Nonparametric Models for Uncertainty Visualization

Abstract

An uncertain (scalar, vector, tensor) field is usually perceived as a discrete random field with a priori unknown probability distributions. To compute derived probabilities, e.g. for the occurrence of certain features, an appropriate probabilistic model has to be selected. The majority of previous approaches in uncertainty visualization were restricted to Gaussian fields. In this paper we extend these approaches to nonparametric models, which are much more flexible, as they can represent various types of distributions, including multimodal and skewed ones. We present three examples of nonparametric representations: (a) empirical distributions, (b) histograms and (c) kernel density estimates (KDE). While the first is a direct representation of the ensemble data, the latter two use reconstructed probability density functions of continuous random variables. For KDE we propose an approach to compute valid consistent marginal distributions and to efficiently capture correlations using a principal component transformation. Furthermore, we use automatic bandwidth selection, obtaining a model for probabilistic local feature extraction. The methods are demonstrated by computing probabilities of level crossings, critical points and vortex cores in simulated biofluid dynamics and climate data.