Nic Lewis (a co-author of O’Donnell et al 2010) is a very sharp analyst who’s recently taken an interest in climate sensitivity estimates and has an interesting guest post at Judy Curry’s today.
In his studies, he noticed that the IPCC’s representation in AR4 Figure 9.20 of the probability distribution for climate sensitivity arising from observationally-based Forster and Gregory 2006 differed substantially from the distribution in the original article. He reports that the alteration had the effect of fattening the tails of high-end climate sensitivity. He reports:
The IPCC did not attempt, in the relevant part of AR4:WG1 (Chapter 9), any justification from statistical theory, or quote authority for, restating the results of Forster/Gregory 06 on the basis of a uniform prior in S. Nor did the IPCC challenge the Forster/Gregory 06 regression model, analysis of uncertainties or error assumptions. The IPCC simply relied on statements [Frame et al. 2005] that ‘advocate’ – without any justification from statistical theory – sampling a flat prior distribution in whatever is the target of the estimate – in this case, S. In fact, even Frame did not advocate use of a prior uniform distribution in S in a case like Forster/Gregory 06. Nevertheless, the IPCC concluded its discussion of the issue by simply stating that “uniform prior distributions for the target of the estimate [the climate sensitivity S] are used unless otherwise specified”.
The transformation effected by the IPCC, by recasting Forster/Gregory 06 in Bayesian terms and then restating its results using a prior distribution that is inconsistent with the regression model and error distributions used in the study, appears unjustifiable. In the circumstances, the transformed climate sensitivity PDF for Forster/Gregory 06 in the IPCC’s Figure 9.20 can only be seen as distorted and misleading.
Update- A commenter at Judy Curry’s has drawn attention to AR4 Review Comments. I’ve uploaded the more convenient version that used to be available (IPCC took this down in favor of a less usable version.) Search “uniform prior” for interesting discussion.