Mathematical methods have been developed to perform arms-control-treaty verification tasks for enhanced information security. The purpose of these methods is to verify and classify inspected items while shielding the monitoring party from confidential aspects of the objects that the host country does not wish to reveal. Advanced medical-imaging methods used for detection and classification tasks have been adapted for list-mode processing, useful for discriminating projection data without aggregating sensitive information. These models make decisions off of varying amounts of stored information, and their task performance scales with that information. Development has focused on the Bayesian ideal observer, which assumes com- plete probabilistic knowledge of the detector data, and Hotelling observer, which assumes a multivariate Gaussian distribution on the detector data. The models can effectively discriminate sources in the presence of nuisance parameters. The chan- nelized Hotelling observer has proven particularly useful in that quality performance can be achieved while reducing the size of the projection data set. The inclusion of additional penalty terms into the channelizing-matrix optimization offers a great benefit for treaty-verification tasks. Penalty terms can be used to generate non- sensitive channels or to penalize the model's ability to discriminate objects based on confidential information. The end result is a mathematical model that could be shared openly with the monitor. Similarly, observers based on the likelihood probabilities have been developed to perform null-hypothesis tasks. To test these models, neutron and gamma-ray data was simulated with the GEANT4 toolkit. Tasks were performed on various uranium and plutonium in- spection objects. A fast-neutron coded-aperture detector was simulated to image the particles.