Spatiotemporal modelling of groundwater contaminants

QA Mathematics

Molinari, Daniel Alberto ; Bowman, Adrian

University:University of Glasgow

Department:School of Mathematics and Statistics

关键词: spatiotemporal, groundwater, contaminants;   

Others  :  http://theses.gla.ac.uk/5873/7/2014MolinariPhD.pdf

来源: University of Glasgow

【 摘 要 】

Spatiotemporal data have become very common, particularly through environmentalsettings where a spatial array of sampling sites generates data over time. Thisthesis deals with aspecific spatio-temporal setting of groundwater contaminationand aims to construct suitable statistical models. One of the motivating featuresof the application is that the model has to be implemented in an unsupervisedmanner and there is a high premium on the results being available very quickly,with a response time of a few seconds only.Many routes to spatiotemporal models are possible, but in order to achieve theaims outlined above we have proposed a model based on P-splines. A Bayesianapproach to fitting is used to provide the stability required in an unsupervisedsetting. The speed requirement makes computationally intensive methods suchas MCMC unsuitable for the determination of the optimal penalisation parameterand so conjugate priors and highlyefficient methods of linear algebra have beenbrought to bear.Use of the modelidentified a problematic issue due to the irregular spatio-temporaldesign of some data sets, giving rise to cases of \ballooning", where unexpectedlyhigh predictions, not supported by the observations, can appear. This matterwas also tackled within the Bayesian framework mentioned above. The proposedprocedures were assessed both by means of a simulation study and on real data.Finally, as an extension of the proposed methodology, we address the issue ofnon-detects, namely observations which are known only to lie below some limit ofdetection. The task is accomplished using a Laplace-type approximation to theposterior distribution of the parameters and the suitability of this approximationis analysed through examples.The problems addressed in the thesis are motivated by the need to ensure environmentalquality in and around installations operated by the multinational companyShell. The assistance of Shell in advising on the context of the issues, and in providingdata sets for case studies, is much appreciated.