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A composite Bayesian hierarchical model of compositional data with zeros
Author(s) -
Napier Gary,
Neocleous Tereza,
Nobile Agostino
Publication year - 2015
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.2681
Subject(s) - compositional data , bayesian probability , bayesian hierarchical modeling , set (abstract data type) , computer science , data set , posterior probability , hierarchical database model , data mining , bayesian inference , artificial intelligence , pattern recognition (psychology) , algorithm , mathematics , machine learning , programming language
We present an effective approach for modelling compositional data with large concentrations of zeros and several levels of variation, applied to a database of elemental compositions of forensic glass of various use types. The procedure consists of the following: (i) partitioning the data set in subsets characterised by the same pattern of presence/absence of chemical elements and (ii) fitting a Bayesian hierarchical model to the transformed compositions in each data subset. We derive expressions for the posterior predictive probability that newly observed fragments of glass are of a certain use type and for computing the evidential value of glass fragments relating to two competing propositions about their source. The model is assessed using cross‐validation, and it performs well in both the classification and evidence evaluation tasks. Copyright © 2014 John Wiley & Sons, Ltd.