Mapping complex biological processes across the landscape: the problem of non-stationarity

Lead Research Organisation: Rothamsted Research
Department Name: Unlisted


The overall aim of this proposal is to develop a methodological framework for spatial analysis and estimation of variables that are incompatible with assumptions of stationarity in the variance, based on the linear mixed model. A framework would be based on the following hypotheses. Hypothesis (i). The non-stationarity in key soil variables can be modelled by an appropriate parameterization of the random-effect(s) in a linear mixed model, and these parameters can be estimated by residual maximum likelihood (REML). This will lead to improvement in spatial predictions. Hypothesis (ii). Evidence for differing kinds of non- stationarity in the variance can be identified by an exploratory analysis, and tested against a null hypothesis of stationarity. Hypothesis (iii). The non-stationarity in key soil variables can be emulated by process models that reflect our mechanistic understanding of how they arise. These hypotheses determine the objectives of the proposal, which are as follows. 1. To develop variance models with parameters to describe different aspects of non-stationarity for spatial linear mixed models (LMM). 2. To develop logically structured exploratory procedures to test the plausibility of assumptions of stationarity in the variance and to identify what non-stationary parameters might be needed for a suitable LMM. 3. To test Hypotheses (i) to (iii) above with the procedures developed under objectives 1 and 2. Thereby, to quantify the practical advantages of these new variance models over conventional geostatistics.4. To use the data and methods arising from the above objectives to test Hypothesis (iii) and to develop methods to use predictions from process models to improve the sampling and statistical modelling of data where non-stationarity in the variance is implausible.


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