Title: Comparative study of Bayesian and Frequentist methods for epidemic forecasting: Insights from simulated and historical data Show Chinese title

Title: 贝叶斯方法与频率学派方法在流行病预测中的比较研究：来自模拟数据和历史数据的见解

Abstract: Accurate epidemic forecasting is critical for effective public health interventions. This study compares Bayesian and Frequentist estimation frameworks within deterministic compartmental epidemic models, focusing on nonlinear least squares optimization versus Bayesian inference using MCMC sampling via Stan. We compare forecasting performance under shared modeling structure and error assumptions for specific implementations of both approaches. We assess performance on simulated datasets (with R0 values of 2 and 1.5) and historical datasets including the 1918 influenza pandemic, 1896-97 Bombay plague, and COVID-19 pandemic. Evaluation metrics include Mean Absolute Error, Root Mean Squared Error, Weighted Interval Score, and 95% prediction interval coverage. Forecasting performance depends on epidemic phase and dataset characteristics, with no method consistently outperforming across all contexts. Frequentist methods perform well at peak and post-peak phases but are less accurate pre-peak. Bayesian methods, particularly with uniform priors, offer better early-epidemic accuracy and stronger uncertainty quantification, especially valuable when data are sparse or noisy. Frequentist methods often yield more accurate point forecasts with lower error metrics, though their interval estimates may be less robust. We examine how prior choice influences Bayesian forecasts and how extending forecasting horizons affects convergence. These findings offer practical guidance for choosing estimation strategies tailored to epidemic phase and data quality, supporting more effective public health interventions. Show Chinese abstract

Abstract: 准确的流行病预测对于有效的公共卫生干预至关重要。 本研究比较了确定性分 compartment 流行病模型中的贝叶斯和频率学派估计框架，重点在于非线性最小二乘优化与使用 Stan 进行 MCMC 抽样的贝叶斯推断。 我们比较了在共享建模结构和误差假设下，两种方法特定实现的预测性能。 我们在模拟数据集（R0 值为 2 和 1.5）和历史数据集上评估性能，包括 1918 年流感大流行、1896-97 年孟买瘟疫和 COVID-19 大流行。 评估指标包括平均绝对误差、均方根误差、加权区间得分和 95% 预测区间覆盖率。 预测性能取决于流行阶段和数据集特征，在所有情境中没有一种方法始终优于其他方法。 频率学派方法在峰值和峰值后阶段表现良好，但在峰值前阶段准确性较低。 贝叶斯方法，特别是使用均匀先验时，能提供更好的早期流行准确性以及更强的不确定性量化，这在数据稀疏或噪声较大时尤其有价值。 频率学派方法通常能提供更准确的点预测，误差指标更低，尽管其区间估计可能不够稳健。 我们研究了先验选择如何影响贝叶斯预测，以及延长预测范围如何影响收敛性。 这些发现为根据流行阶段和数据质量选择估计策略提供了实用指导，有助于支持更有效的公共卫生干预。