Confidence regions for the location of peaks of a smooth random field

TL;DR

This paper develops statistical methods to construct confidence regions for the locations of peaks in smooth random fields, useful in neuroimaging and other spatial data analyses.

Contribution

It introduces asymptotic and Monte Carlo confidence regions for peak locations of mean and effect size in stationary random fields, with proven central limit theorems.

Findings

Monte Carlo regions outperform classical methods in finite samples

Methods successfully applied to MEG and fMRI data

Provides theoretical guarantees for peak location inference

Abstract

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.