  The problem of optimal data collection to efficiently learn the model
parameters of a graphite nitridation experiment is studied in the context of
Bayesian analysis using both synthetic and real experimental data. The paper
emphasizes that the optimal design can be obtained as a result of an
information theoretic sensitivity analysis. Thus, the preferred design is where
the statistical dependence between the model parameters and observables is the
highest possible. In this paper, the statistical dependence between random
variables is quantified by mutual information and estimated using a k-nearest
neighbor based approximation. It is shown, that by monitoring the inference
process via measures such as entropy or Kullback-Leibler divergence, one can
determine when to stop the data collection process. The methodology is applied
to select the most informative designs on both a simulated data set and on an
experimental data set, previously published in the literature. It is also shown
that the sequential Bayesian analysis used in the experimental design can also
be useful in detecting conflicting information between measurements and model
predictions.
