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

Davide Altomare, Guido Consonni and Luca La Rocca
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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

No 140, Quaderni di Dipartimento from University of Pavia, Department of Economics and Quantitative Methods

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.

Keywords: Fractional Bayes factor; High-dimensional sparse graph; Moment prior; Non-local prior; Objective Bayes; Pathway based prior; Regulatory network; Stochastic search; Structural learning. (search for similar items in EconPapers)
Pages: 28 pages
Date: 2011-03
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