This section is kind of confusing, and I have tweaked the wording a little bit to try to be clearer. The reason for the confusion is that there are two nested distributions here.
The first is that when a bunch of people get infected, they have different incubation periods; some of them start showing symptoms more quickly than others. This is what the 99th percentile refers to. This makes us uncertain about the incubation period that a particular person will have, but it is not a confidence interval; if we learned how long the incubation periods were for a very large number of people, it wouldn’t make the 99th-percentile person’s incubation period any closer to the mean incubation period.
The second distribution is our uncertainty about the first distribution; we don’t know exactly what fraction of people will have extra-long incubation periods, or how long those periods will be—but we would if we observed enough people. This uncertainty is what the 9.7-17.2, 10.9-20.6, and 12.6-32.2 ranges are referring to.
After some more looking and thinking I still find both the claim and the answer a bit confusing. Given the, to me, somewhat cryptic comment below which seems to have a some backing, I want to see if I can figure out where I’m missing something everyone sees as so obvious.
The days for incubation at the 99% level were estimates of the longest incubation period in days we should expect. Am I still on the same page with everyone on on that?
If so then we have the 95% CI range about that mean estimate for the longest expect incubation period. The paper calls CI a credible interval which is a term I’ve never heard used for statistics. I had taken CI be to the standard confidence interval for the estimated value. From what I can understand the credible interval older (I suppose) confidence interval are similar but not quite the same. The credible interval appears to be narrower in smaller observations than the confidence internal—but the tend to converge as a limit.
If they are really similar concepts then I would think the same interpretation applies as I was using before. That is one cannot say a very strong statement about the estimated value per se using CI ranges. The CI is telling us that the “true” value has a likelihood of falling between the upper and lower range but we don’t really know where.
So if credible intervals do work as confidence intervals then the claim that out of 100 quarantined people on would have an incubation period at least as long as the estimated days (11.9, 14.1 or 18.5) is not a correct interpretation. What we should be able to say is that we have a credibility level or confidence level of 95% that the longest period we would observer would be between the upper and lower ranges.
This section is kind of confusing, and I have tweaked the wording a little bit to try to be clearer. The reason for the confusion is that there are two nested distributions here.
The first is that when a bunch of people get infected, they have different incubation periods; some of them start showing symptoms more quickly than others. This is what the 99th percentile refers to. This makes us uncertain about the incubation period that a particular person will have, but it is not a confidence interval; if we learned how long the incubation periods were for a very large number of people, it wouldn’t make the 99th-percentile person’s incubation period any closer to the mean incubation period.
The second distribution is our uncertainty about the first distribution; we don’t know exactly what fraction of people will have extra-long incubation periods, or how long those periods will be—but we would if we observed enough people. This uncertainty is what the 9.7-17.2, 10.9-20.6, and 12.6-32.2 ranges are referring to.
Thanks.
After some more looking and thinking I still find both the claim and the answer a bit confusing. Given the, to me, somewhat cryptic comment below which seems to have a some backing, I want to see if I can figure out where I’m missing something everyone sees as so obvious.
The days for incubation at the 99% level were estimates of the longest incubation period in days we should expect. Am I still on the same page with everyone on on that?
If so then we have the 95% CI range about that mean estimate for the longest expect incubation period. The paper calls CI a credible interval which is a term I’ve never heard used for statistics. I had taken CI be to the standard confidence interval for the estimated value. From what I can understand the credible interval older (I suppose) confidence interval are similar but not quite the same. The credible interval appears to be narrower in smaller observations than the confidence internal—but the tend to converge as a limit.
If they are really similar concepts then I would think the same interpretation applies as I was using before. That is one cannot say a very strong statement about the estimated value per se using CI ranges. The CI is telling us that the “true” value has a likelihood of falling between the upper and lower range but we don’t really know where.
So if credible intervals do work as confidence intervals then the claim that out of 100 quarantined people on would have an incubation period at least as long as the estimated days (11.9, 14.1 or 18.5) is not a correct interpretation. What we should be able to say is that we have a credibility level or confidence level of 95% that the longest period we would observer would be between the upper and lower ranges.
So where am I really getting off track here?
Well, the two of you have now been seen in the same place at the same time, putting to bed that theory...