Bayesian selective inference: sampling models and non-informative priors
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We discuss Bayesian inference for parameters selected using the data. We argue that, in general, an adjustment for selection is necessary in order to achieve approximate repeated-sampling validity, and discuss two issues that emerge from such adjustment. The first one concerns a potential ambiguity in the choice of posterior distribution. The second one concerns the choice of non-informative prior densities that lead to well-calibrated posterior inferences. We show that non-informative priors that are independent of the sample size tend to overstate regions of the parameter space with low selection probability.
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