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Interactive Visualization and Computation of 2D and 3D Probability Distributions

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Abstract

Mathematical modeling, probability estimation, and statistical inference represent core elements of modern artificial intelligence (AI) approaches for data-driven prediction, forecasting, classification, risk estimation, and prognosis. Currently, there are many tools that help calculate and visualize univariate probability distributions. However, very few resources venture beyond into multivariate distributions, which are commonly used in advanced statistical inference and AI decision-making. This article presents a new web-calculator that enables some calculation and visualization of bivariate and trivariate probability distributions. Several methods are explored to compute the joint bivariate and trivariate probability densities, including the optimal multivariate modeling using Gaussian copula. We developed an interactive webapp to visually illustrate the parallels between the mathematical formulation, computational implementation, and graphical depiction of multivariate probability density and cumulative distribution functions. To ensure the interface and functionality are hardware platform independent, scalable, and functional, the app and its component widgets are implemented using HTML5 and JavaScript. We validated the webapp by testing the multivariate copula models under different experimental conditions and inspecting the performance in terms of accuracy and reliability of the estimated multivariate probability densities and distribution function values. This article demonstrates the construction, implementation, and utilization of multivariate probability calculators. The proposed webapp implementation is freely available online (https://socr.umich.edu/HTML5/BivariateNormal/BVN2/) and can be used to assist with education and research of a diverse array of data scientists, STEM instructors, and AI learners.

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Acknowledgements

Partial support for this work was provided by NSF grants 1916425, 1734853, 1636840, 1416953, 0716055 and 1023115, NIH grants P20 NR015331, UL1 TR002240, R01 CA233487, R01 MH121079, R01 MH126137, T32 GM141746. The funders played no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. Colleagues at the University of Michigan Statistics Online Computational Resource (SOCR) and the Michigan Institute for Data Science (MIDAS) contributed ideas, infrastructure, and support for the project.

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  1. Statistics Online Computational Resource (SOCR), University of Michigan, Ann Arbor, MI, 48109, USA

    Mark Bobrovnikov, Jared Tianyi Chai & Ivo D. Dinov

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  1. Mark Bobrovnikov
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Correspondence to Ivo D. Dinov.

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Bobrovnikov, M., Chai, J.T. & Dinov, I.D. Interactive Visualization and Computation of 2D and 3D Probability Distributions. SN COMPUT. SCI. 3, 327 (2022). https://doi.org/10.1007/s42979-022-01206-w

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