Abstract:
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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 the
confirmatory modeling process.
As the great applied statistician George Box, has famously said “all models
are wrong, but some are useful”. My version would be “all models are wrong, but
some 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 Gibbs
sampler, which allows Bayesian analysis of complex non-linear models and
particularly random effects models.
The beauty of Bayesian analysis is that it allows us to build models
hierarchically to incorporate all our knowledge about the structure of the data
generation process, not just about the parameters.
In practice, we often know quite a lot about how data might have been
generated and that knowledge can make a dramatic difference in how precise our
inference can be.
The paper examines the use of Bayesian inference in statistical models that
include a compositional process. It discusses the insights that may be obtained from
this approach, including as examples: distinguishing between structural and censored
zeros, examining the choice between compositional or multivariate covariates,
identifying the number of end-members in a composition and identifying changepoints
in compositional processes |