Multivariate statistics is a branch of statistics that involves the simultaneous observation and analysis of more than one outcome variable. The need and motivation for using multivariate statistics arise from various aspects:
1. Complexity of Real-World Data: In many real-world scenarios, particularly in fields like biology, sociology, economics, and psychology, multiple variables interact with each other. Multivariate statistics allow for a more realistic and comprehensive analysis of these complex relationships than univariate methods do.
2. Understanding Interdependencies: Multivariate methods enable researchers to explore the interdependencies and correlations among multiple variables.
3. Increased Accuracy and Insight: Analyzing multiple variables simultaneously can provide a more accurate and deeper understanding of the phenomena under study. It helps in capturing the essence of complex systems where the interaction between variables is as important as the
individual variables themselves.
4. Prediction and Forecasting: Multivariate statistical models are essential for making predictions in scenarios where multiple outcomes are of interest.
5. Data Reduction and Pattern Recognition: Techniques such as principal component analysis and independent component analysis help in data reduction — simplifying large datasets to their most informative components.
6. Customization of Analysis: Different multivariate techniques cater to different types of data and research questions, allowing for a tailored approach to data analysis. This customization leads to more precise and relevant findings.
In summary, multivariate statistics are pivotal in a world increasingly characterized by big data and complex systems. They offer the tools to not only keep pace with the richness of this data but also to extract meaningful insights that would be impossible to detect using only univariate methods.
Our research group develops modern and efficient multivariate statistical methods tailored for different types of multivariate data, such as time series, spatial data, spatio-temporal data, or
tensor-valued observations.
Key areas of our research are dimension reduction, where our focus lies in blind source separation approaches, and nonparametric and robust multivariate methods, which provide reliable knowledge from noisy data.
Our methods have been used, for example, in areas such as climate modeling, geochemical exploration, neuroimaging, customer loyalty data analysis, quality control, predictive maintenance, financial time series, medical data, and more.
If you are interested in a master's thesis topic, a doctoral thesis, or some other kind of cooperation, please contact Klaus Nordhausen.