INTERACTIVE VISUALIZATION OF PROBABILITY AND CUMULATIVE DENSITY FUNCTIONS

Area of Science:

• Data Visualization
• Computational Statistics
• Scientific Computing

Background:

• Probability density functions (PDFs) and cumulative density functions (CDFs) are crucial for characterizing random processes and fields.
• Assessing global stochastic features in two-dimensional fields with spatially varying PDFs is challenging.
• Existing methods often lack interactive tools for detailed examination of localized statistical information.

Purpose of the Study:

• To present a new visualization system for exploring two-dimensional data with available PDF/CDF information at each point.
• To enable users to interactively analyze stochastic properties within complex data fields.
• To facilitate the understanding of uncertainty quantification in scientific domains like electrophysiology.

Main Methods:

• Development of a visualization system capable of processing two-dimensional datasets with spatially distributed PDFs.
• Implementation of a contour display to visualize the normed difference between local PDFs and a user-selected ansatz PDF.
• Integration of interactive features for on-demand PDF examination at any domain position.

Main Results:

• The system effectively visualizes the spatial distribution of stochastic information within two-dimensional fields.
• The contour display provides a clear overview of deviations from a reference PDF.
• Interactive exploration allows for detailed analysis of local statistical properties.

Conclusions:

• The developed visualization system offers a powerful approach for analyzing complex stochastic data.
• It enhances the interpretability of uncertainty quantification results, particularly in fields like electrophysiology.
• The tool bridges the gap between raw data and actionable statistical insights.