Distributional Uncertainty in Uncertainty Quantification

08.12.2017, 10:15-11:45  –  Campus Golm, Haus 28, Raum 0.108

Tim Sullivan (Zuse Institut Berlin und FU Berlin)

Many problems in forward and inverse uncertainty quantification assume a single probability distribution of interest, e.g. a distribution of random inputs or a prior measure for Bayesian inference. However, on close inspection, many of these probability distributions are not completely determined by the available information, and this introduces an additional source of uncertainty. For example there may be good grounds for assuming a particular form for the distribution, but the "correct" values of a few parameters may be known only approximately; at another extreme, only a few moments or statistics of the distribution may be known, leaving an infinite-dimensional non-parametric distributional uncertainty to be reckoned with.
Such so-called distributional or Knightian uncertainties may be particularly important if critical features of the system depend upon underdetermined aspects of the probability distribution such as tail behaviour. This talk will give a brief introduction to the treatment of such uncertainties, in both finite-and infinite-dimensional settings, including maximum entropy and optimisation approaches.

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