Participants in achievement tests or psychometric scales can be naturally divided into various sub-groups such as gender, race, social economic status, school district, etc. In order to make meaningful comparison between groups, each item in the test/scale should measure the same underlying construct for participants came from different groups.…

This thesis deals with "large-scale" detection problems that arise in many real world applications such as sensor networks, mapping with mobile robots and group testing for biological screening and drug discovery. These are problems where the values of a large number of inputs need to be inferred from noisy observations and where the…