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Covariate-adjusted Graphical Models and Essential Graphs: An Objective Bayes Approach

Dott. Stefano Peluso - Università Cattolica del Sacro Cuore

Lunedì 15 maggio 2017, ore 12.30

Aula 101

Abstract: We present an objective Bayes method for covariance selection in
Gaussian multivariate regression models having a sparse regression and
covariance structure, the latter being Markov with respect to a Directed
Acyclic Graph (DAG). Our procedure can be easily complemented with a
variable selection step, so that variable and graphical model selection
can be performed jointly. The input of our method is a single default
prior, essentially involving no subjective elicitation, while its output
is a closed-form marginal likelihood for every covariate-adjusted DAG
model, which is constant over each class of Markov equivalent DAGs. We
then apply the procedure to the problem of structural learning of
Essential Graphs (EG), chain graphs representing Markov equivalence
classes of DAGs. We propose an MCMC strategy to explore the space of EGs
and we show that in realistic experimental studies our method is highly
competitive, especially when the number of responses is large relative to
the sample size.

Joint work with Federico Castelletti, Guido Consonni, Marco Della Vedova
and Luca La Rocca.



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