论文标题
光滑随机场峰位置的置信区
Confidence regions for the location of peaks of a smooth random field
论文作者
论文摘要
随机过程的局部最大值对于查找重要区域很有用，并且通常使用感兴趣的特征（例如，在神经影像学中）。在这项工作中，我们为在随机过程的多个实现的情况下，为平均值和标准化效应大小（即Cohen d）的本地最大值（即Cohen d）的位置提供了置信区域。我们证明了平均值和T统计随机场的最大位置的中心限制定理，并使用这些定理为平均值和Cohen d的峰位置提供渐近置信区。在平稳性的假设下，我们为平均峰位置开发了蒙特卡洛置信区域，其有限样品覆盖率比基于经典渐近差异的区域更好。我们说明了来自英国生物库的1D MEG数据和2D fMRI数据的方法。
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.
