Uncertainty in outcomes can orginate from multiple sources such as measurement errors in data collection, model identification, parameter uncertainty, and process stochasticity. In this workshop we will primarily focus on the last two types of uncertainties, since the data used in the model are from multiple sources and are used as fixed point estimates for parameters. The predictions of a model are highly dependent on the quality of the data used for parameterization. Hence, it is critical that care be given to the precision of the data available and that uncertainty in model outcomes are addressed. Sensitivity analysis will be demonstrated and the relative importance of parameters' contributions to uncertainty in model outcomes will be determined. Quantifying such uncertainty bounds in model outcomes would strengthen confidence in the interpretation of results and provide the extent of variations possible in changing policy decision. the sensitivity analysis will explore the relationship between model parameters and outcomes while one or more parameters are pertrubed over their plausible ranges or probability distributions and corresponding efffects on outcomes will be examined (wu et al, 2013).
Uncertainty in parameter values can be accounted for by sampling randomly from empiracle data or from estimated probability density distribution via a Latin hypercube sampling procedure. The model output generated from parameter samples can then be analyzed using nonlinear but monotonic (e.g. partial rank correlation coefficients (PTRCC)) and non-monotonic statistical tests (e.g. sensitivity index using extended Fourier amplitude sensitivity testing (eFAST)) to determine the contribution of each parameter to the variation in output values (Saltelli et al., 2004; Frey et al., 2002). We will carry out both PRCC and eFAST sensitivity analysis to provide robustness in our results.
Model development consists of several logical steps, one of which is the determination of parameters, which are most influential on model results. A 'sensitivity analysis' of these parameters is not only critical to model validation but also serves to guide future research efforts. Uncertainty captures how accurately a mathematical model describes the true physics or biology and addresses the question: What is the impact of less precise known components in a model on its outputs? Sensitivity studies how the uncertainty in the output of a modeled system can be apportioned to different sources of uncertainty in its inputs. Uncertainty and sensitivity quantification is a modern inter-disciplinary science that cuts across traditional research groups and combines statistics, numerical analysis and computational applied mathematics. We will use Matlab in this workshop to show the steps.
Instructor: Anuj Mubayi - Assistant Professor, School of Human Evolution and Social Change, ASU
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Dr. Anuj Mubayi is currently an assistant professor of applied mathematics in the School of Human Evolution and Social Change (SHESC) as well as in the Simon A. Levin Mathematical Computational Modeling Science Center (MCMSC) at Arizona State University-Tempe. Mubayi is also a co-director of Mathematical Theoretical Biology Institute (MTBI) and director of the B.S. program in Applied Mathematics in Life and Social Sciences (AMLSS) undergraduate program. He also holds adjunct affiliations at multiple institutions including the University of Texas at Arlington, Northeastern Illinois University at Chicago, the Prevention Research Center in Berkeley, the National Alliance for Doctoral Studies in the Mathematical Sciences, and the Barrett Honors College and T. Denny Sanford School of Social and Family Dynamics both at Arizona State University. He received his doctorate from Arizona State University in 2008 and held a Gates Foundation’s and a National Institutes of Health’s fellowship at the Cleveland Clinic and the Case Western Reserve University School of Medicine, respectively.
He is an applied and computational mathematical scientist whose research program is driven by the mathematical and computational modeling of problems of interest to the public health or social sciences communities. He has extensive experience in the successful development of strong mathematical sciences training programs. His recent research includes development of novel mathematical modeling tools to understand transmission dynamics and control of neglected tropical diseases such as Visceral Leishmaniasis and Chagas as well as to study issues in human social interactions and contextual influences leading to complex societal problems.
Co - Instructors:
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Dheeraj Lokam, Intel Corporation - MS in computer engineering, ASU. Research interests include Error Resilient Processor design, Semi Conductor Functional Safety & integrated Vector Management. Currently working on the Platform Architecture team at Intel's Internet of Things Group (IOTG)
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Anamika Mubayi, Simon A. Levin Mathematical Computational and Modeling Science Center, ASU. MS from University of Iowa and PhD in Physical Chemistry, Allahabad University, India. Research interests are modeling dynamics of chemical kinetics of nanoparticles in green therapeutic drug for chronic diseases.
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Mugdha Thakur, School of Human Evolution and Social Change (SHESC). MS from Indian Institute of Science Education and Research, Mohali, India. PhD candidate in Applied Mathematics in life and social sciences program, ASU. Research interests include dynamical modeling of peoples treatment behavior in Visceral Leishmaniasis and its effect on disease elimination.
Date: February 22, 2019
Time: 9:00 am - 12 noon
Location: Cowden 124
Workshop Fee: 0
Register HERE