Insufficient stats

[sangeetabhatia03]

Again, I was trying to show that the behavior in the tail would be different, so having mean/sd, and even less so a median is highly suboptimal.

[ruthmccabe]

This looks good Sangeeta! I think the idea is similar to what I've done for the incubation period so I think we could maybe combine these?

[joshwlambert]

Thanks for adding @sangeetabhatia03. I'm not sure fully understand the message with this use case. Is it that when certain summary statistics are reported then we don't know the distribution exactly and therefore also don't have a good characterisation of the tail of the distribution?

If so I think we can merge this example with Ruth's in #6 to make the point on the tail of the distribution, which Ruth nicely provides context with isolation using the incubation period. For the other points I think we can be specific and mention them in the text. To me to the main aspects to cover are:

• identifiability issues (this is what I understand from your example with the mode of the gamma distribution)
• non-analytical conversion (when summary statistics cannot be directly converted to distribution parameters and require fitting)

[sangeetabhatia03]

yes, i agree that this can be merged with Ruth's example.

[joshwlambert]

After giving some thought to this example I don't think it should be merged with Ruth's use case on incubation period uncertainty (#6), but instead should be integrated into the text in the Summary statistics section. Within the text this point can be linked to the uncertainty on the 95th consequence as a downstream affect of not knowing the complete distribution.