Developing decision support based on field data and partial order theory

The corner stone in the development of decision support systems is to secure that the partial ordering of descriptors does reflect reality. The similarity between descriptor ranking and field scale data ranking is thus highly critical and this chapter shows how to establish this linkage. The partial order technique is used as a robust and non-parametric similarity quantification method and illustrated using monitoring data of pesticide findings in streams of Denmark. The approach has a general appeal where the consequence of false positives (accidentally identification of a similarity) is critical and/or only rough knowledge exist about relations between the data sets that are going to be analysed for similarity. A simple and transparent mapping of a correlation profile is possible and the software named Po Correlation supports the principle described in this chapter. The principle is an extension of the conventional

Kendalls Tau

that is modified to include ordering using more than two data sets simultaneously and thus being a kind of a multi-variate rank correlation analysis. The multi-variate nature opens up for several measures of discordance that shows different aspects of discrepancy between the data set. A graphical display using Hasse diagrams of respectively concordant and discordant rankings shows how individual objects are respectively correlated and anti-correlated with regard to all the other objects. A testing algorithm using randomized data sets are included in order to test for statistically significance of both similarity and discrepancy.