Probability Seminar - Patricia Alonso-Ruiz
Institution: University of Connecticut
Title: Entropy-based inhomogeneity detection in marked Poisson point processes
Date: Thursday, April 12, 2018
Location: C405 Wells Hall
Time: 3:00 PM - 3:50 PM
Glass fiber reinforced polymers constitute a type of plastics characterized by their light weight, versatility and strength. For instance, they are present in many automotive components: the lower a vehicle's weight, the less fuel it uses and the fewer carbon dioxide it emits. This type of materials can be modeled by marked Poisson point processes, whose marks correspond to any quantity of interest, as for instance the direction of the fibers.
In this talk we will discuss a non-parametric estimator for the entropy of the mark distribution based on classical constructions for sequences of random variables and kernel density estimation on Riemannian manifolds. We will also explain how the asymptotic normality of the estimator and scan statistics can be applied to develop a method to detect inhomogeneities that may arise in the production process of pieces made out of glass fiber reinforced polymers. The entropy will be used as a measure of changes in the directional distribution of fibers.
Joint work with E. Spodarev.