Journal
BERNOULLI
Volume 25, Issue 2, Pages 848-876Publisher
INT STATISTICAL INST
DOI: 10.3150/17-BEJ1005
Keywords
Bayesian network; DAG; nested Markov model; parameterization
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Funding
- National Institute on Aging
- EPSRC [EP/N020294/1]
- U.S. National Institutes of Health [R01 AI032475]
- U.S. Office of Naval Research [N00014-15-1-2672]
- SQuaRE grant from the American Institute of Mathematics
- EPSRC [EP/N020294/1] Funding Source: UKRI
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We provide a parameterization of the discrete nested Markov model, which is a supermodel that approximates DAG models (Bayesian network models) with latent variables. Such models are widely used in causal inference and machine learning. We explicitly evaluate their dimension, show that they are curved exponential families of distributions, and fit them to data. The parameterization avoids the irregularities and unidentifiability of latent variable models. The parameters used are all fully identifiable and causally-interpretable quantities.
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