Abstract: Reliable detection of glaucomatous deterioration remains one of the most difficult problems facing clinicians in glaucoma management. The difficulty is due to the complex structure of visual field data and the high level of noise in visual field measurements. Visual field assessment typically consists of visual sensitivity values at 52 different locations in an eye. To monitor the progression of glaucoma, visual field measurements are acquired periodically, yielding spatially correlated longitudinal data. Previous methods have not modeled the hierarchical structure and the intrinsic spatial-temporal correlations of visual field data properly. In this dissertation I develop a Bayesian hierarchical model with spatial and longitudinal covariance structures for visual field data from stable glaucomatous eyes. Outlier statistics representing different types of progressive glaucomatous eyes are then proposed and used to identify progressive glaucomatous eyes. Finally, I propose a Bayesian hierarchical changepoint and mixture model for visual field data from progressive glaucomatous eyes. Our methodology is demonstrated through applications to data from the Advanced Glaucoma Intervention Study (AGIS).