Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have developed increasing interest in Bayesian inference. In Bayesian settings, inference for these models is typically performed via Markov chain Monte Carlo methods, which may be computationally intensive for models with a large number of manifest variables or complex structures. Variational approximations can be a fast alternative; however, they have not been adequately explored for this class of models. We develop a mean field variational Bayes approach for fitting elemental structural equation models and demonstrate how bootstrap can considerably improve the variational approximation quality. We show that this variational approximation method can provide reliable inference while being significantly faster than Markov chain Monte Carlo.

翻译：通常使用结构方程式模型来捕捉已观察到的和不可观察的变量之间的关系,这些模型传统上采用常态方法来安装,但最近研究人员和从业人员对贝叶斯人的推理越来越感兴趣。在贝叶西亚环境中,这些模型的推理通常通过Markov链式蒙特卡洛方法进行,这些推理对于具有大量明显变量或复杂结构的模型来说可能是计算密集的。变式近似值可以是一个快速的替代方法;但对于这类模型来说,这些近似值没有得到充分的探索。我们为适当的元素结构方程式模型开发了一种平均的场外变异性贝斯方法,并演示了靴带如何大大改进变近距离质量。我们表明,这种变异近似法可以提供可靠的推理,但比Markov链式蒙特卡洛快得多。