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SUMMARY:Complete collineations for Maximum Likelihood Estimation - Eloise 
 Hamilton (University of Cambridge)
DTSTART:20240125T100000Z
DTEND:20240125T110000Z
UID:TALK208069@talks.cam.ac.uk
DESCRIPTION:Given a statistical model and some observed data\, an importan
 t problem is identifying the parameters of the model that make the observe
 d data the most probable. These parameters are encoded in the Maximum Like
 lihood Estimate (MLE) given the observed data. However\, an MLE given obse
 rved data does not necessarily exist\, and even if it does it may not be u
 nique\, in other words it may not be identifiable. The aim of this talk is
  to explain how complete collineations (a concept from algebraic geometry)
  can be used to resolve non-identifiability of the MLE in the case of Dire
 cted Acyclic Graphical models. More precisely\, I will show how given init
 ial data\, choosing a complete collineation based on this data produces a 
 perturbation of the data\, which can in turn be used to obtain a unique ML
 E given the initial data. Time permitting\, I will outline open questions 
 regarding statistical interpretations of the moduli space of complete coll
 ineations. This is joint work with Gergely Berczi\, Philipp Reichenbach an
 d Anna Seigal.
LOCATION:Seminar Room 1\, Newton Institute
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