کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1148079 | 1489757 | 2015 | 16 صفحه PDF | دانلود رایگان |
We investigate the problem of constructing Bayesian credible sets that are honest and adaptive for the L2L2-loss over a scale of Sobolev classes with regularity ranging between [D,2D][D,2D], for some given DD in the context of the signal-in-white-noise model. We consider a scale of prior distributions indexed by a regularity hyper-parameter and choose the hyper-parameter both by marginal likelihood empirical Bayes and by hierarchical Bayes method, respectively. Next we consider a ball centred around the corresponding posterior mean with prescribed posterior probability. We show by theory and examples that both the empirical Bayes and the hierarchical Bayes credible sets give misleading, overconfident uncertainty quantification for certain oddly behaving truth. Then we construct a new empirical Bayes method based on risk estimation, which provides the correct uncertainty quantification and optimal size.
Journal: Journal of Statistical Planning and Inference - Volume 166, November 2015, Pages 36–51