Dear Authors,

thank you for this valuable contribution and for the comparison with the method proposed by Höhle and an der Heiden (2014). If I understand the methodology and comparison correctly, you show that considering auto-correlation in the underlying case numbers is an important feature to get good prediction intervals.

- Auto-correlation: What the authors describe as the Höhle and an der Heiden (2014) method is implemented as the „bayes.trunc“ method in the function nowcast of the R package surveillance. However, the paper and the implementation contains an additional method „ddcp“, which also allows one to specify a prior model for the \lambda_t function. The theory for this is covered in Section 4.1 of Höhle and an der Heiden (2014). The surveillance package currently reliably implements a penealized truncated power spline for this, but in principle one has the option to use a random walk here (see ddcp argument logLambda = „rw1“). It would be interesting to see, how the comparison looks when using the surveillance package with this option. Is the code of your comparison publically available?

- Time varying delays: As the authors point out it can be difficult to know any changes in the delay distribution beforehand. However, in the STEC/EHEC example, the breakpoint was obvious, because it was due to a change in the instruction on how to transmit cases as part of the surveillance system. But even in case of lack of knowledge, one can mimic a non-parametric setting with the nowcast function in the surveillance package by simply placing several change-points. This is, e.g., done in the work of

https://www.stablab.stat....

and is now also easily parametrizable in the nowcast function in the development version of the surveillance package (https://r-forge.r-project...). It is expected to appear on CRAN.

Based on your results, it appears prudent to provide better advice/default configuration for the nowcast function in the surveillance package. For the comparison between implementations, it would be interesting though to also compare apples with apples. It will probably depend a bit on how smooth \lambda_t really is, but I do believe as you, that for most outbreaks it's going to be smooth. Even for the STEC/EHEC outbreak data discussed in Höhle and an der Heiden (2014) we got better results using "ddcp".

Thanks for doing this careful analysis and evaluation and for pointing out an important way to improve the nowcasts!

Best regards,

Michael Höhle