  Monitoring the evolution of the Covid19 pandemic constitutes a critical step
in sanitary policy design. Yet, the assessment of the pandemic intensity within
the pandemic period remains a challenging task because of the limited quality
of data made available by public health authorities (missing data, outliers and
pseudoseasonalities, notably), that calls for cumbersome and ad-hoc
preprocessing (denoising) prior to estimation. Recently, the estimation of the
reproduction number, a measure of the pandemic intensity, was formulated as an
inverse problem, combining data-model fidelity and space-time regularity
constraints, solved by nonsmooth convex proximal minimizations. Though
promising, that formulation lacks robustness against the limited quality of the
Covid19 data and confidence assessment. The present work aims to address both
limitations: First, it discusses solutions to produce a robust assessment of
the pandemic intensity by accounting for the low quality of the data directly
within the inverse problem formulation. Second, exploiting a Bayesian
interpretation of the inverse problem formulation, it devises a Monte Carlo
sampling strategy, tailored to a nonsmooth log-concave a posteriori
distribution, to produce relevant credibility intervalbased estimates for the
Covid19 reproduction number. Clinical relevance Applied to daily counts of new
infections made publicly available by the Health Authorities for around 200
countries, the proposed procedures permit robust assessments of the time
evolution of the Covid19 pandemic intensity, updated automatically and on a
daily basis.
