Online Bayesian Model Averaging with Joint Uncertainty Quantification for Models and Regression Coefficients in Binary Regression

2026-09-15

AI Summary

本文针对二元回归中模型和回归系数的不确定性问题，提出了一种在线贝叶斯模型平均方法，通过可再生估计技术降低计算成本，同时保持了模型不确定性的量化。

Abstract

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.

Problem

• Bayesian model averaging
• uncertainty quantification
• binary regression
• streaming data
• renewable estimation

Innovation

• Online Bayesian Model Averaging
• Joint Uncertainty Quantification
• Renewable Estimation
• Binary Regression
• Streaming Data