大量的牵连

大量的牵连

結果 (英文) 1:

A lot of involvement

結果 (英文) 2:

These priors have been studied extensively and have been shown to have a number of good theoretical properties.
For example, Armagan et al. [1] gave sufficient conditions for posterior consistency in univariate linear regression
when several well-known shrinkage priors are placed on the coefficients. Ghosh and Chakrabarti [21], van der Pas et al.
[41], and van der Pas et al. [42] showed that when these priors are used to estimate sparse normal means, the posterior
distributions concentrate around the true means at the minimax rate under mild conditions. van der Pas et al. [44] also
obtained minimax-optimal posterior contraction rates for the horseshoe under both empirical Bayes and hierarchical
Bayesian choices for the global shrinkage parameter τ in (2). For the normal means model, the theoretical properties
of model selection (including the variable selection method applied in this article) and uncertainty quantification
under scale-mixture priors were also recently investigated by Salomond [36] and van der Pas et al. [43]. Finally, in
the context of multiple hypothesis testing, Bhadra et al. [6], Datta and Ghosh [16], Ghosh and Chakrabarti [21], and
Ghosh et al. [22] showed that multiple testing rules induced by these shrinkage priors can achieve optimal Bayes risk
in terms of 0-1 symmetric loss (or expected number of misclassified signals).
Ghosh et al. [22] observed that for a large number of global-local shrinkage priors of the form (2), the local
parameter ξi has a hyperprior distribution π(ξi) that can be written as
π(ξi) = Kξ
−a−1
i L(ξi), (3)
where K > 0 is the constant of proportionality, a is positive real number, and L is a positive measurable, non-constant,
slowly varying function over (0, ∞).