Selective peak inference: Unbiased estimation of raw and standardized effect size at local maxima

The spatial signals in neuroimaging mass univariate analyses can be characterized in a number of ways, but one widely used approach is peak inference: the identification of peaks in the image. Peak locations and magnitudes provide a useful summary of activation and are routinely reported, however, the magnitudes reflect selection bias as these points have both survived a threshold and are local maxima. In this paper we propose the use of resampling methods to estimate and correct this bias in order to estimate both the raw units change as well as standardized effect size measured with Cohen's d and partial R². We evaluate our method with a massive open dataset, and discuss how the corrected estimates can be used to perform power analyses. Keywords: fMRI, selective inference, winner's curse, regression to the mean, bias, bootstrap, local maxima, UK biobank, power analyses, massive linear modeling.