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