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Causal Discovery algorithms attack the challenging problem of learning the causal relationships among a set of variables from observational data, but are often partly ad-hoc and give the researcher no measure of confidence in the correctness of the learned causal structure. I introduce Bayesian Causal Model Selection (BCMS), a Bayesian framework for causal discovery that unifies existing methods by expressing identifiability assumptions through the model prior. I formulate ANMs and LiNGAMs, two general and popular discovery algorithms, via BCMS; discuss computation of the evidence for each model; and illustrate BCMS's novel ability to quantify the uncertainty in the learned causal model.