In an Istanbul neighbourhood of 200,000 people, an OM worker, prompted by God, asks a question to the only person who knows the answer.

In an Istanbul neighbourhood of 200,000 people, an OM worker, prompted by God, asks a question to the only person who knows the answer.

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King Midas has left his mark again on the same Western Australian gold mine which made global headlines last year after producing some of the biggest gold specimens ever seen.

An 'island-rock' formation in South Australian is believed to have formed billions of years ago and while it is eroding, experts say it is not likely to disappear anytime soon.

Eduard Belitser, Nurzhan Nurushev.

Source: Bernoulli, Volume 26, Number 1, 191--225.

Abstract:
In the general signal$+$noise (allowing non-normal, non-independent observations) model, we construct an empirical Bayes posterior which we then use for uncertainty quantification for the unknown, possibly sparse, signal. We introduce a novel excessive bias restriction (EBR) condition, which gives rise to a new slicing of the entire space that is suitable for uncertainty quantification. Under EBR and some mild exchangeable exponential moment condition on the noise, we establish the local (oracle) optimality of the proposed confidence ball. Without EBR, we propose another confidence ball of full coverage, but its radius contains an additional $sigma n^{1/4}$-term. In passing, we also get the local optimal results for estimation , posterior contraction problems, and the problem of weak recovery of sparsity structure . Adaptive minimax results (also for the estimation and posterior contraction problems) over various sparsity classes follow from our local results.