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Monitoring the evolution of the Covid19 pandemic constitutes a critical stepin sanitary policy design. Yet, the assessment of the pandemic intensity withinthe pandemic period remains a challenging task because of the limited qualityof data made available by public health authorities (missing data, outliers andpseudoseasonalities, notably), that calls for cumbersome and ad-hocpreprocessing (denoising) prior to estimation. Recently, the estimation of thereproduction number, a measure of the pandemic intensity, was formulated as aninverse problem, combining data-model fidelity and space-time regularityconstraints, solved by nonsmooth convex proximal minimizations. Thoughpromising, that formulation lacks robustness against the limited quality of theCovid19 data and confidence assessment. The present work aims to address bothlimitations: First, it discusses solutions to produce a robust assessment ofthe pandemic intensity by accounting for the low quality of the data directlywithin the inverse problem formulation. Second, exploiting a Bayesianinterpretation of the inverse problem formulation, it devises a Monte Carlosampling strategy, tailored to a nonsmooth log-concave a posterioridistribution, to produce relevant credibility intervalbased estimates for theCovid19 reproduction number. Clinical relevance Applied to daily counts of newinfections made publicly available by the Health Authorities for around 200countries, the proposed procedures permit robust assessments of the timeevolution of the Covid19 pandemic intensity, updated automatically and on adaily basis.

Temporal evolution of the Covid19 pandemic reproduction number: Estimations from proximal optimization to Monte Carlo sampling