Imprecise probabilities
Gert de Cooman · Risk Decision and Policy · 2000
The papers in the present symposium are a selection of contributions presented at ISIPTA '99, the ®rst International Symposium on Imprecise Probabilities and Their Applications, held in Ghent, Belgium, from 29 June to 2 July 1999.`Imprecise probability' is meant as a generic term for the many mathematical models which measure chance or uncertainty without sharp numerical probabilities.Such models are needed in inference problems where the relevant information is scarce, vague, or con¯icting, and in decision problems where preferences are imcomplete.Imprecise probability models are currently being studied and applied by a large number of researchers working in a great variety of ®elds.The aim of ISIPTA '99 was (i) to bring these people together to present research and to discuss issues of common interest, and (ii) to provide a common meeting place that would enable the various theories of imprecise probabilities that have been developed to be discussed and compared.More than ®fty carefully reviewed papers were presented at ISIPTA '99 (Cooman, Cozman, Moral and Walley, 1999), on a wide range of topics: mathematical models for uncertainty, conditioning rules, models for independence, combination of uncertainties, algorithms for computing inferences, coherence, hierarchical models, imprecise Markov processes, decision theory, ambiguity aversion, and Ellsberg's experiment.There were also papers on applications in economics, decision making, statistical inference, experimental studies of human judgement, arti®cal intelligence, reliability, dynamical systems, robotics, civil engineering, classi®cation, and legal problems.In preparing this RDP symposium, I faced the problem of selecting important papers that, taken together, would be representative for the rest of the contributions to ISIPTA '99, in the sense that they would somehow convey the distinct ambiance of open debate, free exchange of ideas and multidisciplinarity that many ISIPTA '99 participants were so enthusiastic about.I believe my ®nal choice to be fairly balanced: you will ®nd two theoretical survey papers, one on independence and one on decision making; two papers on psychological experiments related to interesting problems in imprecise probability theory, namely updating beliefs and sample space ignorance; and an applied mathematical paper dealing with optimal pollution control.In A survey of concepts of independence for imprecise probabilities, Couso et al. discuss, motivate, and compare various de®nitions of independence in the context of imprecise probabilities.They argue that, whereas there is essentially only one de®nition of independence for precise probabilities, there are at least six different notions or aspects of independence when imprecision is allowed, all of which are useful in different contexts.Some may see this as a disadvantage of working with imprecise probabilities.I prefer to think it is an advantage: imprecise models allow us