Gaussian graphical models are graphs that represent the conditional relationships among multivariate normal variables. The process of uncovering the structure of these graphs is known as structure learning. Despite the fact that Bayesian methods in structure learning offer intuitive and well-founded ways to measure model uncertainty and integrate prior information, frequentist methods are often preferred due to the computational burden of the Bayesian approach. Over the last decade, Bayesian methods have seen substantial improvements, with some now capable of generating accurate estimates of graphs up to a thousand variables in mere minutes. Despite these advancements, a comprehensive review or empirical comparison of all cutting-edge methods has not been conducted. This paper delves into a wide spectrum of Bayesian approaches used in structure learning, evaluates their efficacy through a simulation study, and provides directions for future research. This study gives an exhaustive overview of this dynamic field for both newcomers and experts.

翻译：高斯图模型是表示多元正态变量之间条件关系的图形。揭示这些图结构的过程被称为结构学习。尽管贝叶斯方法在结构学习中提供了直观且理论基础坚实的途径来衡量模型不确定性并整合先验信息，但由于贝叶斯方法的计算负担，频率学派方法往往更受青睐。在过去十年中，贝叶斯方法取得了显著改进，有些方法现在能够在几分钟内生成多达一千个变量的图的精确估计。尽管取得了这些进展，但目前尚未对所有前沿方法进行全面的综述或实证比较。本文深入探讨了结构学习中广泛使用的贝叶斯方法，通过模拟研究评估其效能，并为未来研究提供方向。本研究为这一活跃领域的新手和专家提供了详尽的概述。