11 citations · 14 across the 8 of their papers we have counts for
8 papers
Random Measures, ANOVA Models and Quantifying Uncertainty in Randomized Controlled Trials
Caleb Deen Bastian, Herschel Rabitz, Grzegorz A Rempala
The paper introduces a novel approach to global sensitivity analysis, grounded in the variance-covariance structure of random variables derived from random measures. The proposed m…
A field equation for induction-transduction of activation-deactivation probability on measurable space
Caleb Deen Bastian, Herschel Rabitz
Induction-transduction of activating-deactivating points are fundamental mechanisms of action that underlie innumerable systems and phenomena, mathematical, natural, and anthropoge…
Random Graphs by Product Random Measures
Caleb Bastian, Herschel Rabitz
A natural representation of random graphs is the random measure. The collection of product random measures, their transformations, and non-negative test functions forms a general r…
The Jacobi Theta Distribution
Caleb Deen Bastian, Grzegorz Rempala, Herschel Rabitz
We form the Jacobi theta distribution through discrete integration of exponential random variables over an infinite inverse square law surface. It is continuous, supported on the p…
Uncertainty Quantification by Random Measures and Fields
Caleb Deen Bastian, Herschel Rabitz
We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitiv…
Orthogonal Dice
Caleb Deen Bastian, Herschel Rabitz, Grzegorz A Rempala
In this paper, we introduce a family of discrete rectangular uniform distributions on the natural numbers-referred to as orthogonal dice-characterized by the property that their me…
High Dimensional Model Representation as a Glass Box in Supervised Machine Learning
Caleb Deen Bastian, Herschel Rabitz
Prediction and explanation are key objects in supervised machine learning, where predictive models are known as black boxes and explanatory models are known as glass boxes. Explana…
Throwing Stones and Collecting Bones: Looking for Poisson-like Random Measures
Caleb Deen Bastian, Grzegorz A. Rempala
We show that in a broad class of random counting measures one may identify only three that are rescaled versions of themselves when restricted to a subspace. These are Poisson, bin…