INTERACTIVE VISUALIZATION OF PROBABILITY AND CUMULATIVE DENSITY FUNCTIONS

Potter, Kristin; Kirby, Robert Michael; Xiu, Dongbin; Johnson, Chris R.

INTERACTIVE VISUALIZATION OF PROBABILITY AND CUMULATIVE DENSITY FUNCTIONS

Type

Article

Authors

Potter, Kristin
Kirby, Robert Michael
Xiu, Dongbin
Johnson, Chris R.

KAUST Grant Number

KUS-C1-016-04

Date

2012

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.

Citation

Potter K, Kirby RM, Xiu D, Johnson CR (2012) INTERACTIVE VISUALIZATION OF PROBABILITY AND CUMULATIVE DENSITY FUNCTIONS. International Journal for Uncertainty Quantification 2: 397–412. Available: http://dx.doi.org/10.1615/Int.J.UncertaintyQuantification.2012004074.

Acknowledgements

This is a collaborative research project based on work supported in part by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), and supported under NSF IIS-0914564 (R.M.K.) and NSF IIS-0914447 (D.X.) and through DOE NETL DE-EE0004449 (C.R.J./R.M.K.) and NIH 2P41 RR0112553-12 (C.R.J.). Infrastructure support provided through NSF-IIS-0751152.