A new inverse numerical modeling method is used to constrain the environmental parameters (e.g., relative-sealevel, sediment-supply, and wave climate histories) that control stratigraphic architecture in wave-dominated shallow-marine deposits. The method links a ''process-response'' forward stratigraphic model that simulates wave and storm processes (BARSIM) to a combination of inverse methods formulated in a Bayesian framework that allows full characterization of uncertainties. This method is applied for the first time to a real geologic dataset, collected at outcrop from two shoreface-shelf parasequences in the Aberdeen Member, Blackhawk Formation of the Book Cliffs, east-central Utah, USA. The environmental parameters that controlled the observed stratigraphic architecture are quantified, and key aspects of stratigraphic architecture are successfully predicted from limited data. Stratigraphic architecture at parasequence-stacking and intra-parasequence scales was driven principally by relative sea level (varying by up to about 55 m) and sediment supply (varying by up to 70 m2/yr), whose interplay determines the shoreline trajectory. Within zones of distinctive shoreline trajectory, variations in wave climate (of up to about 3 m in fairweather-wave height) controlled superimposed variations in sandstone and shale content (e.g., the development of upward-coarsening and upward-fining bedsets). The modeling results closely match the observed stratigraphic architecture, but their quality is limited by: (1) the formulation and assumptions of the forward-modeling algorithms, and (2) the observed data distribution and quality, which provide poor age constraint.