Approximate Parametrisation of Confidence Sets
In various geometrical applications, the analysis and the visualization of the error of calculated or constructed results is required. This error has very often character of a nontrivial multidimensional probability distribution. Such distributions can be represented in a geometrically interesting way by a system of so called confidence sets. In our paper we present a method for an approximate parametrisation of these sets. In sect. 1 we describe our motivation, which consists in the study of the errors of so called Passive Observation Systems (POS). In sect. 2 we give a result about the intersection of quadric surfaces of revolution, which is useful in the investigation of the POS. In sect. 3 we give a general method for an approximate parametrisation of the confidence sets via simultaneous Taylor expansion. This method, which can be applied in a wide range of geometrical situations, is demonstrated on a concrete example of the POS.
KeywordsTaylor Expansion Observation Site Multivariate Normal Distribution Multivariate Distribution Quadric Surface
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