  Measuring incomplete sets of mutually unbiased bases constitutes a sensible
approach to the tomography of high-dimensional quantum systems. The unbiased
nature of these bases optimizes the uncertainty hypervolume. However, imposing
unbiasedness on the probabilities for the unmeasured bases does not generally
yield the estimator with the largest von Neumann entropy, a popular figure of
merit in this context. Furthermore, this imposition typically leads to mock
density matrices that are not even positive definite. This provides a strong
argument against perfunctory applications of linear estimation strategies. We
propose to use instead the physical state estimators that maximize the Shannon
entropy of the unmeasured outcomes, which quantifies our lack of knowledge
fittingly and gives physically meaningful statistical predictions.
