## Research

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# Statistical modeling

Researchers: Lubomír Kubáček, Karel Hron, Eva Fišerová, Ondřej Vencálek, Ivo Müller

Our group concentrate on linear regression models and statistical analysis of compositional data, though other branches of statistics are also included, e.g. statistical analysis of a so-called data depth. Regression analysis, traditionally having a broad range of applications primarily in science (physics, chemistry, biology etc.), studies relationships among variables, and through statistical reasoning (e.g. tests of hypotheses) can answer many pertinent questions of quantifying the effect of input (independent) variables on output (dependent) variables. Statistical analysis of compositional data is a new area of statistics which is devoted to developing a systematic approach to analyzing data containing a relative type of information (in particular percentage or proportional data, but commonly also measurements of chemical or geological variables). Results obtained so far suggest that this approach holds great promise for statistical analysis of data sets not only from natural science but also from economics and social science (sociology, demography). We closely cooperate with experts on applied problems, e.g. in metrology, geology (analyzing data from the international geological project GEMAS mapping the composition of soils throughout Europe, see figure), analytical chemistry, medicine, and biomedical research (Biomedreg), and we are open to making new contacts with everybody who need to statistically analyze data in their work.

Figure:Geological composition of soils in Northern Europe with highlighted outlying observations (above); plotted in a line graph (below)..

Filzmoser, P., Hron, K., Reimann, C. *Interpretation of multivariate outliers for compositional data*. Computers &
Geosciences, *39* (2012), 77-85.