Statistics Colloquium

Please join the Mathematics Department Colloquium on April 3rd at 5 pm in NYS 250 Main CAS Innovation Lab Instruction Space. Our speaker is Kyung Ingargiol. The title and abstract are

Title: Exploring Copulas: Understanding Dependence Modeling 

Abstract: A copula is a beautiful statistical tool for modeling dependence structures between random variables, independently of their individual distributions. This presentation offers an intuitive and practical introduction to copulas, beginning with foundational probability concepts - including the probability and quantile transformations - and leading into key theorems such as Sklar’s Theorem, the Invariance Property, and the Fréchet-Hoeffding bounds. We explore several families of copulas - including Gaussian, t, and Archimedean - highlighting their strengths and limitations supported by visualizations. Measures of dependence such as Pearson’s correlation, rank-based coefficients, and tail dependence will also be discussed.

The second part of the talk connects theory to real-world dependence modeling. We revisit the infamous role of the Gaussian Copula in finance, where a misunderstanding of tail dependence contributed to the 2008 financial crisis. Finally, we introduce an engaging research case study that addresses the challenge of estimating dependence when the data is unordered. Through empirical and nonparametric methods, we demonstrate that meaningful dependence structures can still be recovered even when information is incomplete.