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

sd,

or indeed never to leave the simplex

sd,

is clearly a matter of individual choice, possibly depending on the mathematical

skills of the statistician's client.

(A1)

(A2)

(A3)

(A4)

(A5)

[A6)

(A7)

(A8)

(A9)

(A10)

(All)

(A12)

(A13)

(A14)

[A-B)

[A-L]

[A-S]

[A-T]

(Az-D]

(C]

(G1]

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