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Title: Confidence regions for the location of peaks of a smooth random field Authors:  Samuel Davenport - University of California, San Diego (United Kingdom) [presenting]
Abstract: Local maxima of random processes are useful for finding important regions and are routinely used, in areas such as neuroimaging, for summarising features of interest. 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 peak mean and Cohen's $d$. Under the assumption of stationarity, we develop Monte Carlo confidence regions for 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.