INTAMAP developments

Scientific developments

Projected spatial gaussian process (psgp) methods

The projected spatial gaussian process method was developed and implemented at the Aston University. The main aim of the method is to address two issues:

  1. the cubic growth in computational complexity for likelihood based inference in Gaussian process models (model based Geostatics) which limits their application to smallish data sets of less than 2000 observations;
  2. The inability of most geostatistical methods to deal with non-Gaussian errors on observations, or non-linear sensor models.
These are important issues, since data sets are likely to become larger and sensing technology allows progressively cheaper sensors to be developed, and sensors are increasingly developed to measure quantities remotely, and often using indirect methods. For example a scatterometer can be used to infer wind speed and direction, but the observation is made of backscattered radar power - this is unlikely to have a Gaussian distribution (power must be postive for example) and has a strongly non-linear relationship to wind speed and direction. Encoding the representation of the sensor model (the mapping from the state variable of interest to the observed quantity) uses the MathML encoding in a SensorML document. The representation of the error characteristics of the sensor can use UncertML.

psgps can work with a range of observation and error models

The psgp method addresses the issue of computational complexity by utilising a projected representation of the posterior process, which limits the complexity of the approach. Within the INTAMAP service no more than 400 active points are used to ensure large data sets can be handled. The sequential aspects comes from the fact each observation is processed in turn. This allows us to replace very high dimensional integrals that would be required in the batch processing case, with low (typically single) dimensional integrals that can be relatively quickly an accurately evaluated. This is what enables us to handle any sensor model (described in MathML) and arbitrary error distirbutions (currently only Gaussian and Exponential are implemented in the operational system). A full description is beyond the scope of this page however more complete descriptions of the method can be found in the following papers and reports:

Deliverable 4.4 Sparse, sequential methods for a range of observation types and spatial supports

Deliverable 2.3 Improved methods for hyper-parameter identification in the sparse, sequential framework

D 3.3 Sequential methods using robust likelihood models

Ingram, B., Cornford, D. and Barillec, R., 2009. Projected Sequential Gaussian Processes: Flexible Interpolation for Large Data Sets. StatGIS2009, 16-18 June 2009, Milos, Greece.

Ingram, B., D. Cornford, and D. Evans (2008) Fast algorithms for automatic mapping with space–limited covariance functions. Stochastic Environmental Research and Risk Assessment, 22(5): 661-670