Understanding and predicting reservoir presence and characteristics at regional to basin scales is important for evaluating risk and uncertainty in hydrocarbon exploration. Simulating reservoir distribution within a basin by a stratigraphic forward model enables the integration of available prior information with fundamental geologic processes embedded in the numerical model. Stratigraphic forward model predictions can be significantly improved by calibrating the models to independent constraints, such as thicknesses from seismic or well data. A three-dimensional basin-scale stratigraphic forward-modeling tool is coupled with an inversion algorithm. The inversion algorithm is a modification of the neighborhood algorithm (a type of genetic algorithm), which is designed to sample complex multimodal objective functions and is parallelized on computer clusters to accelerate convergence. The process generates a set of representative geological models that are consistent with prior ranges for uncertain parameters, calibration constraints, and associated tolerance thresholds. The workflow is first demonstrated on two data sets: a synthetic example based on a elastic passive margin and a real hydrocarbon exploration example for slope and basin-floor stratigraphic traps in the Neocomian (Lower Cretaceous) of the West Siberian Basin. The analysis of calibrated models provides constraints on stratigraphic controls, and allows prediction of locations with higher potential to develop stratigraphic traps. These locations are related to complex interactions between paleobathymetry, subsidence, eustatic fluctuations, characteristics of sediment-input sources, and sediment-transport parameters. Results show the potential of stratigraphic forward modeling combined with inverse methods as an additional tool to support conventional play-based exploration and reservoir-presence prediction.