Zhigljavsky. "Optimal directional statistic for general regression." Statistics & Probability Letters 143 (December 2018): 74–80. http://dx.doi.org/10.1016/j.spl.2018.07.025.

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32

Mardia, K. V. "Directional data analysis:an overview." Journal of Applied Statistics 15, no. 2 (January 1988): 115–22. http://dx.doi.org/10.1080/02664768800000018.

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33

Jupp, P. E. "Residuals for directional data." Journal of Applied Statistics 15, no. 2 (January 1988): 137–47. http://dx.doi.org/10.1080/02664768800000021.

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34

Santos, Nuno Pessanha, Victor Lobo, and Alexandre Bernardino. "Directional Statistics for 3D Model-Based UAV Tracking." IEEE Access 8 (2020): 33884–97. http://dx.doi.org/10.1109/access.2020.2973970.

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35

Guo, Jie, Yanwen Guo, Jingui Pan, and Wenzhou Lu. "BRDF Analysis with Directional Statistics and its Applications." IEEE Transactions on Visualization and Computer Graphics 26, no. 3 (March 1, 2020): 1476–89. http://dx.doi.org/10.1109/tvcg.2018.2872709.

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36

Pokorny, Dan, and Regina A. Kurth. "Zur Validierung eines interpersonalen Zirkumplexmodells mittels “directional statistics“." Diagnostica 51, no. 3 (July 2005): 113–23. http://dx.doi.org/10.1026/0012-1924.51.3.113.

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Zusammenfassung. Interpersonale Zirkumplexmodelle werden zunehmend als Grundlage verschiedener Selbstbeurteilungsinstrumente genutzt. Kann die Zweidimensionalität dieser Verfahren faktorenanalytisch nachgewiesen werden, wird die kreisförmige Anordnung mittels “directional statistics“ untersucht. Da es widersprüchliche Ansätze zur Kennzeichnung der Zirkumplex-Skalen gibt, soll diese Studie mittels “directional statistics“ einen Beitrag zur Validierung eines interpersonalen Zirkumplexmodells aus der Selbsteinschätzungsperspektive leisten. Dazu wurde die Einordnung unterschiedlicher Verben, die interpersonales Verhalten beschreiben, ins Zirkumplexmodell durch verschiedene Stichproben (Experten, psychologische Laien, Patienten) untersucht. Experten nahmen die Einordnung im Vergleich zu den anderen Stichproben sowohl differenzierter als auch theoriekonformer vor. Es gab auch Verben, über deren Positionierung sich alle Stichproben einig waren, die jedoch nicht-theoriekonform vorgenommen wurden. Demzufolge ist das interpersonale Zirkumplexmodell zwar für die Selbsteinschätzung geeignet, jedoch muss sich die Entwicklung von Items und Skalen für zirkumplexbasierte Fragebögen empirisch an der jeweiligen Zielpopulation orientieren. Darüber hinaus stellt die zyklische Betrachtungsweise einen fruchtbaren Ansatz auch für andere psychodiagnostische Fragestellungen dar.
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37

Cruz-Orive, L. M., H. Hoppeler, O. Mathieu, and E. R. Weibel. "Stereological Analysis of Anisotropic Structures Using Directional Statistics." Applied Statistics 34, no. 1 (1985): 14. http://dx.doi.org/10.2307/2347881.

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38

Stansberg, C. T. "Statistical Properties of Directional Sea Measurements." Journal of Offshore Mechanics and Arctic Engineering 109, no. 2 (May 1, 1987): 142–47. http://dx.doi.org/10.1115/1.3257002.

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The statistical variability of directional sea estimates is considered. A general, but brief study in the mean and variance of the spatial coherence estimate is first presented. This function is found to be relatively unstable when it is not close to 1. A directional sea estimation procedure based on Fourier Series Expansion of the directional spectrum combined with a Maximum Entropy Condition is then described. This method is used in a numerical directional analysis test in order to demonstrate the effect on sea state estimates from the variability in the spatial coherence. Numerical sea states for this test are generated with 2049 frequencies and 100 directions per frequency. Significant statistical scatter is observed in the resulting estimated directional spectra and their parameters, in qualitative agreement with the spatial coherence statistics considered theoretically.
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39

Itskov, Mikhail, Vu Ngoc Khiêm, and Sugeng Waluyo. "Electroelasticity of dielectric elastomers based on molecular chain statistics." Mathematics and Mechanics of Solids 24, no. 3 (February 21, 2018): 862–73. http://dx.doi.org/10.1177/1081286518755846.

