基于熵优化的摘要统计量的梯度近似贝叶斯推断用于 compartmental 模型
Gradient-Based Approximate Bayesian Inference with Entropy-Optimized Summary Statistics for Compartmental Models
AI总结：
本文提出一种三阶段框架，结合了似然基于和似然自由方法，通过熵优化摘要统计量提高 compartmental 模型参数估计的可靠性与效率。
摘要：
近年来的流行病大流行凸显了传染病模型在指导公共卫生决策中的关键作用，推动了对能够提供及时答案的现实模型的需求。Compartmental 模型广泛用于捕捉疾病动态，随着数据可用性、计算资源和流行病学理解的提高，已开发出能够包含人口结构、疾病进展和干预效果的详细模型。尽管这些进步提高了模型的保真度，但也增加了模型的复杂性，导致高维参数空间、不可解的似然和在实时有限监测数据下拟合模型的计算挑战。现有的似然自由方法，如近似贝叶斯计算（ABC）和贝叶斯合成似然（BSL），已 largely 独立发展，各自有独特的优缺点。我们提出一个综合的三阶段框架，结合了似然基于和似然自由方法的进展：（1）基于 ABC 的熵最小化以识别低维、近似正交的摘要统计量；（2）使用这些优化的摘要进行 BSL 推断以构建可解的高斯近似；（3）利用哈密顿蒙特卡洛采样进行高效的后验探索。通过 SEIR 模拟研究和对 1978 年英国寄宿学校流感爆发的应用，我们证明了我们的框架在保持计算效率的同时实现了可靠的参数估计和不确定性量化。
英文摘要：
Recent pandemics have highlighted the critical role of infectious disease models in guiding public health decision-making, driving demand for realistic models that can provide timely answers under uncertainty. Compartmental models are widely used to capture disease dynamics, and advances in data availability, computational resources, and epidemiological understanding have allowed the development of models that incorporate detailed representations of population structure, disease progression, and intervention effects. While these improvements improve model fidelity, they also increase model complexity, leading to high-dimensional parameter spaces, intractable likelihoods, and computational challenges for fitting models to limited surveillance data in real time. Existing likelihood-free methods, such as Approximate Bayesian Computation (ABC) and Bayesian Synthetic Likelihood (BSL), have developed largely independently, each with distinct strengths and limitations. We propose an integrated three-stage framework that synthesizes advances from both likelihood-based and likelihood-free method: (1) ABC-based entropy minimization to identify low-dimensional, approximately orthogonal summary statistics; (2) BSL inference using these optimized summaries to construct tractable Gaussian approximations; and (3) Hamiltonian Monte Carlo sampling for efficient posterior exploration. Through SEIR simulation study and application to the 1978 British boarding school influenza outbreak, we demonstrate that our framework achieves reliable parameter estimation and uncertainty quantification while maintaining computational efficiency.
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