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SUMMARY:On statistical models associated with acyclic directed mixed graph
 s - Qingyuan Zhao (Statistical Laboratory)
DTSTART:20241101T153000Z
DTEND:20241101T170000Z
UID:TALK223795@talks.cam.ac.uk
CONTACT:Martina Scauda
DESCRIPTION:Causal models in statistics are often described by acyclic dir
 ected mixed graphs (ADMGs)\, which contain directed and bidirected edges a
 nd no directed cycles. This article surveys various interpretations of ADM
 Gs\, discusses their relations in different sub-classes of ADMGs\, and arg
 ues that one of them—nonparametric equation system (the E model below)
 —should be used as the default interpretation. The E model is closely re
 lated to but different from the interpretation of ADMGs as directed acycli
 c graphs (DAGs) with latent variables that is commonly found in the litera
 ture. Our endorsement of the E model is based on two observations. First\,
  in a subclass of ADMGs called unconfounded graphs (which retain most of t
 he good properties of directed acyclic graphs and bidirected graphs)\, the
  E model is equivalent to many other interpretations including the global 
 Markov and nested Markov models. Second\, the E model for an arbitrary ADM
 G is exactly the union of that for all unconfounded expansions of that gra
 ph. This property is referred to as completeness\, as it shows that the mo
 del does not commit to any specific latent variable explanation. In provin
 g that the E model is nested Markov\, we also develop an ADMG-based theory
  for causality that may be of independent interest.\n\nPreprint available 
 at: https://www.statslab.cam.ac.uk/~qz280/publication/admg-model/paper.pdf
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberforce Road\, Camb
 ridge
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