The rule of conditional probability is valid in quantum theory [Comment on Gelman & Yao's "Holes in Bayesian Statistics"]

In a recent manuscript, Gelman & Yao (2020) claim that "the usual rules of conditional probability fail in the quantum realm" and that "probability theory isn't true (quantum physics)" and purport to support these statements with the example of a quantum double-slit experiment. The present comment recalls some relevant literature in quantum theory and shows that (i) Gelman & Yao's statements are false; in fact, the quantum example confirms the rules of probability theory; (ii) the particular inequality found in the quantum example can be shown to appear also in very non-quantum examples, such as drawing from an urn; thus there is nothing peculiar to quantum theory in this matter. A couple of wrong or imprecise statements about quantum theory in the cited manuscript are also corrected.

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