论文标题
根据估计标准误差缩放的信息默认先验的提案
A proposal for informative default priors scaled by the standard error of estimates
论文作者
论文摘要
如果我们对某些感兴趣的参数有公正的估计，则其绝对值将对参数的绝对值产生积极偏差。当信噪比（SNR）较小时，这种偏差很大，并且在我们的统计显着性下，它会变得更大。获胜者的诅咒。这是正规化的常见动机。为了确定合适的收缩量，我们建议估计SNR从大型研究或类似研究的语料库中的分布，并将其用作先前的分布。语料库的范围越宽，先前的信息较小，但更广泛的范围并不一定会导致先验更加分散。我们表明，如果我们要求后验推断在数据的线性转换下是等效的，那么对先前的估计会简化。我们通过86项心理学的复制研究和178阶段临床试验进行了86项复制研究的态度。我们的建议并不是要根据有关特定问题的完整信息来替代先验；相反，它代表了一种家庭选择，该选择应比当前的默认统一之前产生更好的长期特性，这导致了效应大小的系统过度估计和复制危机，而这些膨胀的估计未在以后的研究中出现。
If we have an unbiased estimate of some parameter of interest, then its absolute value is positively biased for the absolute value of the parameter. This bias is large when the signal-to-noise ratio (SNR) is small, and it becomes even larger when we condition on statistical significance; the winner's curse. This is a frequentist motivation for regularization. To determine a suitable amount of shrinkage, we propose to estimate the distribution of the SNR from a large collection or corpus of similar studies and use this as a prior distribution. The wider the scope of the corpus, the less informative the prior, but a wider scope does not necessarily result in a more diffuse prior. We show that the estimation of the prior simplifies if we require that posterior inference is equivariant under linear transformations of the data. We demonstrate our approach with corpora of 86 replication studies from psychology and 178 phase 3 clinical trials. Our suggestion is not intended to be a replacement for a prior based on full information about a particular problem; rather, it represents a familywise choice that should yield better long-term properties than the current default uniform prior, which has led to systematic overestimates of effect sizes and a replication crisis when these inflated estimates have not shown up in later studies.
