TITLE:
Bayesian Variable Selection for Mixture Process Variable Design Experiment
AUTHORS:
Sadiah M. A. Aljeddani
KEYWORDS:
Variable Selection, Bayesian Analysis, Mixture Experiment, Split-Plot Design
JOURNAL NAME:
Open Journal of Modelling and Simulation,
Vol.10 No.4,
October
18,
2022
ABSTRACT: This paper
discussed Bayesian variable selection methods for models from split-plot mixture
designs using samples from Metropolis-Hastings within the Gibbs sampling
algorithm. Bayesian variable selection is easy to implement due to the
improvement in computing via MCMC sampling. We described the Bayesian
methodology by introducing the Bayesian framework, and explaining Markov Chain
Monte Carlo (MCMC) sampling. The Metropolis-Hastings within Gibbs sampling was
used to draw dependent samples from the full conditional distributions which
were explained. In mixture experiments with process variables, the response
depends not only on the proportions of the mixture components but also on the
effects of the process variables. In many such mixture-process variable
experiments, constraints such as time or cost prohibit the selection of
treatments completely at random. In these situations, restrictions on the
randomisation force the level combinations of one group of factors to be fixed
and the combinations of the other group of factors are run. Then a new level of
the first-factor group is set and combinations of the other factors are run. We
discussed the computational algorithm for the Stochastic Search Variable
Selection (SSVS) in linear mixed models. We extended the computational
algorithm of SSVS to fit models from split-plot mixture design by introducing
the algorithm of the Stochastic Search Variable Selection for Split-plot Design
(SSVS-SPD). The motivation of this extension is that we have two different
levels of the experimental units, one
for the whole plots and the other for subplots in the split-plot mixture
design.