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Cyan comments on Case study: abuse of frequentist statistics - Less Wrong
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I don't see how being a Bayesian gets you out of cherry-picking your causal structure from a large set. You still have to decide which variables are conditional on which other variables.
You put in all the variables, use a hierarchical structure for the prior, use a weakly informative hyperprior, and let the data sort itself out if it can. Key phrase: automatic relevance determination; David MacKay originated the term while doing Bayesian inference for neural nets.