Statistical Modelling of Compositional Problems Involving Finite Probability Distributions

Aitchison, John
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Finite probability distributions and compositional data are mathematically similar, consisting of D-dimensional positive vectors with sum 1. Despite this similarity the meaningful forms of analysis in these different areas may require substantially different concepts and statistical modelling. This paper highlights these differences, but also poses the question of how such differences may contribute to understanding in the different areas. At CoDa workshops we have become so accustomed to, even obsessed with, modelling all compositional data problems within a simplex sample space together with its algebraic-geometric Hilbert space structure. The context of this Hilbert sample space is certainly often relevant to the formulation of a number of compositional data problems, but its mathematical elegance should not override appropriate meaningful statistical modelling to resolve the real compositional problem. In this paper I illustrate some relevant modelling by consideration of how a variety of persons differ in their ability to perform inferential tasks particularly in the process of differential diagnosis ​
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