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Objective Bayesian Search of Gaussian DAG Models with Non-local Priors

Author

Listed:
  • Davide Altomare

    (Department of Mathematics, University of Pavia)

  • Guido Consonni

    (Department of Economics and Quantitative Methods, University of Pavia)

  • Luca La Rocca

    (Dipartimento di Comunicazione e Economia, University of Modena and Reggio Emilia)

Abstract

Directed Acyclic Graphical (DAG) models are increasingly employed in the study of physical and biological systems, where directed edges between vertices are used to model direct influences between variables. Identifying the graph from data is a challenging endeavor, which can be more reasonably tackled if the variables are assumed to satisfy a given ordering; in this case, we simply have to estimate the presence or absence of each possible edge, whose direction is established by the ordering of the variables. We propose an objective Bayesian methodology for model search over the space of Gaussian DAG models, which only requires default non-local priors as inputs. Priors of this kind are especially suited to learn sparse graphs, because they allow a faster learning rate, relative to ordinary local priors, when the true unknown sampling distribution belongs to a simple model. We implement an efficient stochastic search algorithm, which deals effectively with data sets having sample size smaller than the number of variables. We apply our method to a variety of simulated and real data sets.

Suggested Citation

  • Davide Altomare & Guido Consonni & Luca La Rocca, 2011. "Objective Bayesian Search of Gaussian DAG Models with Non-local Priors," Quaderni di Dipartimento 140, University of Pavia, Department of Economics and Quantitative Methods.
    • Handle: RePEc:pav:wpaper:140
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    References listed on IDEAS

    as
    1. James O. Berger & German Molina, 2005. "Posterior model probabilities via path‐based pairwise priors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(1), pages 3-15, February.
    2. Jose M. Perez, 2002. "Expected-posterior prior distributions for model selection," Biometrika, Biometrika Trust, vol. 89(3), pages 491-512, August.
    3. Ali Shojaie & George Michailidis, 2010. "Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs," Biometrika, Biometrika Trust, vol. 97(3), pages 519-538.
    4. Mathias Drton, 2004. "Model selection for Gaussian concentration graphs," Biometrika, Biometrika Trust, vol. 91(3), pages 591-602, September.
    5. Guido Consonni & Jonathan J. Forster & Luca La Rocca, 2010. "Enhanced Objective Bayesian Testing for the Equality of two Proportions," Quaderni di Dipartimento 125, University of Pavia, Department of Economics and Quantitative Methods.
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