  Sphere packings are essential to the development of physical models for
powders, composite materials, and the atomic structure of the liquid state.
There is a strong scientific need to be able to assess the fit of packing
models to data, but this is complicated by the lack of formal probabilistic
models for packings. Without formal models, simulation algorithms and
collections of physical objects must be used as models. Identification of
common aspects of different realizations of the same packing process requires
the use of new descriptive statistics, many of which have yet to be developed.
Model assessment will require the use of large samples of independent and
identically distributed realizations, rather than the large single stationary
realizations found in conventional spatial statistics. The development of
procedures for model assessment will resemble the development of thermodynamic
models, and will be based on much exploration and experimentation rather than
on extensions of established statistical methods.
