在线贝叶斯模型平均及其在二元回归中对模型和回归系数的联合不确定性量化
Online Bayesian Model Averaging with Joint Uncertainty Quantification for Models and Regression Coefficients in Binary Regression
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中文总结 AI 辅助
针对流式二元响应数据，提出基于可再生估计的在线贝叶斯模型平均方法，在降低计算成本的同时近似离线推断，并量化模型与系数的不确定性，支持自适应问题分配。
中文摘要 AI 辅助
流式二元响应数据出现在许多应用中，包括虚拟学习平台，其中学生的响应按顺序收集，估计的正确响应概率可能为后续的问题分配提供信息。逻辑回归为此类分析提供了一个可解释的框架，但数据可能支持多个合理的预测变量子集。贝叶斯模型平均（BMA）通过对竞争模型进行平均推断来考虑这种模型不确定性。由于对累积数据重复应用BMA在计算上可能很繁重，我们开发了一种基于可再生估计的在线实现。在每次更新时，保留的摘要和新观测值用于近似模型和特定模型系数的联合后验分布，而无需重新访问历史数据，从而能够提供包含模型不确定性的点和区间估计。模拟表明，在线BMA在系数估计、模型和变量重要性、预测以及预测概率的区间估计方面与离线对应方法非常接近，同时大幅降低了计算成本。在一个虚拟学习应用中，我们发现竞争预测变量子集之间存在相当大的不确定性，并且不同问题的可信区间宽度存在很大变异性。我们的方法将具有精确估计的问题与具有较大不确定性的问题区分开来，为自适应问题分配提供了超出点估计的信息。
英文摘要
Streaming binary response data arise in many applications, including virtual learning platforms where student responses are collected sequentially and estimated probabilities of correct responses may inform future question assignment. Logistic regression provides an interpretable framework for such analysis, but the data may support multiple plausible predictor subsets. Bayesian model averaging (BMA) accounts for such model uncertainty by averaging inference across competing models. Since repeatedly applying BMA to accumulating data can be computationally burdensome, we develop an online implementation based on renewable estimation. At each update, retained summaries and new observations are used to approximate the joint posterior of models and model-specific coefficients without revisiting historical data, enabling point and interval estimates that incorporate model uncertainty. Simulations show that online BMA closely approximates its offline counterpart in coefficient estimation, model and variable importance, prediction, and interval estimation of predictive probabilities, while substantially reducing computational cost. In a virtual learning application, we find substantial uncertainty across competing predictor subsets and large variability in credible interval widths across questions. Our method distinguishes questions with precise estimates from those with substantial uncertainty, providing information beyond point estimates for adaptive question assignment.
发表机构
- The University of Iowa（爱荷华大学）
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