Sensitivity analysis and uncertainty analysis for vector geographical applications

The problem of the quality assessment of results from geographical applications can be tackled with the help of sensitivity analysis and uncertainty analysis techniques. Sensitivity analysis studies the relationships between the output and the inputs of an application. Uncertainty analysis aims at quantifying the overall uncertainty associated with the response of an application. Both techniques rely on the description of a geographical application by a numerical model. Uncertainty and sensitivity analyses are very well established techniques, with applications in many fields (nuclear, environmental, etc.). They rely on an array of techniques including Monte-Carlo simulations and ANOVA. However, they can only be performed when the output and input variables are scalar variables. This restriction can be handled when the geographical data is in raster format, but has many consequences for vector data. We discuss this point, and propose methods to overcome these limitations in case of vector and raster data. Our methods rely on a statistical modeling of uncertainty in the input variables that takes into account correlation, on the definition of summaries of the results in non-Euclidean spaces, and on simple meta-models linking the summaries of the output to the input variables. We also investigate the use of functional analysis, and high-dimensional model representations.