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Saturday, August 10, 2019

Mathematicians develop new statistical indicator | Mathematics - Phys.Org

Most of us know this phenomenon only too well: when it's hot outside, you feel the urge for a cooling ice cream. But would you have thought that mathematics could be involved? by TU Dresden.

Photo: Pexels
Let us explain: The rising temperatures and rising ice consumption are two statistical variables in linear dependence; they are correlated.
In statistics, correlations are important for predicting the future behaviour of variables. Such scientific forecasts are frequently requested by the media, be it for football or election results.

To measure linear dependence, scientists use the so-called correlation coefficient, which was first introduced by the British natural scientist Sir Francis Galton (1822-1911) in the 1870s. Shortly afterwards, the mathematician Karl Pearson provided a formal mathematical justification for the correlation coefficient. Therefore, mathematicians also speak of the "Pearson product-moment correlation" or the "Pearson correlation."...

Martin Keller-Ressel explains: "To calculate the dependence measure, not only the values of the observed variables themselves, but also their mutual distances are recorded and from these distance matrices, the distance multivariance is calculated. This intermediate step allows for the detection of complex dependencies, which the usual correlation coefficient would simply ignore. Our method can be applied to questions in bioinformatics, where big data sets need to be analysed."
Read more... 

Additional resources
Björn Böttcher et al. Distance multivariance: New dependence measures for random vectors, The Annals of Statistics (2019).  
DOI: 10.1214/18-AOS1764 

Source: Phys.Org