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math.PR2022
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…
math.PR2020
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…
math.PR2018
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…