Monitoring a pandemic is critical to design sanitary policies. The question is to learn a pandemic reproduction number from daily new infection counts made public; for example, such counts for the COVID19 were provided by National Health Agencies and centralized by Johns Hopkins University.
Recent works rely on a Bayesian statistical model designed to fit epidemiology requirements and to be robust to the low quality of the data (outliers, pseudo-seasonalities, . . . ). The maximum a posteriori can be obtained from nonsmooth convex optimization procedure; credibility intervals for the reproduction number, necessitate Monte Carlo methods for the exploration of the a posteriori density.
In this talk, we will first introduce this statistical model, which yields a non-smooth log-concave a posteriori distribution.
We will then explain our main contribution, which consists in designing new Markov chain Monte Carlo (MCMC) samplers able to deal with a composite log-density. This new sampler stems from an original combination of the Langevin Monte Carlo algorithm with Proximal operators.
Our methods will be compared to other MCMC samplers proposed in the literature for such target distributions.
Finally, the relevance and practical efficiency to produce meaningful credibility intervals for the Covid19 reproduction number will be discussed, making use of real daily new infection counts.
This is a joint work with Patrice Abry (CNRS & Laboratoire de Physique de l'ENS Lyon, Lyon) and Barbara Pascal (CNRS & LS2N, Nantes).
