The paper proves that two forms of ancillarity are preserved under conditioning on a selection event and uses this to guide sampling-model choice in selective inference.
Bayesian Selective Inference: Non-informative Priors
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abstract
We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of non-informative priors for selection models. These priors may be employed to produce a posterior distribution in the absence of prior information as well as to provide well-calibrated frequentist inference for the selected parameter. We test the proposed priors empirically in several scenarios.
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Sampling models for selective inference
The paper proves that two forms of ancillarity are preserved under conditioning on a selection event and uses this to guide sampling-model choice in selective inference.