I recently attended a talk by Gernot Wagner (with some commentary by Richard Zeckhauser) on the implications of the IPCC's widening of their "likely" 2100 global temperature rise from 2.0 to 4.5 degrees to 1.5 to 4.5 degrees. It is entitled: "Expecting a Black Swan but Getting a Dragon: Deep Uncertainty and Climate Change"
The major point of their argument was that a shift in the kurtosis of the distribution (made by taking out the "most likely" estimate of climate sensitivity) increased the net cost (in a metric known as willingness to pay (WTP)) by increasing the uncertainty of future predictions. There is nothing wrong with this as an exercise: two different pdfs passed through a certain set of filters and evaluated will produce different things. In this cases, pdfs of varying kurtosis produce more of a net WTP as the kurtosis increases. Nothing to see here.
The problem is that this is taken incredibly seriously by the public, as the results from this and similar studies have been used to price carbon. This increase in IPCC related uncertainty has the potential effect of doubling the cost of carbon from $40 to $80 per ton, though this depends on your pricing metric. These exercises are interpreted (and the author's are entirely complicit, spending a majority of the presentation talking about climate science) as being real authoritative pricing schemes, which they can not be.
Suppose I have a pdf of future warming which peaks at 3 degrees with a kurtosis of 2, and variance of 1 degree, a gaussian. The IPCC's release would indicate that the mean of the distribution would shift by half a degree, the kurtosis would increase, and so would the variance. So why is this not considered? How can we price carbon using the kurtosis shift but not include the mean shift too? It's a damning question, but not one that is considered. The authors, when confronted, go at great lengths to discuss the limitations of the model. Yet when left to speak freely, and in publications, the results are discussed as saying something real about the world. The rather bald-faced contradiction is difficult to swallow.
A link to the discussed paper is here
Oceanographer, Mathemagician, and Interested Party