Bayesian Synchronization of Proxy Paleorecords with Reference Chronologies

Many scientific fields compare two or more noisy time series that integrate the same underlying process but are recorded on different time scales. In paleoclimate studies, for example, proxy measurements are collected versus stratigraphic depth in a climate archive and then converted to calendar time. Synchronizing two proxy records often requires estimating an alignment that maps the depth (or preliminary age) of an input record onto the calendar--time scale of an absolutely--dated target record so that corresponding proxy signals line up. Existing alignment approaches are generally optimization--based and return a single transformation, providing limited formal uncertainty quantification. Here, we introduce BSync, a Bayesian synchronization framework that treats alignments as inference over a monotone time--mapping function to match an input to a target record. The alignment is expressed as a transformation of the input depth (or age) scale to match the target record, achieved through a link function that locally expands and compresses the input scale. The model is parameterized through interpretable local rate parameters, enabling the specification of priors on deposition times to regularize the alignment toward physically plausible deformations. BSync jointly infers the aligned chronology and provides posterior uncertainty for the time--warping function and the resulting age scale. In synthetic data experiments and a real--data case study, BSync yields well--calibrated credible intervals for the aligned time scale and achieves more accurate alignments than a state--of--the--art automated method, particularly when independent age constraints are sparse.