Optimization of Complex Systems in the Presence of Uncertainty and Approximations
Final rept. 1 Aug 2001-31 Jul 2014
WASHINGTON UNIV SEATTLE
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Engineering decisions are invariably made under substantial uncertainty about current and future system cost and response, including cost and response associated with low-probability but high-consequence events. Such events motivate approaches that typically have centered on constraining or minimizing probability of failure, in contrast to the risk-neutral approach of constraining or minimizing expected values. The research under this proposal has, instead, developed concepts of risk-averse decision making between these extremes with the aim of achieving an advanced methodology better able to deal with risks and reliability in engineering design. Measures of risk that go beyond statistical quantiles to so-called superquantiles CVaR and their mixtures have been the main focus. The results have explored their superior properties and enhanced computability along with surprising implications that standard least-squares regression in statistical approximations might better be supplanted by generalizations like quantile and even superquantile regression. Superquantile regression, which provides a cautious and powerful tool, is completely new. It is entirely a product of this grant research.
- Statistics and Probability
- Operations Research