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The mechanical response of dielectric elastomers can be influenced or even controlled by an imposed electric field. It can, for example, cause mechanical stress or strain without any applied load; this phenomenon is referred to as electrostriction. There are many purely phenomenological hyperelastic models describing this electroactive response of dielectric elastomers. In this contribution, we propose an electromechanical constitutive model based on molecular chain statistics. The model considers polarization of single polymer chain segments and takes into account their directional distribution. The latter results from non-Gaussian chain statistics, taking finite extensibility of polymer chains into account. The resulting (one-dimensional) electric potential of a single polymer chain is further generalized to the (three-dimensional) network potential. To this end, we apply directional averaging on the basis of numerical integration over a unit sphere. In a special case of the eight-direction (Arruda–Boyce) model, directional averaging is obtained analytically. This results in an invariant-based electroelastic constitutive model of dielectric elastomers. The model includes a small number of physically interpretable material constants and demonstrates good agreement with experimental data, with respect to the electroactive response and electrostriction of dielectric elastomers.
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40

Karmpadakis, I., C. Swan, and M. Christou. "Laboratory investigation of crest height statistics in intermediate water depths." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2229 (September 2019): 20190183. http://dx.doi.org/10.1098/rspa.2019.0183.

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This paper concerns the statistical distribution of the crest heights associated with surface waves in intermediate water depths. The results of a new laboratory study are presented in which data generated in different experimental facilities are used to establish departures from commonly applied statistical distributions. Specifically, the effects of varying sea-state steepness, effective water depth and directional spread are investigated. Following an extensive validation of the experimental data, including direct comparisons to available field data, it is shown that the nonlinear amplification of crest heights above second-order theory observed in steep deep water sea states is equally appropriate to intermediate water depths. These nonlinear amplifications increase with the sea-state steepness and reduce with the directional spread. While the latter effect is undoubtedly important, the present data confirm that significant amplifications above second order (5–10%) are observed for realistic directional spreads. This is consistent with available field data. With further increases in the sea-state steepness, the dissipative effects of wave breaking act to reduce these nonlinear amplifications. While the competing mechanisms of nonlinear amplification and wave breaking are relevant to a full range of water depths, the relative importance of wave breaking increases as the effective water depth reduces.
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41

Arai, Hiroyoshi. "Circular statistics for the analysis of directional geological data." Journal of the Geological Society of Japan 117, no. 10 (2011): 547–64. http://dx.doi.org/10.5575/geosoc.117.547.

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42

SANINA, ELENA. "STATISTICS OF WAVE KINEMATICS IN RANDOM DIRECTIONAL WAVE FIELDS." Bulletin of the Australian Mathematical Society 93, no. 1 (October 27, 2015): 169. http://dx.doi.org/10.1017/s0004972715001124.

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43

Hutchinson, Elizabeth B., Paul A. Rutecki, Andrew L. Alexander, and Thomas P. Sutula. "Fisher statistics for analysis of diffusion tensor directional information." Journal of Neuroscience Methods 206, no. 1 (April 2012): 40–45. http://dx.doi.org/10.1016/j.jneumeth.2012.02.004.

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44

Emre Celebi, M. "Real-time implementation of order-statistics-based directional filters." IET Image Processing 3, no. 1 (February 1, 2009): 1–9. http://dx.doi.org/10.1049/iet-ipr:20080080.

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45

Kerouh, F., D. Ziou, and Q. Jiang. "Directional statistics-based quality measure for spotlight color images." Signal, Image and Video Processing 14, no. 6 (February 11, 2020): 1125–32. http://dx.doi.org/10.1007/s11760-020-01653-z.

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46

Xu, Shujing, Frank D. Gilliland, and David V. Conti. "Elucidation of causal direction between asthma and obesity: a bi-directional Mendelian randomization study." International Journal of Epidemiology 48, no. 3 (April 21, 2019): 899–907. http://dx.doi.org/10.1093/ije/dyz070.

