Nonparametric Models for Uncertainty Visualization

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...

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Vydáno v:	Computer graphics forum Ročník 32; číslo 3pt2; s. 131 - 140
Hlavní autoři:	Pöthkow, Kai, Hege, Hans-Christian
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Oxford, UK Blackwell Publishing Ltd 01.06.2013
Témata:	Analysis Computer based modeling Computer graphics Density Fluid dynamics G.3 [Mathematics of Computing]: Probability and Statistics-Nonparametric statistics I.3.3 [Computer Graphics]: Picture/Image Generation-Viewing algorithms I.6.8 [Simulation and Modeling]: Types of Simulation-Monte Carlo I.6.8 [Simulation and Modeling]: Types of Simulation—Monte Carlo, Visual Mathematical analysis Mathematical models Probabilistic methods Probability Probability theory Random variables Representations Studies Uncertainty Visual Visualization
ISSN:	0167-7055, 1467-8659
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Popis
Shrnutí:	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.
Bibliografie:	istex:A625F47DC0CA0CFC98A3C262A39E2B8A81A6329A ark:/67375/WNG-TD4KP2ZL-F ArticleID:CGF12100 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0167-7055 1467-8659
DOI:	10.1111/cgf.12100