Statistical Inference for Disordered Sphere Packings

TL;DR

This paper discusses the challenges and potential approaches for statistically assessing and modeling disordered sphere packings, which are important in materials science and physics, emphasizing the need for new descriptive statistics and large sample analysis.

Contribution

It highlights the lack of formal probabilistic models for sphere packings and proposes exploring new descriptive statistics and large-sample methods for model assessment.

Findings

Identifies the need for new descriptive statistics for disordered packings.

Emphasizes the importance of large sample analysis for model assessment.

Suggests that development will be exploratory and experimental.

Abstract

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.