DUGi

Compositional Data, Bayesian Inference and the Modeling Process

http://dugi.udg.edu/item/http:@@@@hdl.handle.net@@2072@@273437

Statistical modeling in practice encompasses both the exploratory process,which is an inductive scientific approach and the confirmatory modeling process,which uses the deductive scientific approach. This paper will focus primarily on theconfirmatory modeling process.As the great applied statistician George Box, has famously said “all modelsare wrong, but some are useful”. My version would be “all models are wrong, butsome are essential for progress”!While John Aitchison has changed the world of compositional data analysis,the world of Bayesian statistics has also changed dramatically thanks to the Gibbssampler, which allows Bayesian analysis of complex non-linear models andparticularly random effects models.The beauty of Bayesian analysis is that it allows us to build modelshierarchically to incorporate all our knowledge about the structure of the datageneration process, not just about the parameters.In practice, we often know quite a lot about how data might have beengenerated and that knowledge can make a dramatic difference in how precise ourinference can be.The paper examines the use of Bayesian inference in statistical models thatinclude a compositional process. It discusses the insights that may be obtained fromthis approach, including as examples: distinguishing between structural and censoredzeros, examining the choice between compositional or multivariate covariates,identifying the number of end-members in a composition and identifying changepointsin compositional processes

Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada