Multivariate statistics

 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 Sara Taskinen or Klaus
Nordhausen.