Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.547961
Title: Spatio-temporal models : low-rank approximation, inference and applications
Author: Rodrigues, Alexandre Loureiros
Awarding Body: Lancaster University
Current Institution: Lancaster University
Date of Award: 2010
Availability of Full Text:
Access from EThOS:
Abstract:
In this thesis we propose new statistical models and methods relevant to two broad areas of spatial statistics, namely geostatistics and point processes. The main body of the thesis is composed of three papers. In the first paper we propose a new parametric family of models for local-valued Spatio-temporal stochastic processes S(x,t) with non-separable covariance function. We show how low-rank approximations can be used to overcome the computational problems that arise in fitting the proposed class of models to large datasets. We define positive, zero and negative non-separability and show how our proposed family can capture all three cases by varying the value of a single parameter. In the second paper we use the new class of models from the first paper, together with results concerning the superposition of Cox processes, to propose a method for conducting likelihood-based inference for spatio-temporal log-Gaussian Cox processes. We use the methodology to propose a surveillance system for the detection of emergent spatio-temporal clustering in the distribution of homicides in the city of Belo Horizonte, Brazil. In the third paper we present. a semi-parametric approach to modelling the effect of point-source interventions on the intensity function of a spatial point process. We apply our methodology to a crime dataset from Belo Horizonte, Brazil The primary goal of the application is to quantify the effect of the installation of 60 CCTV cameras on "the spatial distribution of crimes. Again using the data from Belo Horizonte, we extend our ideas to the spatio-temporal setting, to enable investigation of a possible dilution of the cameras' effect over time. The first paper has been accepted for publication in the Scandinavian Journal of Statistics (Rodrigues and Diggle, 2009a), the second is under submission to the Journal of the American Statistical Association (Rodrigues and Diggle, 2009b), the third has been provisionally accepted by the Journal of the Royal Statistical Society: Series C (Rodrigues et al., 2009)
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.547961  DOI: Not available
Share: