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### On Bicompositional Correlation

(2010) In Doctoral Theses in Statistics
Abstract
A composition is a vector of positive components summing to a constant, usually taken to be 1. Hitherto the research on compositional correlation has mainly focused on the correlation between the components of composition. This thesis is concerned with modelling the correlation between two compositions.

We introduce a generalization of the Dirichlet distribution to simultaneously describe two compositions, i.e. a bicompositional Dirichlet distribution. The covariation between the two compositions is modelled by a parameter γ. If γ=0, then the two compositions are independent. For compositions with two components, we prove for which γ the distribution exists. We also give expressions for the normalization constant and... (More)
A composition is a vector of positive components summing to a constant, usually taken to be 1. Hitherto the research on compositional correlation has mainly focused on the correlation between the components of composition. This thesis is concerned with modelling the correlation between two compositions.

We introduce a generalization of the Dirichlet distribution to simultaneously describe two compositions, i.e. a bicompositional Dirichlet distribution. The covariation between the two compositions is modelled by a parameter γ. If γ=0, then the two compositions are independent. For compositions with two components, we prove for which γ the distribution exists. We also give expressions for the normalization constant and other properties, such as moments, marginal and conditional distributions. For compositions that have more than two components, we present expressions for the normalization constant and other properties for all non-negative integers γ. We also present a method for generating random numbers from the distribution for all γ≥0 and for some γ<0 if the compositions have two components. The method is based on the rejection method.

We use this bicompositional distribution and a general measure of correlation based on the concept of information gain to calculate a measure of correlation between two compositions for a large number of models. Finally we present an estimator of the general measure of correlation. We compare two suggestions of confidence intervals for the general measure of correlation. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
• Professor Guttorp, Peter, University of Washington
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Joint correlation coefficient, Empirical confidence coefficient, Dirichlet distribution, Correlation, Composition, Compositional data, Random variate generation, Simplex
in
Doctoral Theses in Statistics
pages
93 pages
defense location
EC3:207, Holger Crafoords Ekonomicentrum
defense date
2010-04-16 10:15
ISSN
1651-7938
ISBN
978-91-628-8028-6
language
English
LU publication?
yes
id
c9dc09ed-4776-4ed9-a0df-103dc473efe0 (old id 1567445)
date added to LUP
2010-03-17 10:58:21
date last changed
2016-09-19 08:45:00
```@misc{c9dc09ed-4776-4ed9-a0df-103dc473efe0,
abstract     = {A composition is a vector of positive components summing to a constant, usually taken to be 1. Hitherto the research on compositional correlation has mainly focused on the correlation between the components of composition. This thesis is concerned with modelling the correlation between two compositions. <br/><br>
<br/><br>
We introduce a generalization of the Dirichlet distribution to simultaneously describe two compositions, i.e. a bicompositional Dirichlet distribution. The covariation between the two compositions is modelled by a parameter γ. If γ=0, then the two compositions are independent. For compositions with two components, we prove for which γ the distribution exists. We also give expressions for the normalization constant and other properties, such as moments, marginal and conditional distributions. For compositions that have more than two components, we present expressions for the normalization constant and other properties for all non-negative integers γ. We also present a method for generating random numbers from the distribution for all γ≥0 and for some γ&lt;0 if the compositions have two components. The method is based on the rejection method. <br/><br>
<br/><br>
We use this bicompositional distribution and a general measure of correlation based on the concept of information gain to calculate a measure of correlation between two compositions for a large number of models. Finally we present an estimator of the general measure of correlation. We compare two suggestions of confidence intervals for the general measure of correlation.},
author       = {Bergman, Jakob},
isbn         = {978-91-628-8028-6},
issn         = {1651-7938},
keyword      = {Joint correlation coefficient,Empirical confidence coefficient,Dirichlet distribution,Correlation,Composition,Compositional data,Random variate generation,Simplex},
language     = {eng},
pages        = {93},
series       = {Doctoral Theses in Statistics},
title        = {On Bicompositional Correlation},
year         = {2010},
}

```