AI 中文总结
本研究提出结合参数学习与祖先采样的p(参数)-CSMC算法，在分支过程模型的合成与真实数据应用中，相比标准粒子吉布斯采样，混合速度更快、自相关性更低，参数估计性能显著提升。
AI 中文摘要
本研究探索用于联合估计条件序贯蒙特卡洛（CSMC）算法中静态参数与潜态的粒子学习策略。基于该思路，我们提出p(参数)-CSMC算法，其结合了参数学习与祖先采样，在内部强相关性可能阻碍有效探索的场景下，相比（粒子）吉布斯采样具备更优的混合特性。我们在分支过程模型框架下开展两项应用：其一为合成数据应用，在假设繁殖数已知的前提下估计感染性剖面；其二为真实数据应用，基于2021年2月挪威SARS-CoV-2变异株B.1.1.7（Alpha）输入后的每日医院发病率，联合推断繁殖数与感染性剖面。结果显示，在上述场景中，与标准粒子吉布斯相比，该算法性能显著提升，混合速度大幅加快，自相关性明显降低。
英文摘要
In this work, we explore particle learning strategies for the joint estimation of static parameters and latent states within conditional sequential Monte Carlo (CSMC) algorithms. Building on this idea, we propose the p(parameter)-CSMC algorithm, which incorporates both parameter learning and ancestor sampling, leading to much better mixing properties compared to (particle) Gibbs sampling in settings where strong internal correlations may challenge effective exploration. We also include two applications in the context of a branching process model: one using synthetic data, where we estimate the infectivity profile while assuming the reproductive number to be known, and another using real data, where we address the joint inference of the reproductive number and the infectivity profile based on daily hospital incidence from the arrival of the SARS-CoV-2 lineage B.1.1.7 (Alpha) in Norway in February 2021. We show that, in these settings, performance is dramatically enhanced, with substantially faster mixing and markedly reduced autocorrelation compared with standard particle Gibbs.
