Elastic Tie-Pointing—Transferring Chronologies between Records via a Gaussian Process

We consider a general methodology for the transferral of chronologies from a master reference record containing direct dating information to an undated record of interest that does not. Transferral is achieved through the identification, by an expert, of a series of tie-points within both records that are believed to correspond to approximately contemporaneous events. Through tying of the 2 records together at these points, the reference chronology is elastically deformed onto the undated record. The method consists of 3 steps: creation of an age-depth model for the reference record using its direct dating information; selection of the tie-points and translation of their age estimates from the reference to the undated record; and finally, creation of an age-depth model for the undated record using these uncertain tie-point age estimates. Our method takes full account of the uncertainties involved in all stages of the process to create a final chronology within the undated record that allows joint age estimates to be found together with their credible intervals. To achieve computational practicality, we employ a Gaussian process to create our age-depth models. Calculations can then be performed exactly without resort to extremely slow Monte Carlo methods involving multiple independent model fits that would be required by other age-depth models.