Guided wave structural health monitoring offers the potential for efficient defect detection and localization on large plate-like structures. The aim of this article is to demonstrate that the performance of guided wave structural health monitoring on complex structures can be quantified, predicted, and enhanced through basic stochastic modeling and application of a likelihood-based detector. These are necessary steps in enabling such structural heath monitoring techniques to be used more robustly on safety-critical structures. Extensive ensembles of measurements were taken using a sparse array of transducers on an aluminum plate with geometric complexities (stiffeners), before and after introducing several sizes of damage at several locations, and in the presence of large noise processes. This enabled a full statistical treatment of performance evaluation using a modification of the standard receiver operating characteristic curve. The incorporation of stochastic modeling produced on average a 44% reduction in missed detections among the damage modes tested, with up to a 95% reduction in some cases.