I think these additional layers of uncertainty are epistemically important, and incorporating them would likely serve to “dampen” the effect that the mean result of the model affects our all-things-considered judgement about the welfare capacity of any species.
I tend to agree.
But there are other ways to aggregate the estimates, which could (and likely would) be better than using the median.
I wondered whether it would be better for you to aggregate the results from the different models with the geometric mean of odds. For example, if models 1 and 2 implied a probability of 50 % and 90 % of the welfare range being smaller than 0.2, corresponding to odds of 1 (= 0.5/(1 − 0.5)) and 9 (= 0.9/(1 − 0.9)), the aggregated model would imply odds of 3 (= (1*9)^0.5) of the welfare range being smaller than 0.2, corresponding to a probability of 75 % (= 1/(1 + 1⁄3)). There is some evidence for using the geometric mean of odds, so I believe an approach like this combined with using the means of the aggregated distributions would be better than your approach of using the medians of the final distributions at the end.
Thanks for the good reply too, Laura.
I tend to agree.
I wondered whether it would be better for you to aggregate the results from the different models with the geometric mean of odds. For example, if models 1 and 2 implied a probability of 50 % and 90 % of the welfare range being smaller than 0.2, corresponding to odds of 1 (= 0.5/(1 − 0.5)) and 9 (= 0.9/(1 − 0.9)), the aggregated model would imply odds of 3 (= (1*9)^0.5) of the welfare range being smaller than 0.2, corresponding to a probability of 75 % (= 1/(1 + 1⁄3)). There is some evidence for using the geometric mean of odds, so I believe an approach like this combined with using the means of the aggregated distributions would be better than your approach of using the medians of the final distributions at the end.