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URL;TYPE=URI:https://www.wpi.edu/news/calendar/events/mathematical-sciences
 -department-discrete-math-seminar-francisco-ponce-carrion-wpi
SUMMARY:Mathematical Sciences Department Discrete Math Seminar: Francisco P
 once-Carrion\, WPI
DESCRIPTION:Speaker: Francisco Ponce-Carrion\, WPI\nTitle: Marginal indepen
 dence and the poset of partial set partitions.\nAbstract: Marginal indepen
 dence models are commonly studied by attaching to them a combinatorial str
 ucture to encode the independence relations between random variables. The 
 choice of combinatorial structure oftenlimitsthe family of models that can
  be described by it. In this talk\, we will tackle the problem of finding 
 a combinatorial structure that describes every marginal independence model
  by establishing a bijection between marginal independence models and a fa
 mily of order ideals of the poset of partial set partitions. We will also 
 discuss the varieties that define such models for discrete random variable
 s and show that every binary marginal independence model is toric after a 
 linear change of coordinates. This generalizes results of Boege\, Petrovic
 \, and Sturmfels (simplicial complex models)\, and Drton and Richardson (g
 raphical models)\, and provides a unified framework for discussing margina
 l independence models. This talk is based on joint work with Seth Sullivan
 t.
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