Bayesian Knowledge Tracing (BKT) is a widely used and interpretable student modeling approach in intelligent tutoring systems and educational data mining. However, most implementations rely on expectation-maximization or related optimization methods that yield only point estimates, limiting uncertainty quantification and principled comparisons across learners and conditions. We introduce StanBKT, an open-source Python package for estimating BKT models using Bayesian inference in Stan. StanBKT provides a unified framework supporting Hamiltonian Monte Carlo, variational inference, Pathfinder, and optimization-based estimation while preserving the hidden Markov structure and interpretability of classical BKT. It supports standard, grouped, and hierarchical BKT models, flexible prior specification, posterior predictive inference, and utilities for visualization and diagnostics. We evaluate StanBKT on large-scale observational and controlled educational datasets. On the ASSISTments 2020 dataset, we show that supported inference methods achieve comparable predictive performance while differing in computational efficiency and posterior fidelity. We further demonstrate how posterior inference enables principled comparison of condition-specific parameters in an educational intervention involving perceptual cue manipulations. Results illustrate how uncertainty quantification facilitates more reliable interpretation of differences in learning, forgetting, guessing, and slipping parameters across experimental conditions. Overall, StanBKT extends BKT beyond point estimation by providing a flexible framework for probabilistic student modeling, uncertainty quantification, and hierarchical inference in educational data mining.

翻译：摘要：贝叶斯知识追踪（BKT）是智能辅导系统与教育数据挖掘中广泛使用且具可解释性的学生建模方法。然而，大多数实现依赖期望最大化或其相关优化方法，仅能生成点估计，这限制了不确定性量化以及跨学习者与实验条件的严谨比较。我们提出StanBKT，一个基于Stan进行贝叶斯推断来估计BKT模型的开源Python包。StanBKT提供统一框架，支持哈密顿蒙特卡洛、变分推断、Pathfinder及基于优化的估计方法，同时保留经典BKT的隐马尔可夫结构与可解释性。其支持标准、分组与层次化BKT模型、灵活的先验设定、后验预测推断，以及可视化与诊断工具。我们在大规模观测性与受控教育数据集上评估StanBKT。基于ASSISTments 2020数据集，我们展示了所支持的推断方法在预测性能上可比，但在计算效率与后验保真度上存在差异。我们进一步展示了后验推断如何实现对涉及感知线索操控的教育干预中条件特异性参数进行严谨比较。结果表明，不确定性量化能促进对跨实验条件的学习、遗忘、猜测与滑移参数差异进行更可靠的解读。总体而言，StanBKT通过提供概率化学生建模、不确定性量化及教育数据挖掘中层次化推断的灵活框架，将BKT拓展至点估计之外的范畴。