Markov Fields and Log-Linear Interaction Models for Contingency Tables

Darroch, J. N.; Lauritzen, Steffen; Speed, T. P.

doi:10.1214/aos/1176345006

Cited by 405 publications

(215 citation statements)

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“…Pearl [1,20] already investigated constraints imposed by the special instrumental variable model. Furthermore, Darroch et al [21] and, recently, Sullivant et al [22] looked at linear Gaussian graphical models and determined constraints in terms of the entries on the covariance matrix describing the data (tetrad constraints). Further, methods of algebraic statistics were applied (e.g., [23]) to derive constraints that are induced by latent variable models directly on the level of probabilities.…”

Section: Discussionmentioning

confidence: 99%

Information-Theoretic Inference of Common Ancestors

Steudel

2015

Entropy

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A directed acyclic graph (DAG) partially represents the conditional independence structure among observations of a system if the local Markov condition holds, that is if every variable is independent of its non-descendants given its parents. In general, there is a whole class of DAGs that represents a given set of conditional independence relations. We are interested in properties of this class that can be derived from observations of a subsystem only. To this end, we prove an information-theoretic inequality that allows for the inference of common ancestors of observed parts in any DAG representing some unknown larger system. More explicitly, we show that a large amount of dependence in terms of mutual information among the observations implies the existence of a common ancestor that distributes this information. Within the causal interpretation of DAGs, our result can be seen as a quantitative extension of Reichenbach's principle of common cause to more than two variables. Our conclusions are valid also for non-probabilistic observations, such as binary strings, since we state the proof for an axiomatized notion of "mutual information" that includes the stochastic as well as the algorithmic version.

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Section: Discussionmentioning

confidence: 99%

Information-Theoretic Inference of Common Ancestors

Steudel

2015

Entropy

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“…Primal contributions to the methodology are due to Dempster (1972) and Darroch et al (1980). DAGs and CIGs imply a different definition of joint probability.…”

Section: Graphical Modellingmentioning

confidence: 99%

Identification of monetary policy in SVAR models: a data-oriented perspective

Fragetta

Melina

2012

Empir Econ

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This is the unspecified version of the paper.This version of the publication may differ from the final published version. Permanent AbstractIn the literature using short-run timing restrictions to identify monetary policy shocks in vector-autoregressions (VAR) there is a debate on whether (i) contemporaneous real activity and prices or (ii) only data typically observed with high frequency should be assumed to be in the information set of the central bank when the interest rate decision is taken. This paper applies graphical modelling theory, a data-based tool, in a small-scale VAR of the US economy to shed light on this issue. Results corroborate the second type of assumption.

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“…The IPFP does this one dimension at a time but there is no reason why several dimensions can not be simultaneously adjusted. This idea underlies the estimation scheme for partially decomposable graphical models outlined in Darroch, Lauritzen and Speed (1980). They show that for many models it is possible to fit certain subsets of the marginal totals and to combine the resulting partial estimates using a Tables by Fienberg).…”

Section: Some Computational Properitesmentioning

confidence: 99%