新冠病毒肺炎再生数：基于分块近端蒙特卡洛采样器的可信区间
Covid19 Reproduction Number: Credibility Intervals by Blockwise Proximal Monte Carlo Samplers
AI总结：
针对非光滑反问题再生数估计缺乏可信区间的问题，本文将其纳入贝叶斯框架，提出结合 Langevin Monte Carlo 与近端算子的分块采样算法，并在多国新冠数据上验证。
摘要：
监测新冠病毒肺炎疫情是一项关键的社会议题，已受到大量研究投入。特定区域内的疫情强度可由再生数有效衡量，该指标量化每日新增感染的增长率。最近，研究人员通过一种非光滑泛函最小化的反问题表述，给出了再生数随时间演化的估计。尽管该方法被设计为能够对新冠病毒肺炎数据质量有限的问题（异常值、缺失计数）保持稳健，但这一过程无法输出基于可信区间的估计。对于流行病学家在实际疫情监测中的应用而言，这仍是一项严重局限，而本工作旨在通过蒙特卡洛采样加以克服。在将非光滑泛函解释到贝叶斯框架之后，本文定制了若干采样方案，以适应所得后验分布的非光滑性质。所设计算法的创新性源于将 Langevin Monte Carlo 采样方案与 Proximal（近端）算子相结合。文中比较了新算法在为再生数估计及去噪计数生成相关可信区间方面的性能。评估基于 Johns Hopkins University 提供的真实每日新增感染计数开展。所设计监测工具的价值在多个不同国家的新冠病毒肺炎数据上得到展示。
英文摘要：
Monitoring the Covid19 pandemic constitutes a critical societal stake that received considerable research efforts. The intensity of the pandemic on a given territory is efficiently measured by the reproduction number, quantifying the rate of growth of daily new infections. Recently, estimates for the time evolution of the reproduction number were produced using an inverse problem formulation with a nonsmooth functional minimization. While it was designed to be robust to the limited quality of the Covid19 data (outliers, missing counts), the procedure lacks the ability to output credibility interval based estimates. This remains a severe limitation for practical use in actual pandemic monitoring by epidemiologists that the present work aims to overcome by use of Monte Carlo sampling. After interpretation of the nonsmooth functional into a Bayesian framework, several sampling schemes are tailored to adjust the nonsmooth nature of the resulting posterior distribution. The originality of the devised algorithms stems from combining a Langevin Monte Carlo sampling scheme with Proximal operators. Performance of the new algorithms in producing relevant credibility intervals for the reproduction number estimates and denoised counts are compared. Assessment is conducted on real daily new infection counts made available by the Johns Hopkins University. The interest of the devised monitoring tools are illustrated on Covid19 data from several different countries.
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