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Ancestral graph models, introduced by Richardson and Spirtes (2002),generalize both Markov random fields and Bayesian networks to a class of graphswith a global Markov property that is closed under conditioning andmarginalization. By design, ancestral graphs encode precisely the conditionalindependence structures that can arise from Bayesian networks with selectionand unobserved (hidden/latent) variables. Thus, ancestral graph models providea potentially very useful framework for exploratory model selection whenunobserved variables might be involved in the data-generating process but noparticular hidden structure can be specified. In this paper, we present theIterative Conditional Fitting (ICF) algorithm for maximum likelihood estimationin Gaussian ancestral graph models. The name reflects that in each step of theprocedure a conditional distribution is estimated, subject to constraints,while a marginal distribution is held fixed. This approach is in duality to thewell-known Iterative Proportional Fitting algorithm, in which marginaldistributions are fitted while conditional distributions are held fixed.

Iterative Conditional Fitting for Gaussian Ancestral Graph Models