One may argue the geometric mean is not adequate based on the following. If the soot injected into the stratosphere per countervalue yield I deduced from Reisner’s and Toon’s view respects the 5th and 95th percentile of a lognormal distribution, the geometric mean is the median of the distribution, but what matters is its mean. This would be 5.93*10^-4 Tg/kt, i.e. 2.28 (= 5.93*10^-4/(2.60*10^-4)) times my best guess. I did not follow this approach because:
It is quite easy for an apparently reasonable distribution to have a nonsensical right tail which drives the expected value upwards. For instance, setting the soot injected into the stratosphere per countervalue yield I deduced from Reisner’s and Toon’s view to the 25th and 75th percentile of a lognormal distribution, its mean would be 0.0350 Tg/kt, which is 16.3 (= 0.0350/0.00215) times the 0.00215 Tg/kt I deduced for Toon’s view, i.e. apparently too high.
I do not have a good sense of the quantiles corresponding to the results I calculated based on Reisner’s and Toon’s views.
I guess it is better to treat the results I inferred from Reisner’s and Toon’s view as random samples of a lognormal distribution, as opposed to matching them to specific quantiles. I used the geometric mean, which is the MLE of the median of a lognormal distribution[18].
In the post, I used the geometric mean to get the MLE of the mean of lognormal distributions, which I assumed for variables with 2 estimates differing a lot between them that did not range from 0 to 1. I have now realised the geometric mean is the MLE of the median (not mean) of a lognormal distribution, and corrected the text accordingly. However, I would ideally update the post using the MLE of the mean (not median) of lognormal distributions. If I did this, since, from the above, the soot injected into the stratosphere per countervalue yield would become around 2.28 times as large, and I think famine deaths due to the climatic effects are roughly proportional to it, I guess these would roughly double. On the other hand, I commented I may well have overestimated such deaths due to another reason. I guess accounting for the 2 opposing factors would lead to my best guess for the famine deaths due to the climatic effects becoming 1⁄3 to 3 times as large with 50 % probability.
In the post, I used the geometric mean to get the MLE of the mean of lognormal distributions, which I assumed for variables with 2 estimates differing a lot between them that did not range from 0 to 1. I have now realised the geometric mean is the MLE of the median (not mean) of a lognormal distribution, and corrected the text accordingly. However, I would ideally update the post using the MLE of the mean (not median) of lognormal distributions. If I did this, since, from the above, the soot injected into the stratosphere per countervalue yield would become around 2.28 times as large, and I think famine deaths due to the climatic effects are roughly proportional to it, I guess these would roughly double. On the other hand, I commented I may well have overestimated such deaths due to another reason. I guess accounting for the 2 opposing factors would lead to my best guess for the famine deaths due to the climatic effects becoming 1⁄3 to 3 times as large with 50 % probability.