Public lecture: Randomness and imprecision
The randomness of a sequence of numbers can be defined in many ways. The talk begins with a short survey of the most common definitions of randomness and their relationships, and then focuses on a powerful and intuitive martingale-theoretic definition first suggested by Ville, and further refined by Schnorr and Levin. It essentially requires that there should be no (in some way computationally achievable) strategy for gambling on the successive outcomes in the sequence that allows a player, Skeptic, to become infinitely rich without borrowing. Interestingly, this betting approach allows for a generalisation towards interval (or imprecise) probabilities. As is often the case with the mathematics of imprecise probabilities, this allows for new ideas and structures to emerge, and takes us to a new vantage point from where it becomes easier to appreciate the subtleties and intricacies associated with the precise limit case where intervals reduce to numbers.
The slides for this lecture can be downloaded here:
Randomness And Imprecision
Bio: Gert de Cooman is Professor of Uncertainty Modelling and Systems Science in Ghent University, Belgium. He was a Grey College Alan Richards Fellow in Mathematics (2006) and Visiting Professor at Durham University from 2014 till 2017. His main research interest lies in dealing with robustness, imprecision and indecision in probabilistic modelling, and in particular the mathematical study of lower expectation functionals, the treatment of imprecision in stochastic processes using supermartingales, the foundations of decision making using sets of desirable gambles and choice functions, and most recently the study of the relation between randomness and imprecision. He is a founding member and former President of SIPTA (the international Society for Imprecise Probabilities: Theories and Applications), and is currently a member of its Executive Committee.