Fakultätskolloquium im Wintersemester 2016/17

Termin: Das Kolloquium findet in loser Folge mittwochs statt, mit jeweils zwei Vorträgen von 14:30 – 15:30 Uhr und von 16:00 – 17:00 Uhr im Hörsaal 3 (MI 00.06.011).
In der Pause ist für Getränke und Brez'n in der Magistrale gesorgt.

Ansprechpartner: Felix Krahmer, Robert König.

Vorträge im vergangenen Semester: Sommersemester 16.

Vorträge im Wintersemester 2016/17

Datum und Zeit Sprecher Titel
26.10.2016 um 14:30 Steffen Lauritzen
(Copenhagen)
Multivariate total positivity, Simpson's paradox, and the structure of M-matrices

Steffen Lauritzen — Multivariate total positivity, Simpson's paradox, and the structure of M-matrices

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Simpson's paradox is describing the phenomenon that two quantities can be positively associated in a population, but negatively associated within subpopulations. This can imply quite misleading interpretation of statistical information and it is therefore important to identify situations where this cannot happen. When a distribution is multivariate totally positive of order two (MTP2) this cannot happen. The MTP2 property is closed under marginalization, conditioning, and increasing transformations and has a number of other stability properties. In addition, it has fundamental implications for conditional independence relations. A multivariate Gaussian distribution is MTP2 if and only if its covariance matrix is an inverse M-matrix, i.e.\ if all off-diagonal elements of the concentration matrix (inverse covariance matrix) are non-positive. For other types of distributions, other conditions apply.

In the talk I shall give examples of Simpson's paradox, explain the basic properties associated with the MTP2 condition, give examples of MTP2 distributions and characterize these in a number of special cases. I shall also indicate some of the fundamental consequences that this property implies for conditional independence structures.

 

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