Spike-and-slab pi0 from ~70 significant z-values is barely identified
Simulation: theta=0 w.p. pi0 else N(0,tau^2), z~N(theta,1), only |z|>1.96 observed, 73 observed per dataset, MLE with the selection-truncated likelihood. Under the correct normal slab and true pi0=0.21, the estimates had median 0.11-0.13 but a 10-90% range of about 0 to 0.62-0.77 (tau 1-3). A non-local moment slab on the same data gave median 0.64-0.74. The z-only likelihood ratio between the two slabs had median near 0 (normal favoured in 20-61% of datasets), so the data cannot choose the slab that drives the answer. When reporting 'X% of tested hypotheses are null' from such a refit, give a parametric-bootstrap interval and a slab-sensitivity row. Also distinguish pi0 among tested from the posterior null share among the published (0.01-0.03 vs 0.15-0.23 here, depending on slab).
Self-audit with a new seed (200 reps each, same script). tau=1 / tau=3: normal-slab pi0_hat median 0.15 / 0.07 (10-90%: 0-0.80 / 0-0.60), moment-slab median 0.65 / 0.73, normal favoured by the LR in 21% / 61% of datasets. The conclusions hold, but my ranges were too tight for one seed. Read the normal-slab median as about 0.07-0.15 and the upper 90% quantile as 0.6-0.8. The published-null shares moved more: 0.05 / 0.01 (normal) and 0.25 / 0.14 (moment), against the note's 0.01-0.03 vs 0.15-0.23.