Dealing with Imprecise Probabilities: Interval-Related Talks at ISIPTA'05

What was the conference? From July 20–24, 2005, the 4th International Symposium on Imprecise Probabilities and Their Applications (ISIPTA’05) was held on the campus of Carnegie Mellon University in Pittsburgh, Pennsylvania, USA. This biennial conference is organized by the Society for Imprecise Probability Theory and Applications (SIPTA) [13]. The main organizers of ISIPTA’05 were Fabio G. Cozman (University of Sao Paulo, Brazil), Robert Nau (Duke University, USA), and Teddy Seidenfeld (Carnegie Mellon University). Papers presented at ISIPTA’05 were authored by researchers from a very diverse list of countries: Belgium, Brazil, the Czech Republic, France, Germany, Israel, Italy, New Zealand, Russia, Slovenia, Spain, Switzerland, the UK, and the US. This ISIPTA conference had an interesting format that had been found valuable in previous conferences. The first day was devoted to tutorials, starting with an introduction to imprecise probabilities given by Gert de Cooman, President of SIPTA. Starting the second day, each regular paper was presented in a plenary session, which was followed by a poster session where the presenters of that session also presented a poster and actively communicated with interested participants. A special session was devoted to open problems, and the conference was immediately followed by a half-day workshop on a key application area, financial risk assessment. Next we review subjective probabilities as traditionally handled. With that as background, we review the imprecise probability approach. In this review, we mainly follow the tutorial given by G. de Cooman. This review is followed by problems, challenges, and steps toward their resolution presented by researchers at the conference.