Covid19 Reproduction Number: Credibility Intervals by Blockwise Proximal Monte Carlo Samplers

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. IEEE

Credibility interval Design for Covid19 Reproduction Number from Nonsmooth Langevin-type Monte Carlo sampling

Monitoring the Covid19 pandemic is critical to design sanitary policies. Recently, reliable estimates of the pandemic reproduction number were obtained from a nonsmooth convex optimization procedure designed to fit epidemiology requirements and to be robust to the low quality of the data (outliers, pseudo-seasonalities,...). Applied to daily new infection counts made public by National Health Agencies and centralized by Johns Hopkins University, robust estimates of the reproduction number for 200+ countries are updated and published every day. To further improve estimation procedures and also, and mostly, increase their usability by epidemiologists, the present work exploits the Bayesian paradigm and derives a new Monte Carlo method to sample from a nonsmooth convex a posteriori distribution. This new sampler stems from an original combination of the Langevin Monte Carlo algorithm with Proximal operators. Its relevance and practical efficiency to produce meaningful credibility intervals for the Covid19 reproduction number are assessed from several indices quantifying the statistics of the Monte Carlo chains, and making use of real daily new infection counts. © 2022 European Signal Processing Conference, EUSIPCO. All rights reserved.