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Analysing and visualizing spatial uncertainty

Organised by the Environmental Statistics Section of the Royal Statistical Society and The Food and Environment Research Agency.

Wednesday 27 January 2010, 1-5pm

The Food and Environment Research Agency, York, YO41 1LZ

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Analysing spatial uncertainty is a twofold problem: firstly, how to quantify the spatial uncertainty; secondly, how to visualise this uncertainty cartographically. As policy decision-making increasingly relies on statistical and spatial models, the analysis and visualisation of spatial uncertainty is a very important, but often overlooked, aspect of communicating spatial evidence. This workshop will consist of a series of talks on various statistical and cartographic approaches for quantifying and visualising spatial uncertainty followed by a discussion session to explore future developments.

A summary of the meeting and talks can be found here .


The speakers are


The Food Environment Research Agency is a 20min taxi ride from York station, see the map .

Or a slightly longer bus journey on the ‘Coastliner’, see here.


The programme is yet to be announced.

Please contact Helen Owen for further details.


Vasily Demyanov: Uncertainty in spatial models: geostatistical and machine learning approaches.

Uncertainty is an inherent feature of our understanding of the explored reality. We can distinguish between uncertainty in mathematical models, which reflect our knowledge about nature; numerical errors, related to the accuracy of the computed solution due to discretisation etc.; data uncertainty, which correspond to the quality and relevance of the available observations.

Uncertainty modelling helps to address practical questions, such as: how accurate and variable the prediction is, what is the risk of taking the decision on the prediction, where to obtain further measurements to improve the prediction usability.

The presentation reviews a range of modelling approaches used to solve spatial prediction and classification problems. Geostatistical algorithms (kriging, stochastic simulations) model spatial correlation and variability and are widely used in mapping. Machine learning, more recently applied to spatial modelling, provides an alternative approach to discover patterns in data and build spatial predictions based on the extracted dependencies. Both approaches have their advantages and drawbacks. Thus, the problem of prediction uncertainty is addressed differently in geostatistics and machine learning. Hybrid algorithms combine the benefits of machine learning and geostatistics to model complex multi-scale spatial patterns.

Bayesian thinking is also applied extensively to tackle uncertainty quantification problem. Bayesian Maximum Entropy is one of the approaches, which demonstrates successful integration of prior knowledge into spatial prediction models. Other studies demonstrate how geostatistical and machine learning models are linked with Bayesian approach to quantify uncertainty based on estimated posterior probability of the predictions.

Visualisation of spatial uncertainty is largely tailored by the synergy between the demands of decision-making and by the available spatial prediction modelling tools. Conventional prediction maps are usually supported by spatial error distribution maps. "Thick" contours provide the way to integrate both estimates and errors in a unique decision-oriented map. Probabilistic and stochastic geostatistical models are capable of mapping risk as probability of exceeding decision-making levels. Machine learning algorithms can also provide similar probabilistic results (e.g. probabilistic neural networks) as well as task-oriented maps to optimise further measurement campaigns (e.g. Support Vector Machines).

Peter Atkinson: Spatial uncertainty in remote sensing
Uncertainty arises in remote sensing through the acquisition of data (measurement process), through model choice and model fitting, and through prediction, forecasting or stochastic simulation. This paper will review several sources of uncertainty and discuss the effect of remote sensing operations on input uncertainty. The discussion will be provided in the context of examples of (i) spatial prediction of sleeping sickness in Uganda using logistic regression, (ii) downscaling of remote sensing images in Southampton using look-up-based approaches and and (iii) remote sensing of changes in tropical vegetation phenology in India using Fourier-based smoothing.
Dan Cornford and Lucy Bastin: Computer says maybe ...
In this talk we will discuss the issues around the management of uncertainty in (geospatial) computer models. We will consider spatial uncertainty to mean uncertainty over outputs (or inputs) which are spatial fields. There are a wide range of statistical and deterministic models that can be used for prediction, and other tasks, in such settings. These models are all implemented as computer code, and the increasing use of such models in decision making and policy settings calls for tools to enable their analysis accounting for uncertainty in a principled framework. Computers, however, do not speak probabilities and thus we have developed an interoperable encoding for uncertain information, UncertML, which we are proposing as an international standard to allow computers to say "maybe" (in a carefully quantified setting). Within the soon to start UncertWeb project we will extend UncertML to include further representations of uncertainty, and develop a set of tools to allow users to define, visualise and manage the uncertainties in systems of coupled, or chained models. We will explain how the communication layer will allow us to integrate a range of approaches, and using the INTAMAP project results we will show some simpler interoperable web based systems which can manage spatial uncertainty. We will discuss some of the challenges we face in applying uncertainty propagation to service chains, briefly mentioning emulation approaches as an interesting partial solution. We will suggest directions requiring further research.
James Aegerter: Predicting the establishment and spread of non-native species: n dimensions of uncertainty but only one map
With a changing environment (land use and climate) there is a need to predict how wildlife distributions will change, where populations will become abundant enough to be problematic and how changing wildlife disease epidemiology may cause concern.  Fundamental to all of those predictions are robust and meaningful spatially explicit models of wildlife populations across real landscapes.

