Gavin J. Gibson's invited discussion contribution to the papers in Session 2 of the Royal Statistical Society's Special Topic Meeting on Covid-19 Transmission: 11 June 2021

I congratulate both teams for these welcome contributions on modelling the Covid-19 pandemic. To produce results of such quality within exacting timescales is a genuine achievement. Both studies infer a time-varying reproduction number R t from summary data by construct-ing hierarchical Bayesian frameworks embodying R t as an intrinsic parameter. Observations arise as noisy, time-shifted representations of an autoregressive infection process with weights specified by generation-time probabilities and moderated by R t . With a common root in Flaxman et al. (2020), the papers differ in their treatment of temporal effects and spatial cou-pling (with Teh et al. (2022) adopting an explicitly spatio-temporal Gaussian process for log R t while Mishra et al. (2022) use a random walk prior), in their use of data, and in underlying assumptions. Neither study, in the prior for R t , incorporates foreseeable effects such as step changes follow-ing interventions, the impact of improved testing on track-and-trace measures, or the expected decline in R t due to susceptible depletion. Incidentally, the presentation of the infection model in Mishra et al. (2022) seems confusing, with R t between equations (1) and (2) changing from an instantaneous reproduction number to a ‘raw’ reproduction number, subsequently re-scaled by the susceptible proportion before reporting. The papers’ general approach is arguably the ‘image analyst’s take’ on epidemic modelling, where the objective is to recover a ‘true’ R t from a noisy image, with prior distributions providing regularisation rather than capturing mechanistic thinking. This approach differs