Three-dimensional petroleum systems modeling used in combination with stochastic methods can provide a powerful tool set to predict the presence of oil and gas in undrilled exploration prospects. The stochastic modeling approach has advantages over classical scenario-based modeling because it gives objective predictions of most likely outcomes, as well as their associated uncertainty ranges. Calibration of the stochastic models against observation data from wells and fields can be a challenging task. The a priori input parameter distributions are commonly highly unconstrained, resulting in failures to produce realizations that successfully match the observation data. To make the process of calibrating stochastic models more objective and efficient, we propose an iterative Monte Carlo procedure where the input parameters and uncertainties are adjusted between model iterations. The a posteriori input parameter distributions are computed by weighting each realization in the previous simulation series against the estimated misfits to the observation data. The misfit estimates are typically calculated from the modeled and measured oil and gas columns in drilled wells. The stochastic results include exploration risk maps and predrill estimates of oil and gas column heights, which may be used as input for risk evaluations and ranking of exploration prospects. A postdrill analysis can be performed to obtain a probabilistic measure of the quality of the predictions, and updated predrill predictions may be compiled, with or without running a new Monte Carlo iteration. This allows continuous upgrading and verification of the model as the basin matures and more data and knowledge become available.