Integrating age modeling into a hierarchical Bayesian framework for inferring the pattern and rate of past sea-level changes from uncertainty-prone proxy data

Inferring the pattern and rate of past sea-level changes from uncertainty-prone proxy records requires formal statistical analyses, preferably in a hierarchical framework. The commonly used error-in-variables method treats the relative sea level as a collection of random variables drawn from the multivariate Gaussian distribution. However, this method does not make any use of prior information about the sea-level index points as constraints in the inferential process, thereby leading to anomalously large uncertainties for the time periods when observational data are absent. Here, a hierarchical Bayesian model of past sea-level changes is presented. Specifically, the stochastically varying relative sea level is modeled as a piecewise linear process with an additive independent Brownian increment arriving in a Gaussian fashion. The treatment of temporal uncertainties associated with the sea-level index points in the partially observed proxy records also differs from the existing methods. Instead of calibrating the radiocarbon ages individually, the corresponding calendar ages are treated as random variables and inferred recursively according to their temporal order. Illustrative studies using synthetic and real-world data demonstrate the promise of this model.