We present a Bayesian version of J. Lacroix, J. Murre, and E. Postma's (2006) Natural Input Memory (NIM) model of saccadic visual memory. Our model, which we call NIMBLE (NIM with Bayesian Likelihood Estimation), uses a cognitively plausible image sampling technique that provides a foveated representation of image patches. We conceive of these memorized image fragments as samples from image class distributions and model the memory of these fragments using kernel density estimation. Using these models, we derive class-conditional probabilities of new image fragments and combine individual fragment probabilities to classify images. Our Bayesian formulation of the model extends easily to handle multi-class problems. We validate our model by demonstrating human levels of performance on a face recognition memory task and high accuracy on multi-category face and object identification. We also use NIMBLE to examine the change in beliefs as more fixations are taken from an image. Using fixation data collected from human subjects, we directly compare the performance of NIMBLE's memory component to human performance, demonstrating that using human fixation locations allows NIMBLE to recognize familiar faces with only a single fixation.