This paper addresses the effects of three-dimensional (3-D) radiative transfer on the retrieval of optical depth for inhomogeneous stratiform liquid water clouds from passive satellite imagery. A nonparametric Bayesian classifier is developed to identify locations in a scene where plane-parallel retrievals fail to meet the requirements of a criterion that dictates a specified level of accuracy. Receiver operating characteristics are introduced that provide useful metrics that assess the quality of the error identification procedure as functions of illumination-viewing geometry. By fixing droplet effective radii, distributions of errors for retrieved optical depth are estimated at a scale of 120 m. These estimates suggest the best performance that can be expected for optical depth retrievals when 3-D radiative transfer cannot be ignored. The developments in this paper were made possible through the use of Monte Carlo radiative transfer simulations on stratiform clouds that were generated by a cloud system-resolving model. Plane-parallel retrievals employ the CloudSat optical depth retrieval algorithm.