Robust uncertainty quantification in popular estimators of the instantaneous reproduction number

The instantaneous reproduction number ( R _t ) is a widely used measure of the rate of spread of an infectious disease. Correct quantification of the uncertainty of R _t estimates is crucial for making well-informed decisions. Popular methods for estimating R _t leverage smoothing techniques to distinguish signal from noise. Examples include EpiEstim and EpiFilter, each are controlled by a single “smoothing parameter”, which is traditionally chosen by the user. We demonstrate that the values of these smoothing parameters are unknown and vary markedly with epidemic dynamics. We argue that data-driven smoothing choices are crucial for accurately representing uncertainty about R _t estimates. We derive model likelihoods for the smoothing parameters in both EpiEstim and EpiFilter. Adopting a flexible Bayesian framework, we use these likelihoods to automatically marginalise out the relevant smoothing parameters from these models when fitting to incidence time-series. Applying our methods, we find that the default parameterisations of these models can negatively impact inferences of R _t , delaying detection of epidemic growth, and misrepresenting uncertainty (typically by producing overconfident estimates), with substantial implications for public health decision-making. Our extensions mitigate these issues, provide a principled approach to uncertainty quantification, and improve the robustness of inference of R _t in real-time.