| Event Description: , , Risk, Optimization and Statistics Uncertainty over the future, even if well supported by statistical information, causes a fundamental difficulty in optimization. Decisions can't pin future "costs" to specific values and are instead limited only to shaping their probability distributions as random variables. Hard upper bounds on "costs" may then be impossible or too expensive to enforce. On the other hand, traditional approaches in such a contest in terms of safety margins built around standard deviation, or probability of failure based on quantiles, can have serious mathematical shortcomings. It is essential to build optimization models in which cost variables are kept "adequately" below some threshold. Adequacy can be expressed by a choice of how risk is quantified, but that choice should fit with axioms of "coherency". Questions arise then on the statistical side as well. In estimating the consequences of decisions, through regression or some other means, the handling of databases may need to interact with the particular approach taken to risk. |
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