With the increasing use of detrital geochronology data for provenance analyses, we have also developed new constraints on the age of otherwise undateable sedimentary deposits. Because a deposit can be no older than its youngest mineral constituent, the youngest defensible detrital mineral age defines the maximum depositional age of the sampled bed. Defining the youngest `defensible' age in the face of uncertainty (e.g., analytical and geological uncertainty, or sample contamination) is challenging. The current standard practice of finding multiple detrital minerals with indistinguishable ages provides confidence that a given age is not an artifact; however, we show how requiring this overlap reduces the probability of identifying the true youngest component age. Barring unusual complications, the principle of superposition dictates that sedimentary deposits must get younger upsection. This fundamental constraint can be incoporated into the analysis of depositional ages in sedimentary sections through the use of Bayesian statistics, allowing for the inference of bounded estimates of true depositional ages and uncertainties from detrital geochronology so long as some minimum age constraints are present. We present two approaches for constructing a Bayesian model of deposit ages, first solving directly for the ages of deposits with the prior constraint that the ages of units must obey stratigraphic ordering, and second describing the evolution of ages with a curve that represents the sediment accumulation rate. Using synthetic examples we highlight how this method preforms in less-than-ideal circumstances. In an example from the Magallanes Basin of Patagonia, we demonstrate how introducing other age information from the stratigraphic section (e.g., fossil assemblages or radiometric dates) and formalizing the stratigraphic context of samples provides additional constraints on and information regarding depositional ages or derived quantities (e.g., sediment accumulation rates) compared to isolated analysis of individual samples.