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 nonnegative 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:
http://lup.lub.lu.se/record/1567445
 author
 Bergman, Jakob ^{LU}
 supervisor

 Björn Holmquist ^{LU}
 Krzysztof Nowicki ^{LU}
 opponent

 Professor Guttorp, Peter, University of Washington
 organization
 publishing date
 2010
 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
 20100416 10:15:00
 ISSN
 16517938
 ISBN
 9789162880286
 language
 English
 LU publication?
 yes
 id
 c9dc09ed47764ed9a0df103dc473efe0 (old id 1567445)
 date added to LUP
 20160404 09:16:02
 date last changed
 20190521 13:44:40
@phdthesis{c9dc09ed47764ed9a0df103dc473efe0, 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 nonnegative 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. <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 = {9789162880286}, issn = {16517938}, language = {eng}, school = {Lund University}, series = {Doctoral Theses in Statistics}, title = {On Bicompositional Correlation}, url = {https://lup.lub.lu.se/search/ws/files/5277668/1567450.pdf}, year = {2010}, }