SIMPLICIAL INFERENCE 21
We hope that the above account of how the nature of compositional and prob-
ability statement problems leads to requirements of scale, perturbation and per-
mutation invariance and subcompositional coherence which dictate the form of a
meaningful and appropriate methodology, will encourage the statistician, faced with
simplicial data, to apply these statistical techniques. Whether the statistician opts
to perform log ratio analysis and interpret the results in the transformed space R_d
or to transform back into the simplex
or indeed never to leave the simplex
is clearly a matter of individual choice, possibly depending on the mathematical
skills of the statistician's client.
A new approach to null correlations of proportions,
Math. Geology 13
___ The statistical analysis of compositional data (with discussion),
___ Principal component analysis of compositional data,
___ A generol class of distributions on the simplex, J. R
___ The Statistical Analysis of Compositional Data,
Chapman and Hall, London,
___ Letter to the Editor. Measures of location of compositional data sets,
___ Comment on "Measures of variability for geological data," by D. F. Watson
and G. M. Philip,
___ Letter to the Editor. Delusions of uniqueness and ineluctability,
J. Math Geol-
___ Relative variation diagroms for describing patterns of variability of composi-
___ A plea for precision in Mathematical Geology,
___ On criteria for measures of compositional differences,
___ The one-hour course in compositional data analysis or compositional data
analysis is easy.
In: Vera Pawlowsky Glahn,
Proceedings of the Third Annual Con-
ference of the International Association for Mathematical Geology, CIMNE, Barcelona,
___ Logrotios and naturol laws in compositional data analysis,
Math. Geology 31
( 1999)' 563--580.
___ Biplots for compositional data,
available electronically from author, 1999.
Aitchison, J. and J. Bacon-Shone,
Convex linear combinations of compositions,
K erne! density estimation for compositional data,
Aitchison, J. and S. M. Shen,
Logistic-normal distributions: some properties and uses,
and C. W. Thomas,
Differential perturbation processes: a tool for the
study of compositional processes.
In: A. Buccianti, G. Nardi and R. Potenza,
ceedings of IAMG'98, The Fourth Annual Conference of the International Association
for Mathematical Geology, De Frede, Naples, 1998, 499-504.
Azzalini, A. and A. Dalla Valle,
The multivariate skew-normal distribution,
Chang, T. C.,
The biplot-grophic display of matrices with application to principal
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