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Biometrika 1998 85(4):960-966; doi:10.1093/biomet/85.4.960
© 1998 by Biometrika Trust
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MISCELLANEA

Maximum likelihood estimation in graphical models with missing values

VANESSA DIDELEZ and IRIS PIGEOT

Institute of Statistics, University of Munich Ludwigstrasse 33, D-80539 Munich, Germanydidelez{at}stat.uni-muenchen.de
Institute of Statistics, University of Munich Ludwigstrasse 33, D-80539 Munich, Germanypigeot{at}stat.uni-muenchen.de

In this paper we discuss maximum likelihood estimation when some observations are missing in mixed graphical interaction models assuming a conditional Gaussian distribution as introduced by Lauritzen & Wermuth (1989). The approach via the EM algorithm of Little & Schluchter (1985) for the saturated case is expanded to cover the special restrictions in graphical models. A more efficient way to compute the E-step is indicated. The main purpose of the paper is to show that for certain missing patterns the computational effort can be considerably reduced.

Key Words: EM algorithm • Graphical interaction model • Maximum likelihood estimation • Missing pattern • Missing values


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