title: INTERACTIVE VISUALIZATION OF PROBABILITY AND CUMULATIVE DENSITY FUNCTIONS.
abstract: The probability density function (PDF), and its corresponding cumulative density function (CDF), provide direct statistical insight into the characterization of a random process or field. Typically displayed as a histogram, one can infer probabilities of the occurrence of particular events. When examining a field over some two-dimensional domain in which at each point a PDF of the function values is available, it is challenging to assess the global (stochastic) features present within the field. In this paper, we present a visualization system that allows the user to examine two-dimensional data sets in which PDF (or CDF) information is available at any position within the domain. The tool provides a contour display showing the normed difference between the PDFs and an ansatz PDF selected by the user and, furthermore, allows the user to interactively examine the PDF at any particular position. Canonical examples of the tool are provided to help guide the reader into the mapping of stochastic information to visual cues along with a description of the use of the tool for examining data generated from an uncertainty quantification exercise accomplished within the field of electrophysiology.
authors.affiliation: Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah, 84112, USA.
authors.forename: Kristin
authors.initials: K
authors.lastname: Potter
authors.forename: Robert M
authors.initials: RM
authors.lastname: Kirby
authors.forename: Dongbin
authors.initials: D
authors.lastname: Xiu
authors.forename: Chris R
authors.initials: CR
authors.lastname: Johnson
keywords: cumulative density function; generalized polynomial chaos; probability density function; stochastic Galerkin methods; stochastic collocation methods; visualization
references.citation: IEEE Comput Graph Appl. 2004 Jul-Aug;24(4):13-7
references.pmid: 15628080
references.citation: IEEE Trans Biomed Eng. 2008 Jan;55(1):31-40
references.pmid: 18232344