Bayesian inference in epidemics: linear noise analysis

Samuel Bronstein; Stefan Engblom; Robin Marin; Samuel Bronstein; Stefan Engblom; Robin Marin

doi:10.3934/mbe.2023193

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 4128-4152. doi: 10.3934/mbe.2023193

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Bayesian inference in epidemics: linear noise analysis

1.
Department of Mathematics and Applications, ENS Paris, 75005 Paris, France
2.
Division of Scientific Computing, Department of Information Technology, Uppsala University, SE-751 05 Uppsala, Sweden

Academic Editor: Sen Pei

Received: 30 September 2022 Revised: 07 December 2022 Accepted: 14 December 2022 Published: 20 December 2022

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.
- Parameter estimation,
- Bayesian modeling,
- Stochastic epidemiological models,
- Network model,
- Ornstein-Uhlenbeck process
Citation: Samuel Bronstein, Stefan Engblom, Robin Marin. Bayesian inference in epidemics: linear noise analysis[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 4128-4152. doi: 10.3934/mbe.2023193

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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.

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