A Bayesian Approach to Establishing a Reference Particle Size Distribution in the Presence of Outliers

The presence of observations or measurements that are unlike the majority is fairly common in studies conducted to establish particle size (or weight fraction) distributions. Therefore, there is a need to develop methods that are capable of producing estimates of particle size distributions that are not overly sensitive to the presence of a few observations that might be considered outliers. This article proposes a type of contamination mixture model that probabilistically allocates each observation to either a majority component or a contamination component. Observations that are allocated to a contamination component are down-weighted when estimating the particle size distribution (while the uncertainty of contamination classification is automatically accounted for in estimation). Computational methods are developed and the utility of the proposed methodology is demonstrated via a simulation study. The method is then applied to data produced from an inter-laboratory study conducted to establish a particle size distribution in cement.