Discussion of “Confidence Intervals for Nonparametric Empirical Bayes Analysis”

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Supplementary Materials

The supplementary material contains R and Julia code used to produce results shown in this discussion, and a file README.rtf that summarizes which code produces which results.

Notes

1 The definition of local false sign rate used in Ignatiadis and Wager (2021), $\mathbb{P}({\mu }_{i}z\le 0|Z_i=z)$, differs from that in Stephens (2017), which is $\min \left\{\mathbb{P}({\mu }_i\le 0|Z_i=z),\mathbb{P}({\mu }_i\ge 0|Z_i=z)\right\}$. We use the latter definition in this manuscript.

2 At the time of this work Empirikos does not support fitting a prior with point-mass distributions. However, following discussion with N. Ignatiadis, we mimicked the results that would be obtained with a point mass by (a) using $\mathcal{N}(0,{\tau }^2)$ in place of δ₀, where $\tau =2.22\times {10}^{-16}$; (b) computing the $\mathit{lfsr}$ using a modified definition, $\mathit{lfsr}(z)=\min \{p(\mu \ge -2\tau |z),p(\mu \le 2\tau |z)\}$, which effectively treats the tiny effects from the $N(0,{\tau }^2)$ component as being zero.