Hans R Künsch and Fabio Sigrist's contribution to the Discussion of ‘The Second Discussion Meeting on Statistical aspects of the Covid-19 Pandemic’
本文评论了结合流行病学模型与高级统计方法的研究，介绍了作者开发的联合估计感染数和有效再生数的MCMC算法，并讨论了模型选择与不确定性沟通的重要性。
The authors are to be congratulated for an interesting and timely paper that combines epidemiological modelling with advanced statistical methodology. We are currently working on a related project, developing an Markov chain Monte Carlo algorithm for estimating effective daily reproduction numbers using the model of Cori et al. (2013) (see also p. 3 in the paper under discussion). The standard procedure as described, e.g., in Huisman et al. (2022) estimates first daily infections from confirmed cases by deconvolution and then reproduction numbers from inferred infections whereas our algorithm estimates infections and reproduction numbers jointly based on a coherent statistical model. In our current implementation, the acceptance rate for the number of infections decreases to very low values for long observation periods. To avoid this, we split the data into overlapping smaller windows and merge the posterior samples from different windows. We have also developed an sequential Monte Carlo algorithm for the same model, but even with a more efficient proposal than the bootstrap, sample depletion is a problem. A new observation of confirmed cases has a substantial effect on the smoothing distribution of infections several days earlier, and the auxiliary particle filter can account for this only via resampling, and not via changing the values in the sample. Since our setup differs from the one in the paper not only in the model and the data sources but also in other specifications a direct comparison is not possible. The authors assume that the detection probability of an infected case on some day depends only on the number of tests on that day; see (5) in their paper. We think that the severity of symptoms would be a more important covariate as individuals with no or only mild symptoms are much more likely not to take a test. In epidemic modelling, one has to make many choices: A more complex model is potentially more realistic, but it suffers from a large number of unknown parameters and/or additional assumptions. In view of the many choices that have to be made and the obvious weak points of all assumptions, an honest communication of the uncertainty is challenging. A potential advantage of the model by Cori et al. (2013) is that it is simpler and relies on fewer assumptions compared to an SEIR (susceptible-exposed-infected-recovered) model. In general, we think that sensitivity studies and comparison of results obtained with methods from different groups are important to assess uncertainty.