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

TL;DR

This paper develops novel Monte Carlo sampling algorithms combining Langevin dynamics and proximal operators to accurately estimate credibility intervals for Covid19 reproduction numbers, improving pandemic monitoring tools.

Contribution

It introduces a new Bayesian inference approach with tailored sampling schemes to produce credible intervals for Covid19 reproduction number estimates from limited and noisy data.

Findings

Algorithms effectively produce credible intervals for reproduction numbers.

Performance validated on real Covid19 infection data from multiple countries.

Enhanced robustness of pandemic monitoring through improved uncertainty quantification.

Abstract

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.