Functional connectivity analysis is an important tool for characterizing interactions among brain regions, particularly in studies of neurodegenerative disorders such as Alzheimer's disease (AD). Gaussian graphical models (GGMs) provide a promising statistical framework for estimating functional connectivity by capturing conditional dependence relationships among brain regions. Although a variety of regularized precision matrix estimators have been proposed to estimate sparse conditional dependency structures for GGMs, their comparative performance and practical implications for neuroimaging studies are not well understood. In this work, we present a comprehensive statistical review and empirical evaluation of widely used GGM estimation methods, including the graphical lasso (glasso), ridge-based glasso, graphical elastic net, adaptive glasso, smoothly clipped absolute deviation (SCAD), minimax concave penalty (MCP), constrained $\ell_1$ minimization for inverse matrix estimation (CLIME), and tuning-insensitive graph estimation and regression (TIGER). Their performance is evaluated through extensive data-driven simulations designed to reflect realistic neuroimaging settings, along with an application to an AD cohort study to illustrate methodological differences and their impact on downstream network analysis. In addition, a user-friendly R package, spice, is provided to facilitate implementation and enhance the reproducibility of empirical studies.

翻译：功能连接分析是刻画脑区间相互作用的重要工具，尤其在阿尔茨海默病等神经退行性疾病研究中具有关键价值。高斯图模型通过捕捉脑区间的条件依赖关系，为功能连接估计提供了有效的统计框架。尽管已有多种正则化精度矩阵估计方法用于提取高斯图模型的稀疏条件依赖结构，但这些方法在神经影像研究中的性能对比及实际应用影响尚未得到充分阐释。本文对主流高斯图模型估计方法进行了系统性统计综述与实证评估，涵盖图形套索、岭回归型图形套索、图形弹性网络、自适应图形套索、平滑削边绝对偏差、极小极大凹惩罚、约束$\ell_1$范数逆矩阵估计及调谐不敏感图估计与回归。通过面向真实神经影像场景的大规模数据驱动模拟实验，并结合阿尔茨海默病队列研究案例，系统比较了各方法的差异性及其对下游网络分析的影响。此外，本研究提供了用户友好的R语言工具包spice，以促进实证研究的可重复性。