For linear Gaussian causal models, the posterior probability of the true DAG converges to 1 exponentially if the DAG is maximal, and no faster than 1/sqrt(n) otherwise.
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Bayesian causal discovery: Posterior concentration and optimal detection
For linear Gaussian causal models, the posterior probability of the true DAG converges to 1 exponentially if the DAG is maximal, and no faster than 1/sqrt(n) otherwise.