  A common approach in computational science is to use a set of of highly
precise but expensive calculations to parameterize a model that allows less
precise, but more rapid calculations on larger scale systems. Least-squares
fitting on a model that underfits the data is generally used for this purpose.
For arbitrarily precise data free from statistic noise, e.g. ab initio
calculations, we argue that it is more appropriate to begin with a ensemble of
models that overfit the data. Within a Bayesian framework, a most likely model
can be defined that incorporates physical knowledge, provides error estimates
for systems not included in the fit, and reproduces the original data exactly.
We apply this approach to obtain a cluster expansion model for the Ca[Zr,Ti]O3
solid solution.
