Year: 2025
Type: conference-paper
Abstract: This brief paper gives an overview of our breakthrough Holistic Probabilistic Design (HPD) Software and Methodology that revolutionizes Stochastics with fundamentally new techniques and tools for Stochastic Modeling, Analysis, and Optimization for simple or complex systems.Even more fundamentally, a major implication of two of HPD's key advancements is that it "liberates" probability distributions.One aspect of liberation is the following: Currently Stochastic Analysis utilizes existing, or known, types of distributions, but these are just a small discrete set within the continuum of distribution space consisting of an infinitude of types, or no types at all.We will also discuss why most of the known distribution types are actually not reasonable for real-world applications.The second aspect of liberation is that distributions no longer need to be given as functions; they are digitized and exist as "Data-Type" distribution files and plots.Handling data-type distributions is included in HPD which has taken many intermittent years for the authors to develop.The methodology prescribes how to structure the work process for, and stochastically model, a complex problem with numerous random variables that should be addressed.The software (i) is monumental in size, (ii) has an extremely user-friendly graphical user interface (GUI), and (iii) will be imminently made available open-source.The fundamental breakthrough of the HPD software is being able to compute the "exact" output distribution for any relationship, z = g(x1, x2, …, xN) for "any" set of input distributions, for that led to liberating distributions.HPD is based on our SMB (º Stochastic Modeling Based) technique which has overcome the well-known "curse of dimensionality" issue.The authors are currently completing a book on revolutionizing Stochastics that includes rigorous mathematical concepts and computational techniques for the HPD capabilities.Such documentation is necessary for leaving to posterity.The authors originally intended to market the software, but have now concluded that making it freely available to the Stochastics community is a far more satisfying outcome.Liberating distributions will have a consequential impact on existing literature, techniques, and tools in Applied Probability and Stochastics.And HPD's availability would enable revolutionizing Stochastics to take hold.
Institution: California Polytechnic State University
Language: English
Subfield: Statistics, Probability and Uncertainty
Field: Decision Sciences
Domain: Social Sciences
Open Access status: gold
OpenAlex ID: W4411488924