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Uncertainty Quantification for Unobserved Variables in Dynamical Systems and Optimal Experimental Design

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Technical Report,29 May 2015,28 Feb 2016

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Massachusetts Institute of Technology (MIT) Cambridge United States

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Dynamical systems are frequently used to model biological systems. When these models are fit to data it is necessary to ascertain the uncertainty in the model fit. In our work, we present prediction deviation, a metric of uncertainty that determines the extent to which observed data have constrained the models predictions. This is accomplished by solving an optimization problem that searches for a pair of models that each provide a good fit for the observed data, yet have maximally different predictions. We developed a method for estimating a priori the impact that additional experiments would have on the prediction deviation, allowing the experimenter to design a set of experiments that would most reduce uncertainty. We used prediction deviation to assess uncertainty in a model of interferon-alpha inhibition of HIV infection, and to select a sequence of experiments that reduces this uncertainty. Finally we proved a theoretical result which shows that prediction deviation provides bounds on the trajectories of the underlying true model. These results show that prediction deviation is a meaningful metric of uncertainty that can be used for optimal experimental design. Joint work with Ben Letham, Portia Letham, and Edward P. Browne

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  • Numerical Mathematics

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