The statistical analysis of former sea level.

This thesis provides the first template for estimating relative sea level
curves and their associated uncertainties. More specifically, the thesis
estimates the changing state of sea level in the Humber estuary, UK,
over the course of the Holocene. These estimates are obtained through
Bayesian methods involving Gaussian processes.
Part of the task involves collating data sources from both archaeologists
and geologists which have been collected during frequent study of the
region. A portion of the thesis is devoted to studying the nature of the
data, and the adjustment of the archaeological information so it can be
used in a format suitable for estimating former sea level.
The Gaussian processes are used to model sea-level change via a
correlation function which assumes that data points close together
in time and space should be at a similar elevation. This assumption
is relaxed by incorporating non-stationary correlation functions and
aspects of anisotropy. A sequence of models are fitted using Markov
chain Monte Carlo. The resultant curves do not pre-suppose a
functional form, and give a comprehensive framework for accounting
for their uncertainty.
A further complication is introduced as the temporal explanatory
variables are stochastic: they arise as radiocarbon dates which require
statistical calibration. The resulting posterior date densities are
irregular and multi-modal. The spatio-temporal Gaussian process
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model takes account of such irregularities via Monte Carlo simulation.
The resultant sea-level curves are scrutinised at a number of locations
around the Humber over a selection of time periods. It is hoped that
they can provide insight into other areas of sea-level research, and into
a broader palaeoclimate framework.