It is recommended to use two-part models for analyzing zero-inflated data that exhibit a spike at zero or have a large proportion of participants with zero values. This paper presents a variational Bayesian inference procedure for the analysis of a two-part latent variable model. We take advantage of the Pólya Gamma stochastic representation to approximate the posterior distribution via a mean-field variational method. We propose a scheme to update the variational parameters using the coordinate ascent inference algorithm and develop a variational Bayes based procedure for the variable selection and model assessment. We conduct simulation studies to assess the performance of our proposed method and compare it with the Markov Chains Monte Carlo sampling method. Our results show that the proposed variational Bayesian approach achieves computational efficiency without sacrificing estimation accuracy. We further illustrate the practical merits of the proposed approach by analyzing household finance survey data.

建议使用两部分模型来分析零膨胀数据，这些数据在零处表现出尖峰，或者有很大比例的参与者具有零值。本文提出了一种用于分析两部分潜变量模型的变分贝叶斯推理过程。我们利用 Pólya Gamma 随机表示通过平均场变分方法来近似后验分布。我们提出了一种使用坐标上升推理算法更新变分参数的方案，并开发了基于变分贝叶斯的变量选择和模型评估过程。我们进行模拟研究来评估我们提出的方法的性能，并将其与马尔可夫链蒙特卡罗采样方法进行比较。我们的结果表明，所提出的变分贝叶斯方法在不牺牲估计精度的情况下实现了计算效率。我们通过分析家庭财务调查数据进一步说明了所提出方法的实际优点。