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I mean "with simulations using a probability distribution [for the true parameter] different from the prior used in the Bayesian analysis." (The issue of model
by spekcular 5y ago
I mean "with simulations using a probability distribution [for the true parameter] different from the prior used in the Bayesian analysis." (The issue of model error is a separate question.)
Yes, in this case would should conclude there is something wrong with the Bayesian way. If you hand me a statistical method to e.g. estimate some parameter that frequently returns answers that are far from the truth, that is a problem. One cannot assume the prior exactly describes reality (or there would be no point in doing inference, because the prior already gives you the truth).
- kgwgk 5y agoAt least a Bayesian posterior tries to describe reality. In a way which is consistent with the prior and the data. But again, GIGO. Including prior information into the inferential process will be beneficial if it's correct but detrimental if it isn't. Hardly surprising. On the other hand, Frequentist methods do not claim anything concrete about reality. Only about long-run frequencies in hypothetical replications. You may think that makes them better, it's your choice.
- spekcular 5y agoSure, I agree bad priors will give inaccurate inferences. My point is simply that to make a statement like, "an inaccurate prior generates many inaccurate inferences, and therefore it is garbage," one has to adopt a frequentist criterion for the quality of an estimator (like "gets good results most of the time").