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Box–Cox transformations in Bayesian analysis of compositional data

✍ Scribed by Malini Iyengar; Dipak K. Dey

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
223 KB
Volume
9
Category
Article
ISSN
1180-4009

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✦ Synopsis

Compositional data often result when raw data are normalized or when data is obtained as proportions of a certain heterogeneous quantity. These conditions are fairly common in geology, economics and biology. The result is, therefore, a vector of such observations per specimen. The usual multivariate procedures are seldom adequate for the analysis of compositional data and there is a relative dearth of alternative techniques suitable for the same. The presence of covariates further adds to complexity of the situation. In this manuscript, a complete Bayesian methodology to model such data is developed and is illustrated on a real data set comprising sand, silt and clay compositions taken at various water depths in an Arctic lake. Alternative methods such as maximum likelihood estimates are compared with the proposed Bayesian estimates. Simulation based approach is adopted to ascertain adequacy of the ®t. Several models are ®nally compared via a posterior predictive loss measure.

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