Room "Sala Seminari" - Abacus Building (U14)
Bringing order into statistics
Speaker
Prof. Marco Fattore
University of Milano - Bicocca
Abstract: In this talk, we discuss the role of order theory in statistics and its actual and potential impact on multidimensional data analysis, from both methodological and applied perspectives. Despite their pervasiveness in many research domains, multidimensional ordinal data still lack a sound and comprehensive statistical toolbox. We first discuss why this is historically the case and then show how partially ordered sets (posets), lattices and order theory provide the natural mathematical structure to conceptualize multi-faceted traits, represent multi-dimensional systems of ordinal data and develop the multidimensional analysis of this type of input. We provide many examples of “posetic” algorithms and procedures, pertaining to synthetic indicator construction, multi-criteria decision-making, dimensionality reduction and cluster analysis. We also address the computational challenges connected to the treatment of these discrete combinatoric data structures, briefly introducing the software resources currently available in the R ecosystem. The talk ends with an eye on future research.
Contact person for the seminar: elisabetta.fersini@unimib.it