By a "covering" we mean a Gaussian mixture model fit to observed data.
Approximations of the Bayes factor can be availed of to judge model fit to the
data within a given Gaussian mixture model. Between families of Gaussian
mixture models, we propose the R\'enyi quadratic entropy as an excellent and
tractable model comparison framework. We exemplify this using the segmentation
of an MRI image volume, based (1) on a direct Gaussian mixture model applied to
the marginal distribution function, and (2) Gaussian model fit through k-means
applied to the 4D multivalued image volume furnished by the wavelet transform.
Visual preference for one model over another is not immediate. The R\'enyi
quadratic entropy allows us to show clearly that one of these modelings is
superior to the other.