  We present a holistic Bayesian hierarchical model for reconstructing the
continuous and dynamic evolution of relative sea-level (RSL) change with fully
quantified uncertainty. The reconstruction is produced from biological
(foraminifera) and geochemical ({\delta}13C) sea-level indicators preserved in
dated cores of salt-marsh sediment. Our model is comprised of three modules:
(1) A Bayesian transfer function for the calibration of foraminifera into tidal
elevation, which is flexible enough to formally accommodate additional proxies
(in this case bulk-sediment {\delta}13C values); (2) A chronology developed
from an existing Bchron age-depth model, and (3) An existing
errors-in-variables integrated Gaussian process (EIV-IGP) model for estimating
rates of sea-level change. We illustrate our approach using a case study of
Common Era sea-level variability from New Jersey, U.S.A. We develop a new
Bayesian transfer function (B-TF), with and without the {\delta}13C proxy and
compare our results to those from a widely-used weighted-averaging transfer
function (WA-TF). The formal incorporation of a second proxy into the B-TF
model results in smaller vertical uncertainties and improved accuracy for
reconstructed RSL. The vertical uncertainty from the multi-proxy B-TF is ~28%
smaller on average compared to the WA-TF. When evaluated against historic
tide-gauge measurements, the multi-proxy B-TF most accurately reconstructs the
RSL changes observed in the instrumental record (MSE = 0.003). The holistic
model provides a single, unifying framework for reconstructing and analysing
sea level through time. This approach is suitable for reconstructing other
paleoenvironmental variables using biological proxies.
