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As stakeholders and policy makers increasingly rely upon quantitativepredictions from advanced computational models, a problem of fundamentalimportance is the quantification and reduction of uncertainties in both modelinputs and output data. The typical work-flow in the end-to-end quantificationof uncertainties requires first formulating and solving stochastic inverseproblems (SIPs) using output data on available quantities of interest (QoI).The solution to a SIP is often written in terms of a probability measure, ordensity, on the space of model inputs. Then, we can formulate and solve astochastic forward problem (SFP) where the uncertainty on model inputs ispropagated through the model to make quantitative predictions on eitherunobservable or future QoI data.  In this work, we use a measure-theoretic framework to formulate and solveboth SIPs and SFPs. From this perspective, we quantify the geometriccharacteristics of using hypothetical sets of QoI that describe both theprecision and accuracy in solutions to both the SIP and SFP. This leads to anatural definition of the optimal experimental design, i.e., what the optimalconfiguration a finite set of sensors is in space-time. Several numericalexamples and applications are discussed including the ADvanced CIRCulation(ADCIRC) model using simulated data from Hurricane Gustav to determine anoptimal placement of buoys in the Gulf of Mexico to capture high water marks ofthe storm surge in order to reduce uncertainties in bottom roughnesscharacteristics.

Experimental Design : Optimizing Quantities of Interest to Reliably Reduce the Uncertainty in Model Input Parameters