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Bootstrapping (a special case of resampling) can be used to test the robustness of standard statistics when the data has an unknown or complex distribution. My question is if the technique can also be applied to Bayesian inference: for example, could one perform multiple bayesian inferences on multiple bootstrap samples and compare the final inferences? Do Bayesian methods interact with bootstrapping in a bad way (perhaps by relying 'too much' on the properties of the data such that bootstrapping increases bias? |
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Why would you want to do that? A main use for bootstrapping is that it can allow you to study the variance (or do some averaging) of methods where doing this is normally hard. However, most bayesian methods (variational and sampling, more specifically) already incorporate these informations from the ground up, so there's no obvious need for bootstrapping. that was my thought but I wanted to run it by someone else -- thanks!
(Jul 21 '10 at 16:59)
Mike S
Because you don't trust your model: the posterior given by a Bayesian method is accurate only if your model is right. On the opposite, bootstrapping is a non-parametric method: if some mild independence conditions are satisfied by your different points, your estimate of variance will be unbiased, although maybe noisy. I do think that it makes sens to resample/bootstrap Bayesian methods, mostly to check that the model used is plausible.
(Jan 08 '11 at 05:03)
Gael Varoquaux
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Bootstrapping can make matters worse in some cases. The resampled data set will contain data points that lie on top of each other. If you are using a method that models the variance (i.e. a Bayesian one) then it will take it as a sign that there is very low noise in the data. Why else would multiple data points be exactly the same? |
