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Psychosmurf comments on Thinking in Bayes: Light - Less Wrong Discussion
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Remember that "H causes e" and "H implies e" are two very different statements. The map is not the territory.
In order to show that H causes e you would have to show that the probabilities always factor as P(e & H) = P(H)P(e|H) and not as P(e & H) = P(e)P(H|e).
For example, rain causes wet grass, but wet grass does not cause rain, even though the Bayesian inference goes both ways.
Both of these are mathematical identities. It is not possible for one to hold and not the other; both are always true.
Causal analysis of probabilities is a lot more complicated.