11 citations · 14 across the 8 of their papers we have counts for
5 papers · 1 filter
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…
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…