In this article, we propose a variational Bayes (VB) inference method for the deterministic input noisy AND gate model of cognitive diagnostic assessment. The proposed method, which applies the iterative algorithm for optimization, is derived based on the optimal variational posteriors of the model parameters. The proposed VB inference enables much faster computation than the existing Markov chain Monte Carlo (MCMC) method, while still offering the benefits of a full Bayesian framework. A simulation study revealed that the proposed VB estimation adequately recovered the parameter values. Moreover, an example using real data revealed that the proposed VB inference method provided similar estimates to MCMC estimation with much faster computation.

中文翻译：

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DINA模型的变化贝叶斯推断

在本文中，我们为认知诊断评估的确定性输入噪声和门模型提出了一种变分贝叶斯（VB）推理方法。该方法基于模型参数的最优变分后验，推导了将迭代算法应用于优化的方法。与现有的马尔可夫链蒙特卡洛（MCMC）方法相比，拟议的VB推理实现了更快的计算，同时仍提供了完整的贝叶斯框架的优点。仿真研究表明，建议的VB估计可以充分恢复参数值。此外，使用实际数据的示例显示，提出的VB推理方法以更快的计算速度提供了与MCMC估计相似的估计。