Characterization of interactions between proteins and other molecules is crucial for,understanding the mechanisms of action of biological systems and, thus, drug discovery. An increasingly useful approach to mapping these interactions is measurement of hydrogen/deuterium exchange (HDX) using mass spectrometry (HDX-MS), which measures the time-resolved deuterium incorporation of peptides obtained by enzymatic digestion of the protein. Comparison of exchange rates between apo- and ligand-bound conditions results in a mapping of the differential HDX (Delta HDX) of the ligand. Residue-level analysis of these data, however, must account for experimental error, sparseness, and ambiguity due to overlapping peptides. Here, we propose a Bayesian method consisting of a forward model noise model, prior probabilities, and a Monte Carlo sampling scheme. This method exploits a residue-resolved exponential fate model of HDX-MS data obtained from all peptides simultaneously, and explicitly models experimental error. The result is the best possible estimate of Delta HDX magnitude and significance for each residue given the data. We demonstrate the method by revealing richer structural interpretation of Delta HDX data on two nuclear receptors: vitamin D-receptor (VDR) and retinoic acid receptor gamma (ROR gamma). The method is implemented in HDX Workbench and as a standalone module of the open source integrative Modeling Platform.