The Wilkins Peak Member (WPM) of the Green River Formation in Wyoming, USA, comprises alternating lacustrine and alluvial strata that preserve a record of terrestrial climate during the early Eocene climatic optimum. We use a Bayesian framework to develop age-depth models for three sites, based on new 40Ar/39Ar sanidine and 206Pb/238U zircon ages from seven tuffs. The new models provide two- to ten-fold increases in temporal resolution compared to previous radioisotopic age models, confirming eccentricity-scale pacing of WPM facies, and permitting their direct comparison to astronomical solutions. Starting at ca. 51 Ma, the median ages for basin-wide flooding surfaces atop six successive alluvial marker beds coincide with short eccentricity maxima in the astronomical solutions. These eccentricity maxima have been associated with hyperthermal events recorded in marine strata during the early Eocene. WPM strata older than ca. 51 Ma do not exhibit a clear relationship to the eccentricity solutions, but accumulated 31%−35% more rapidly, suggesting that the influence of astronomical forcing on sedimentation was modulated by basin tectonics. Additional high-precision radioisotopic ages are needed to reduce the uncertainty of the Bayesian model, but this approach shows promise for unambiguous evaluation of the phase relationship between alluvial marker beds and theoretical eccentricity solutions.