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 2 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.