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Exploring Tools of Uncertainty Quantification Motivated by Analyzing Mathematical Models of Complex Biological SystemsSpecial Events
|Speaker:||Michael Stobb, UC Merced|
|Start time:||Fri, May 25 2018, 12:10PM|
Biological systems are typically complex, involving multiple species, non-linear interactions and unknown or confounding mechanisms. Because of this biological systems are often difficult to predict and, when possible, mathematical models are used as a tool. Our models allow us to probe mechanisms, make hypothesis, and conduct experiments, all without having to touch a microscope. This is not without a cost, however, as the complexity of the system usually leads to complex models which may be just as inscrutable as their biological counterpart. In this talk, I will briefly explore three tools that allow us to quantify the uncertainty in our mathematical models: 1) Bayesian inference, which allows us to estimate parameter values in an uncertain model in a natural way, 2) generalized polynomial chaos, where uncertainties are modeled as random variables and expanded using orthogonal polynomials, and 3) Sobol indices, which quantify the fraction of variance attributable to input parameters. For each, we will examine an application arising from a biological system.