  This article introduces a Bayesian nonparametric method for quantifying the
relative evidence in a dataset in favour of the dependence or independence of
two variables conditional on a third. The approach uses Polya tree priors on
spaces of conditional probability densities, accounting for uncertainty in the
form of the underlying distributions in a nonparametric way. The Bayesian
perspective provides an inherently symmetric probability measure of conditional
dependence or independence, a feature particularly advantageous in causal
discovery and not employed in existing procedures of this type.