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Abstract Background Observational associations between asthma and obesity are well established, but inferring causality is challenging. We leveraged publicly available summary statistics to ascertain the causal direction between asthma and obesity via Mendelian randomization in European-ancestry adults. Methods We performed two-sample bi-directional Mendelian randomization analysis using publicly available genome-wide association studies summary statistics. Single nucleotide polymorphisms associated with asthma and body mass index at genome-wide significance were combined using a fixed effect meta-analysis in each direction. An extensive sensitivity analysis was considered. Results There was evidence in support of increasing causal effect of body mass index on risk of asthma (odds ratio 1.18 per unit increase, 95% confidence interval (CI) (1.11, 1.25), P = 2 × 10−8. No significant causal effect of asthma on adult body mass index was observed [estimate −0.004, 95% CI (−0.018, 0.009), P = 0.553]. Conclusions Our results confirmed that in European-ancestry populations, adult body mass index is likely to be causally linked to the risk of asthma; yet the effect of asthma on body mass index is small, if present at all.
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47

Nelsen, Roger B., and Manuel Úbeda-Flores. "Directional dependence in multivariate distributions." Annals of the Institute of Statistical Mathematics 64, no. 3 (March 16, 2011): 677–85. http://dx.doi.org/10.1007/s10463-011-0329-6.

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48

Ribeiro, Dyogo Lesniewski, Tamara Cantú Maltauro, Luciana Pagliosa Carvalho Guedes, Miguel Angel Uribe-Opazo, and Gustavo Henrique Dalposso. "Directional Differences in Thematic Maps of Soil Chemical Attributes with Geometric Anisotropy." Stats 7, no. 1 (January 16, 2024): 65–78. http://dx.doi.org/10.3390/stats7010005.

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In the study of the spatial variability of soil chemical attributes, the process is considered anisotropic when the spatial dependence structure differs in relation to the direction. Anisotropy is a characteristic that influences the accuracy of the thematic maps that represent the spatial variability of the phenomenon. Therefore, the linear anisotropic Gaussian spatial model is important for spatial data that present anisotropy, and incorporating this as an intrinsic characteristic of the process that describes the spatial dependence structure improves the accuracy of the spatial estimation of the values of a georeferenced variable in unsampled locations. This work aimed at quantifying the directional differences existing in the thematic map of georeferenced variables when incorporating or not incorporating anisotropy into the spatial dependence structure through directional spatial autocorrelation. For simulated data and soil chemical properties (carbon, calcium and potassium), the Moran directional index was calculated, considering the predicted values at unsampled locations, and taking into account estimated isotropic and anisotropic geostatistical models. The directional spatial autocorrelation was effective in evidencing the directional difference between thematic maps elaborated with estimated isotropic and anisotropic geostatistical models. This measure evidenced the existence of an elliptical format of the subregions presented by thematic maps in the direction of anisotropy that indicated a greater spatial continuity for greater distances between pairs of points.
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49

Xiao, Wenting, Yuming Liu, Guangyu Wu, and Dick K. P. Yue. "Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution." Journal of Fluid Mechanics 720 (February 27, 2013): 357–92. http://dx.doi.org/10.1017/jfm.2013.37.

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Abstract:
AbstractWe study the occurrence and dynamics of rogue waves in three-dimensional deep water using phase-resolved numerical simulations based on a high-order spectral (HOS) method. We obtain a large ensemble of nonlinear wave-field simulations ($M= 3$ in HOS method), initialized by spectral parameters over a broad range, from which nonlinear wave statistics and rogue wave occurrence are investigated. The HOS results are compared to those from the broad-band modified nonlinear Schrödinger (BMNLS) equations. Our results show that for (initially) narrow-band and narrow directional spreading wave fields, modulational instability develops, resulting in non-Gaussian statistics and a probability of rogue wave occurrence that is an order of magnitude higher than linear theory prediction. For longer times, the evolution becomes quasi-stationary with non-Gaussian statistics, a result not predicted by the BMNLS equations (without consideration of dissipation). When waves spread broadly in frequency and direction, the modulational instability effect is reduced, and the statistics and rogue wave probability are qualitatively similar to those from linear theory. To account for the effects of directional spreading on modulational instability, we propose a new modified Benjamin–Feir index for effectively predicting rogue wave occurrence in directional seas. For short-crested seas, the probability of rogue waves based on number frequency is imprecise and problematic. We introduce an area-based probability, which is well defined and convergent for all directional spreading. Based on a large catalogue of simulated rogue wave events, we analyse their geometry using proper orthogonal decomposition (POD). We find that rogue wave profiles containing a single wave can generally be described by a small number of POD modes.
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50

Brunner, Lawrence J., and Albert Y. Lo. "Nonparametric Bayes methods for directional data." Canadian Journal of Statistics 22, no. 3 (September 1994): 401–12. http://dx.doi.org/10.2307/3315601.

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