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

arXiv: https://arxiv.org/abs/2203.09142 · HTML: https://mlsanity.com/paper/2203.09142/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 63 references that are in the map.
- First posted on arXiv 17 Mar 2022.

## Builds on (most cited first, 9 of 9)

- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [Analysis of Langevin Monte Carlo via convex optimization](https://mlsanity.com/paper/1802.09188/) (2018)
- [Log-concave sampling: Metropolis-Hastings algorithms are fast](https://mlsanity.com/paper/1801.02309/) (2018)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithm](https://mlsanity.com/paper/2006.09270/) (2020)
- [Langevin Monte Carlo without smoothness](https://mlsanity.com/paper/1905.13285/) (2019)
- [A Survey of Monte Carlo Methods for Parameter Estimation](https://mlsanity.com/paper/2107.11820/) (2021)
- [A Review of Multiple Try MCMC algorithms for Signal Processing](https://mlsanity.com/paper/1801.09065/) (2018)
- [Nonsmooth convex optimization to estimate the Covid-19 reproduction number space-time evolution with robustness against low quality data](https://mlsanity.com/paper/2109.09595/) (2021)

## Built on by (most cited first, 1 of 1)

- [Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2305.15988/) (2023)

## Abstract (arXiv)

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.