The 4th International Symposium on Imprecise Probabilities and Their Applications 2005 was held on the campus of Carnegie Mellon University in Pittsburgh, Pennsylvania, USA from July 20-24, 2005. 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). The first day started with an introduction to imprecise probabilities given by Gert de Cooman President of SIPTA. Second day each presenter 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 of financial risk assessment.