  Local maxima of random processes are useful for finding important regions and
are routinely used, for summarising features of interest (e.g. in
neuroimaging). In this work we provide confidence regions for the location of
local maxima of the mean and standardized effect size (i.e. Cohen's d) given
multiple realisations of a random process. We prove central limit theorems for
the location of the maximum of mean and t-statistic random fields and use these
to provide asymptotic confidence regions for the location of peaks of the mean
and Cohen's d. Under the assumption of stationarity we develop Monte Carlo
confidence regions for the location of peaks of the mean that have better
finite sample coverage than regions derived based on classical asymptotic
normality. We illustrate our methods on 1D MEG data and 2D fMRI data from the
UK Biobank.
