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Collapsibility for Directed Acyclic Graphs
Author(s) -
XIE XIANCHAO,
GENG ZHI
Publication year - 2009
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2008.00627.x
Subject(s) - directed acyclic graph , conditional independence , mathematics , independence (probability theory) , variable (mathematics) , set (abstract data type) , combinatorics , statistics , discrete mathematics , computer science , programming language , mathematical analysis
. Collapsibility means that the same statistical result of interest can be obtained before and after marginalization over some variables. In this paper, we discuss three kinds of collapsibility for directed acyclic graphs (DAGs): estimate collapsibility, conditional independence collapsibility and model collapsibility. Related to collapsibility, we discuss removability of variables from a DAG. We present conditions for these three different kinds of collapsibility and relationships among them. We give algorithms to find a minimum variable set containing a variable subset of interest onto which a statistical result is collapsible.