The Annals of Statistics

Addendum on the scoring of Gaussian directed acyclic graphical models

Jack Kuipers, Giusi Moffa, and David Heckerman

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Abstract

We provide a correction to the expression for scoring Gaussian directed acyclic graphical models derived in Geiger and Heckerman [Ann. Statist. 30 (2002) 1414–1440] and discuss how to evaluate the score efficiently.

Article information

Source
Ann. Statist. Volume 42, Number 4 (2014), 1689-1691.

Dates
First available in Project Euclid: 7 August 2014

Permanent link to this document
http://projecteuclid.org/euclid.aos/1407420013

Digital Object Identifier
doi:10.1214/14-AOS1217

Mathematical Reviews number (MathSciNet)
MR3262465

Zentralblatt MATH identifier
1297.62122

Subjects
Primary: 62-07: Data analysis 62F15: Bayesian inference 62H99: None of the above, but in this section

Keywords
Gaussian DAG models Bayesian network learning BGe score

Citation

Kuipers, Jack; Moffa, Giusi; Heckerman, David. Addendum on the scoring of Gaussian directed acyclic graphical models. Ann. Statist. 42 (2014), no. 4, 1689--1691. doi:10.1214/14-AOS1217. http://projecteuclid.org/euclid.aos/1407420013.


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References

  • Friedman, N. and Koller, D. (2003). Being Bayesian about network structure. A Bayesian approach to structure discovery in Bayesian networks. Machine Learning 50 95–125.
  • Geiger, D. and Heckerman, D. (1994). Learning Gaussian networks. In Proceedings of Tenth Conference on Uncertainty in Artificial Intelligence 235–243. Morgan Kaufmann, San Francisco, CA.
  • Geiger, D. and Heckerman, D. (2002). Parameter priors for directed acyclic graphical models and the characterization of several probability distributions. Ann. Statist. 30 1412–1440.
  • Grzegorczyk, M. and Husmeier, D. (2008). Improving the structure MCMC sampler for Bayesian networks by introducing a new edge reversal move. Machine Learning 71 265–305.
  • Heckerman, D. and Geiger, D. (1995). Learning Bayesian networks: A unification for discrete and Gaussian domains. In Uncertainty in Artificial Intelligence (Montreal, PQ, 1995) 274–284. Morgan Kaufmann, San Francisco, CA.
  • Kuipers, J., Moffa, G. and Heckerman, D. (2014). Supplement to “Addendum on the scoring of Gaussian directed acyclic graphical models.” DOI:10.1214/14-AOS1217SUPP.
  • Madigan, D. and York, J. (1995). Bayesian graphical models for discrete data. International Statistical Review 63 215–232.

Supplemental materials

  • Supplementary material: Deriving and simplifying the BGe score. We detail the steps used to derive (2) and simplify the ratios appearing in (1) to improve the numerical computation of the score.