Project Details
Projekt
Development of sequential statistical methods for detection and identification of changes in matrixvariate processes with application to image analysis, finance and network data.
Subject Area
Statistics and Econometrics
Term
since 2022
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 501239383
The goal of the project is to develop statistical methods for the rapid detection and identification of changes in matrix-valued processes. Such process structures are nowadays encountered in many scientific disciplines such as engineering, economics, and information sciences. The fast detection and identification of changes is of great relevance, for example, to reduce production costs and optimize process flows, to detect environmental changes at an early stage, to quickly uncover suspicious activities in networks. The new methods developed in the theoretical part of the project are based on the further development of sequential monitoring methods for vector-valued data to the so far little explored area of matrix-valued data sources. We focus on the construction of tools and methods that capture the complex temporal dependencies and cross-sectional dependencies between components of the matrix-valued data stream. Special attention is given to the scalability of the methods to ensure applicability to high-dimensional data sources. In addition, the associated computational problems for calculating the performance measures of the monitoring methods are analyzed in detail. The proposed methods have a wide range of applications covering all areas characterized by matrix-valued data. In the application part of the project, we focus on important examples from different areas of social and natural sciences, but this by far does not exhaust the possibilities. We study financial risks quantified by covariance matrices, image processes given by matrices of pixel intensities, and networks characterized by adjacency matrices.
DFG Programme
Research Grants
