Founding body: Leverhulme Trust
Duration: October 2002 -- September 2005
Grant Holder: Qiwei Yao
This project is devoted to the research in the following four areas:
(i) We adopt semi-parametric techniques to model probabilistic characteristics of spatial processes. This new approach will facilitate modelling and/or approximating a possibly nonlinear relationship between the variable at one site and its nearest neighbours without manufacturing a unilateral order. As one of consequences, least square prediction will be feasible. (Note that the standard predictive technique --- kriging is merely a least square linear prediction).
(ii) Motivated by modelling predator-prey interaction in biological population data, we propose a class of spatio-temporal models for modelling data collected regularly in time and irregularly over space. The aim here is to model temporal dynamics and spatial correlation simultaneously. Spatial smoothing will be employed to improve the estimation for temporal dynamics. Spatial non-stationarity will be addressed in terms of a deformation approach.
(iii) Spatially global and local ARMA models for spatio-temporal processes will be investigated. In spite of the complex nature of analysing spatio-temporal data, the availability of observations over both space and time does bring in convenience to both statistical modelling and theoretical exploration. The gain is at its clearest in ARMA modelling: any autoregressive model based on its timely lagged variables is automatically unilateral in the sense of Whittle (1953). Such a model not only makes the theoretical exploration tractable, but is also directly applicable to modelling spatial dependence among neighbouring sites. Further we also propose a localised ARMA model for a specified site. The information cumulated over time will make validation and inference for such a model feasible. This approach is particularly useful for modelling data irregularly sampled over space from a spatio-temporal process which may be spatially non-stationary.
(iv) Sampling properties of quasi-maximum likelihood estimation for irregularly indexed spatial processes will be studies. This will fill in a long-standing theoretical gap of significant relevance to practice. We also investigate some advanced theoretical problems in the context of spatial processed defined on lattice, in order to gain fuller appreciation of the difference between spatial processes and time series.
The project offers a Post-Doctoral research-fellowship and a PhD studentship, both for a period of 3 years.