Research Areas of the Department of Mathematical Statistics and Data Mining

The Department’s research encompasses the development of methods in mathematical statistics, probabilistic analysis of system reliability, and applications of statistical methods and machine learning in interdisciplinary research. Current and planned work focuses on three main areas.

High-Dimensional Data, Time Series, and Statistical Estimation

Research includes developing and comparing methods for selecting relevant features in high-dimensional models, where the number of variables is large relative to the number of observations. It also addresses methods for analysing data with partially observed labels and under label shift. Other important research directions include graphical models for time series and continuous-time processes, as well as methods for estimating distribution parameters and investigating their properties under various modelling assumptions.

Probabilistic and Statistical Methods in Reliability Analysis

Research focuses on binary and multi-state systems, in which both individual components and the system as a whole may operate at different performance levels. Particular attention is given to models with discrete component lifetimes, which allow multiple components to fail simultaneously. The structures considered also include systems with cold standby components and weighted systems, in which components differ in their contributions to overall system performance. An important research direction is the development and application of discrete system signatures, extending Samaniego’s approach, to characterise and analyse system reliability.

Statistical Data Analysis and Interdisciplinary Applications

Research includes applications of statistical methods and machine learning to data from fields such as medicine, geology, geography, and ecology. The methods employed include cluster analysis, analysis of variance, hypothesis testing, predictive modelling, and neural networks. This work aims to identify patterns in data, investigate relationships, and draw inferences about the phenomena under study. This work is carried out in collaboration with researchers from other disciplines, including within the Priority Research Areas (Discovery, Diagnostics, Therapy for Healthcare, D2TH) at the Institute of Advanced Studies of Nicolaus Copernicus University.