We have been re-examining some of the popular methodologies of how to conceptualise and undertake a generic spatial population modelling approach and have developed methods that minimise or remove common biases or allow us to more transparently deal with variability and uncertainty throughout the modelling process.  These have included newer ways of representing landscapes in models (helping to deal with some of the uncertainties present in maps of real world landscapes) and better ways of parametrising and modelling population processes.  The list of uncertainties is long and they interacts to produce mapped output whose quality and utility should only be judged alongside its uncertainty.

At the end of this process however we are left with a familiar dilemma, a rich mapped dataset describing a spatially variable landscape of probabilities, often described by varying asymmetrical distributions. For any given scenario (and there may be many) we'd prefer to condense this to one map which will not allow the casual reader to misinterpret it output.

Peter Fisher: Semantic Uncertainty
Much scientific knowledge is summarised and encoded by giving names to things, as is much common knowledge. The act of naming something is often fraught with difficulty, however, due to uncertainty about the boundary con; when is a stool a chair, when is a buildings a house or a home. Formal languages of science sometimes evolve through decades and sometimes are invented by committees giving years of consideration to thresholds to be applied in a particular scheme of naming. The US Soil Conservation Service, for example, went through 7 revisions (Approximations) over many years before publishing their definitive hierarchical Soil Taxonomy (Soil Survey Staff, 1975) and even then they changed from having 10 orders at the highest level of the classification system to having 12 orders in the 1999 second edition (Soil Survey Staff, 1999). In Britain, between the 1990 and 2000 mappings of land cover the system used for classification changed in a number of ways, but most relevantly here in 1990 the classification scheme had 25 “target classes” and in 2000 it had 26 “broad habitats”; there are many-to-many, one-to-many and many-to-one relationships between the classes in the two schemes. Such changes occur for many reasons; to make science more policy relevant, to reflect improved understanding of phenomena, to encompass novel analytical methods.Use of uninitialized value in concatenation (.) or string at E:\listplex\SYSTEM\SCRIPTS\filearea.cgi line 455, line 222. The consequence is, however, to cause some degree of doubt and confusion among those more peripherally involved in using the information. The problem of naming is compounded by the threshold conditions and significance being attached to particular threshold values around boundaries between classes. The question that arises is whether a particular threshold is really significant, and whether objects close to but either side of the boundary are really significantly different in terms of process; if a patch of land is labelled as woodland because it has 41% trees when the threshold for woodland is 40% trees, is it ecologically significantly different form a patch of woodland with only 39% trees?

Fuzzy sets are intended specifically to address the boundary conditions for set membership. In this presentation I will examine the application of fuzzy sets to land cover mapping giving justification and some methodological background. I will outline some of the challenges of using fuzzy sets and discuss some recent research looking at higher order vagueness or type 2 fuzzy sets (Fisher 2009) and at fuzzy land cover change (Fisher et al., 2006).


  • Fisher P.F., 2009. Remote Sensing of Land Cover Classes as Type 2 Fuzzy Sets. Remote Sensing of Environment. doi:10.1016/j.rse.2009.09.004
  • Fisher, P., Arnot, C., Wadsworth, R., and Wellens, J., 2006, Detecting change in vague interpretations of landscapes. Ecological Informatics, 1: 163-178, doi:10.1016/j.ecoinf.2006.02.002   
  • Soil Survey Staff (1975), Soil Taxonomy A Basic System of Soil Classification for Making and Interpreting Soil Surveys. Natural Resources Conservation Service Number 436 US Government Printing Office Washington, DC 20402.
  • Soil Survey Staff (1999), Soil Taxonomy A Basic System of Soil Classification for Making and Interpreting Soil Surveys 2nd Edition. Natural Resources Conservation Service Number 436 US Government Printing Office Washington, DC 20402.

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