Bayes Statistical Analyses for Particle Sieving Studies

Abstract

Particle size is commonly used to determine quality and predict performance of particle systems. We consider particle size distributions inferred from a material sample using a fixed number of sieves with progressively smaller size openings, where the weight of the particles in each size interval is measured. In this article, we propose Bayes analyses for data from particle sieving studies based on parsimoniously parameterized multivariate normal approximate models for vectors of log weight fraction ratios. Additionally, we observe that the basic approach extends directly to modeling mixture contexts, which provides model flexibility and is a very natural extension when physical mixtures of materials with fundamentally different particle sizes are encountered. We also consider hierarchical modeling, where a single process produces lots of particles and the data available are (replicated) weight fraction vectors from different lots. Supplementary materials for this article are available online.

KEY WORDS:

• Compositional data
• Hierarchical models
• Mixtures
• Particle size distribution
• Weight fractions

ACKNOWLEDGMENTS

Norma Leyva's work is independent of her responsibilities at Teva, and does not incorporate Teva confidential or proprietary information. Stephen Vardeman’s work was partially supported by the National Science Foundation grant DMS no. 0502347 EMSW21-RTG awarded to the Department of Statistics, Iowa State University.