Markov Chain Monte Carlo Model Selection for DAG Models

We present two methodologies for Bayesian model choice and
averaging in Gaussian directed acyclic graphs (dags). In both cases
model determination is carried out by implementing a reversible
jump Markov Chain Monte Carlo sampler. The dimension-changing move
involves adding or dropping a (directed) edge from the graph. The
first methodology extends the results in Giudici and Green (1999),
by excluding all non-moralized dags and searching in the space of
their essential graphs. The second methodology employs the results
in Geiger and Heckerman (1999) and searches directly in the space
of all dags. To achieve this aim we rely on the concept of
adjacency matrices, which provides a relatively inexpensive check
for acyclicity. The performance of our procedure is illustrated by
means of two simulated datasets.