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Perturbation is an operation defined on the simplex and can be used for centering compositional data in a ternary diagram, applying objective criteria. Because a straight line in the original diagram is still astraight line in the perturbed diagram, gridlines or compositional fields defined by straight lines can easily be included in the operation. Simultaneous perturbation of data, gridlines, and/or compositional fields is shown to improve both visualization and graphical interpretation of compositions in ternary diagrams. This is illustrated by some examples using simulated as well as real data. 相似文献
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Kriging Regionalized Positive Variables Revisited: Sample Space and Scale Considerations 总被引：1，自引：0，他引：1
Frequently, regionalized positive variables are treated by preliminarily applying a logarithm, and kriging estimates are back-transformed
using classical formulae for the expectation of a lognormal random variable. This practice has several problems (lack of robustness,
non-optimal confidence intervals, etc.), particularly when estimating block averages. Therefore, many practitioners take exponentials
of the kriging estimates, although the final estimations are deemed as non-optimal. Another approach arises when the nature
of the sample space and the scale of the data are considered. Since these concepts can be suitably captured by an Euclidean
space structure, we may define an optimal kriging estimator for positive variables, with all properties analogous to those
of linear geostatistical techniques, even for the estimation of block averages. In this particular case, no assumption on
preservation of lognormality is needed. From a practical point of view, the proposed method coincides with the median estimator
and offers theoretical ground to this extended practice. Thus, existing software and routines remain fully applicable. 相似文献
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G. Mateu-Figueras V. Pawlowsky-Glahn C. Barceló-Vidal 《Stochastic Environmental Research and Risk Assessment (SERRA)》2005,19(3):205-214
There is a dearth of suitable models with which to adequately model compositional data sets, especially those which exhibit skewness after additive logratio-transformation. In order to address this deficit we propose the additive logistic skew-normal distribution, an extension to the additive logistic normal model on the simplex derived from the skew-normal distribution in real space. The purpose of this paper is to outline the potential of this distribution in the modelling of compositional data. We present its most important properties and use an example to exhibit the potential of this distribution. 相似文献
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Problems with compositional data, like spurious correlation and negative bias, are well known in the Geosciences. Not so well known is the fact that the same problems appear when dealing with regionalized compositions. Here, these problems are illustrated, and a solution, based on the principle of working in coordinates using orthonormal logratio representations, is presented. This approach offers a tool for standard geostatistical studies. One of the advantages the method has is that it allows the usual inconsistencies with indicator kriging to be overcome through simplicial indicator kriging. A general way of modelling crossvariograms of coordinates, based on the matrix valued variation variogram, is discussed. In summary, the main aspects related to the modelling and analysis of regionalized compositions have had satisfactory solutions found for them. The proposed methodology is illustrated with public data from a survey concerning arsenic contamination in underground water in Bangladesh.
相似文献8.
V. Pawlowsky-Glahn 《Mathematical Geology》2005,37(7):671-672
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Indicator Kriging without Order Relation Violations 总被引：2，自引：1，他引：1
Raimon Tolosana-Delgado Vera Pawlowsky-Glahn Juan-Jose Egozcue 《Mathematical Geosciences》2008,40(3):327-347
Indicator kriging (IK) is a spatial interpolation technique aimed at estimating the conditional cumulative distribution function
(ccdf) of a variable at an unsampled location. Obtained results form a discrete approximation to this ccdf, and its corresponding
discrete probability density function (cpdf) should be a vector, where each component gives the probability of an occurrence
of a class. Therefore, this vector must have positive components summing up to one, like in a composition in the simplex.
This suggests a simplicial approach to IK, based on the algebraic-geometric structure of this sample space: simplicial IK
actually works with log-odds. Interpolated log-odds can afterwards be easily re-expressed as the desired cpdf or ccdf. An
alternative but equivalent approach may also be based on log-likelihoods. Both versions of the method avoid by construction
all conventional IK standard drawbacks: estimates are always within the (0,1) interval and present no order-relation problems
(either with kriging or co-kriging). Even the modeling of indicator structural functions is clarified. 相似文献
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The study of hydrogeochemical data sets frequently calls for statistical dimension reducing techniques. It is well known that
hydrochemical parameters are compositions and, for this type of data, the direct application of classical statistical methods
based on the correlation matrix yield spurious results. But new results on compositional data analysis have identified the
sampling space, the simplex, with an Euclidean space, a fact that allows us to define a simplicial factor analysis strategy,
thus overcoming the problem. For illustration, we use samples from the Llobregat River and its tributaries (NE Spain). Three
unobservable or latent factorial components are extracted, which are identified with pristine waters, potash-mining influence
and urban sewage influence. These three factorial components or compositional factors are plotted in a factorial ternary diagram,
which reflects the relative influence of each one of these factors on each observation. 相似文献