Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property

Abstract

The AMP Markov property is a recently proposed alternative Markov property for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced LWF Markov property that is coherent with data-generation by natural block-recursive regressions. In this paper, we show that maximum likelihood estimates in Gaussian AMP chain graph models can be obtained by combining generalized least squares and iterative proportional fitting to an iterative algorithm. In an appendix, we give useful convergence results for iterative partial maximization algorithms that apply in particular to the described algorithm.

15 pages, article will appear in Scandinavian Journal of Statistics

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• Counting and Locating the Solutions of Polynomial Systems of Maximum Likelihood Equations, II: The Behrens-Fisher Problem
• Efficient least squares for estimating total effects under linearity and causal sufficiency
• Learning AMP Chain Graphs and some Marginal Models Thereof under Faithfulness: Extended Version
• On the structure of essential graphs for AMP chain graph models
• Bayesian Inference for Latent Chain Graphs
• Identifiability of AMP chain graph models