Bayesian inference in epidemics: linear noise analysis

This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the Bayesian model's convergence with increasing amounts of data under measurement limitations. Depending on how weakly informative the disease measurements are, we offer a kind of 'best case' as well as a 'worst case' analysis where, in the former case, we assume that the prevalence is directly accessible, while in the latter that only a binary signal corresponding to a prevalence detection threshold is available. Both cases are studied under an assumed so-called linear noise approximation as to the true dynamics. Numerical experiments test the sharpness of our results when confronted with more realistic situations for which analytical results are unavailable.

Automated summary

This paper qualitatively investigates the convergence of Bayesian parameter inference in disease modeling. The study focuses on the Bayesian model's convergence with increasing amounts of data under measurement limitations. Depending on the informativeness of the disease measurements, a 'best case' and a 'worst case' analysis are provided. These cases consider direct accessibility to prevalence and binary signals corresponding to prevalence detection threshold, respectively. Numerical experiments are conducted to test the adaptability of the results in more realistic scenarios where analytical results are unavailable.