The Gaussian Kinematic Formula (GKF) is a powerful and computationally efficient tool to perform statistical inference on random fields and became a well-established tool in the analysis of neuroimaging data. Using realistic error models, recent articles show that GKF based methods for \emph{voxelwise inference} lead to conservative control of the familywise error rate (FWER) and for cluster-size inference lead to inflated false positive rates. In this series of articles we identify and resolve the main causes of these shortcomings in the traditional usage of the GKF for voxelwise inference. This first part removes the \textit{good lattice assumption} and allows the data to be non-stationary, yet still assumes the data to be Gaussian. The latter assumption is resolved in part 2, where we also demonstrate that our GKF based methodology is non-conservative under realistic error models.

翻译：高斯运动学公式是进行随机场统计推断的强大且计算高效的工具，并在神经影像数据分析中成为成熟方法。近期文章基于现实误差模型指出，传统高斯运动学公式方法在体素级推断中导致族系错误率（FWER）的保守控制，而在簇规模推断中导致虚报率膨胀。在本系列文章中，我们识别并解决了传统使用高斯运动学公式进行体素级推断时这些缺陷的主要原因。第一部分去除了“良好格点假设”，允许数据非平稳，但仍假设数据服从高斯分布。后一假设将在第二部分中解决，届时我们将证明基于高斯运动学公式的方法在现实误差模型下不具有保守性。