Our research areas

Model-based clustering with vine copulas

Members: Özge Sahin, Claudia Czado
Description: Finite mixture models are convenient statistical tools for model-based clustering. In this framework, one assumes that the data can be clustered using k components. The most prominent finite mixture model for continuous data is the mixture of multivariate Gaussian distributions (GMM). However, GMMs cannot accommodate the true shape of the non-elliptical components and model asymmetric dependencies within them. Since it is well known that vine copulas are very flexible in capturing dependencies, our main objective is to develop a vine copula mixture model and use it for model-based clustering, especially for the non-Gaussian data.
Results: [Talk in Bernoulli-IMS One World Symposium  | Presentation in Bernoulli-IMS One World Symposium]

Vine copula-based classification approach for multivariate time series data

Members: Chunfang Zhang, Claudia Czado
Description:  In applications we often observe multivariate time series exhibiting complex dependence structures as well as nonstationary behavior dependence. It is a difficult task to perform classification based on such multivariate time series data. We introduce a vine copula based approach to model such time series data. For this we use univariate nonstationary time series models for each time series to obtain approximately i.i.d. residuals. The dependence among the residuals are then captured by a vine copula. This approach is applied to each class and classification is now performed using a Bayes classifier.  This approach will be applied to time series derived from  a neural activity experiment to classify the opening and closing of the eyes. The performance to other classification methods will be investigated.

Statistical learning with vines for (quantile) regression

Members: Marija Tepegjozova, Claudia Czado
Description: Quantile regression is a field with growing importance for statistical modeling. It offers a more complete statistical model than mean regression and thus has widespread applications. We aim to develop a new method, that will overcome the usual drawbacks of the standard models, such as quantile crossings, distributional assumptions and misspecification of the tail dependencies. Our idea how to overcome such shortfalls, is to use vine copula based quantile regression. Vine-copulas allow for highly flexible modeling of high-dimensional dependence structures, and developing a  vine based quantile regression with automated covariate selection procedure is the main research objective.
Results: [Talk in Bernoulli-IMS One World Symposium  | Presentation in Bernoulli-IMS One World Symposium]

Flight safety analysis via copula state space models

Members: Hassan Alnasser, Ariane Hanebeck, Claudia Czado
Description: Since airlines are required by law to implement a Safety Management System (SMS) for flight operations, each airline must commit to an Acceptable Level of Safety Performance (AloSP). This leads airlines to express the ALoSP in terms of numerical values. Europe’s vision in 2050, for example, defines a minimum safety target of less than one accident per ten million flights. Methods used to analyze flight data, up until recently, have been often simplistic. For example, accident probabilities are computed as the number of accidents divided by the total number of operations. We aim to propose a flexible stochastic approach to characterize temporal and special noise dependence structures obtained from flight data via copula based state space representations. Here, we want to step away from Gaussian dependencies if necessary. The goal is to build a framework that utilizes flight data, while still combining the physical and statistical representation of aircraft motion. Focus will be on accident probabilities as well as the data during take off and the initial climb.