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Electronic supplement on the fusion of experts’ opinions on climate sensitivity with the Transferable Belief Model

mardi 7 novembre 2006, par Minh Ha Duong

This paper uses the Transferable Belief Model to aggregate experts’ opinion on the climate sensitivity with the dataset from Morgan and Keith (1995) . The non-independence of experts issue is dealt with by organizing experts into schools of thought, requiring non-interactivity only across but not within groups. The issue of dissonance, that is wide qualitative differences in beliefs, is dealt with by using a disjunctive rather than conjunctive rule to combine the groups. We find the fusion do not support the idea that climate sensitivity must necessarily be within the IPCC range at any level, that the plausibility of the [4.5, 12] range is about 0.62, and for [6.0, 12] it is 0.31.


Data come from structured interviews using ``expert elicitation’’ methods drawn from decision analysis with 16 leading U.S. climate scientists. The study obtained quantitative, probabilistic judgments about a number of key climate variables. One of them is the climate sensitivity parameter, which can be defined as how much global warming there would be in the long term, if atmospheric CO$_2$ concentration was doubled relative to its pre-industrial levels.

Reichert et al (2001) noted that two aspects of this dataset are critical if one tries to combine them into a single judgment on climate sensitivity. First, the 16 experts are not independent, they are part of a research community regularly sharing data, models and ideas. Second, opinions on climate sensitivity are widely different in qualitative terms : in terms of Evidence Theory, there is a high degree of dissonance in beliefs.

To deal with this dissonance, this paper groups experts’ probability distributions in four classes, with a low dissonance within each group. Classes are based on the elicited range of possible values for the climate sensitivity parameter. Distributions from experts 2, 3 and 6 are the widest, they allow both a positive probability to cooling and to climate sensitivity well above 6°C. Distributions from experts 4, 7, 8, 9 do not give weight to cooling, but have an upper bound above 8°C. Probability distributions of experts numbered 1 and 10 to 16 are formulated on a range with width between 4.2 and 5.5°C. Expert’s 5 probability distribution lie in the narrowest range [0°C , 1°C].

Section 2 reviews prior works on combining experts opinion on climate sensitivity. In section 3, some acquaintance with the Dempster-Shafer theory of evidence is assumed, as the text briefly reminds the mathematical notations for the elements of the Transferable Belief Model used in this paper. Here, nly three different combination rules will be used. They differ as follows :

- The fusion of independent experts is computed using operators appropriate for ``non-interactive’’ information sources. When there is no independence, the fusion of interactive sources is computed using different operators, called ``cautious’’ combination rules below.
- In the same way that logical propositions can be connected by conjunction (AND) or disjunction (OR), fusion operators can be conjunctive or disjunction. The former are used to combine information sources when assuming that they are all correct. The later are used when assuming that at least one source is right, but one does not know which one.

The three combination rules used below are a noninteractive conjunction, a noninteractive disjunction and a cautious combination operator, the later introduced by Denoeux (2006).

Section 4 aggregates the experts’ opinion using these rules. It uses a two-stages procedure, based on idea that each of the four experts groups distinguished above is a ``school of thought’’. The first stage is to combine within groups beliefs using a cautious combination operator. The second stage is to combine the four groups together using a non-interactive disjunction operator.