  Estimating the impact of environmental processes on vertical reef development
in geological time is a very challenging task. pyReef-Core is a deterministic
carbonate stratigraphic forward model designed to simulate the key biological
and environmental processes that determine vertical reef accretion and
assemblage changes in fossil reef drill cores. We present a Bayesian framework
called Bayesreef for the estimation and uncertainty quantification of
parameters in pyReef-Core that represent environmental conditions affecting the
growth of coral assemblages on geological timescales. We demonstrate the
existence of multimodal posterior distributions and investigate the challenges
of sampling using Markov chain Monte-Carlo (MCMC) methods, which includes
parallel tempering MCMC. We use synthetic reef-core to investigate fundamental
issues and then apply the methodology to a selected reef-core from the Great
Barrier Reef in Australia. The results show that Bayesreef accurately estimates
and provides uncertainty quantification of the selected parameters that
represent the environment and ecological conditions in pyReef-Core. Bayesreef
provides insights into the complex posterior distributions of parameters in
pyReef-Core, which provides the groundwork for future research in this area.
