This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli’s discussion of “convex Bayesianism” (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of “strong independence” (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli’s results and recent developments (...) on the axiomatization of non-binary preferences, and its impact on “complete” independence, are described. (shrink)

The goal of this paper is to describe the mechanism of the public perception of risk of artificial intelligence. For that we apply the social amplification of risk framework to the public perception of artificial intelligence using data collected from Twitter from 2007 to 2018. We analyzed when and how there appeared a significant representation of the association between risk and artificial intelligence in the public awareness of artificial intelligence. A significant finding is that the image of the risk of (...) AI is mostly associated with existential risks that became popular after the fourth quarter of 2014. The source of that was the public positioning of experts who happen to be the real movers of the risk perception of AI so far instead of actual disasters. We analyze here how this kind of risk was amplified, its secondary effects, what are the varieties of risk unrelated to existential risk, and what is the dynamics of the experts in addressing their concerns to the audience of lay people. (shrink)

The purpose of this paper is to show that if one adopts conditional probabilities as the primitive concept of probability, one must deal with the fact that even in very ordinary circumstances at least some probability values may be imprecise, and that some probability questions may fail to have numerically precise answers.

This festschrift for Teddy Seidenfeld is a collection of newly commissioned essays on imprecise probability by leading experts in the field. Each contribution touches on Teddy’s seminal contributions to the field of imprecise probability, and gives an up-to-date state of the field that cannot be found elsewhere. The title, “a reflection on the foundations of probability and statistics”, calls back to Teddy’s seminal book, “Rethinking the Foundations of Probability and Statistics”, bookends to a career that has made fundamental contributions to (...) the foundations of probability and statistics, and shaped the field of imprecise probability. It is aimed at scholars engaged in probability and statistics. (shrink)

This special issue of the International Journal of Approximate Reasoning grew out of the 8th International Symposium on Imprecise Probability: Theories and Applications. The symposium was organized by the Society for Imprecise Probability: Theories and Applications at the Université de Technologie de Compiègne in July 2013. The biennial ISIPTA meetings are well established among international conferences on generalized methods for uncertainty quantification. The first ISIPTA took place in Gent in 1999, followed by meetings in Cornell, Lugano, Carnegie Mellon, Prague, Durham (...) and Innsbruck. Compiègne proved to be a very nice location for ISIPTA 2013, offering wonderful opportunities for collaborations and discussions, as well as sightseeing places such as its imperial palace. (shrink)