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.

翻译：监测 Covid19 疫情是一项关键的社会挑战，已投入大量研究工作。疫情在特定地区的强度可通过再生数有效衡量，该参数量化每日新增感染的增长速率。近期，研究人员采用反问题框架与非光滑函数最小化方法，估算了再生数的时间演化。尽管该方法设计上对 Covid19 数据有限质量（如异常值、缺失计数）具有鲁棒性，但其无法输出基于可信区间的估计值。这严重制约了流行病学家在疫情监测中的实际应用，而本研究旨在通过蒙特卡洛采样克服此局限性。通过将非光滑函数融入贝叶斯框架，我们定制了多种采样方案以适配后验分布的非光滑特性。所设计算法的创新之处在于结合了朗之万蒙特卡洛采样方案与近端算子。我们比较了这些新算法在生成再生数估计及去噪计数的可信区间方面的性能，并利用约翰霍普金斯大学提供的真实每日新增感染计数进行评估，同时通过多国 Covid19 数据展示了所开发监测工具的应用价值。