Bayesian inference in Epidemics: linear noise analysis

TL;DR

This paper analyzes the convergence of Bayesian inference in epidemic modeling using linear noise approximation, examining how data quantity and measurement quality affect inference accuracy through theoretical and numerical methods.

Contribution

It provides a qualitative analysis of Bayesian parameter inference convergence in epidemic models under measurement limitations, including best and worst case scenarios.

Findings

Convergence depends on measurement informativeness and data volume.

Linear noise approximation effectively models epidemic dynamics.

Numerical experiments validate theoretical insights.

Abstract

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.