  Methods for automated discovery of causal relationships from
non-interventional data have received much attention recently. A widely used
and well understood model family is given by linear acyclic causal models
(recursive structural equation models). For Gaussian data both constraint-based
methods (Spirtes et al., 1993; Pearl, 2000) (which output a single equivalence
class) and Bayesian score-based methods (Geiger and Heckerman, 1994) (which
assign relative scores to the equivalence classes) are available. On the
contrary, all current methods able to utilize non-Gaussianity in the data
(Shimizu et al., 2006; Hoyer et al., 2008) always return only a single graph or
a single equivalence class, and so are fundamentally unable to express the
degree of certainty attached to that output. In this paper we develop a
Bayesian score-based approach able to take advantage of non-Gaussianity when
estimating linear acyclic causal models, and we empirically demonstrate that,
at least on very modest size networks, its accuracy is as good as or better
than existing methods. We provide a complete code package (in R) which
implements all algorithms and performs all of the analysis provided in the
paper, and hope that this will further the application of these methods to
solving causal inference problems.
