This dissertation considers several aspects of inference from particle sieving data. Such data comprise interval-censored particle sizes, and weight fractions of particles in each size interval;Under a model of random sampling of particles up to a target total weight, a sample of particles can be described using renewal theory, and the asymptotic distribution of the empirical weight fraction vector is multivariate normal. The model assumptions are that the particle size distribution being sampled has a standard probability density and that the first two moments of the conditional distribution of weight given size can be described with a power law relationship;Maximum likelihood and Bayesian point and interval estimates for population weight fractions in each size interval are possible. The properties of maximum likelihood estimators are studied via simulation and Bayes analyses for one-sample and hierarchical data structures are illustrated. The case of lognormal size is used in these simulations;The design problem associated with inferences in this model is also considered. The focus is on identifying sieve configurations that can be expected to allow effective statistical estimation of important parameters of the particle system.