hymanlab/epimat.github.io

Website of Epidemic Modeling Group at Tulane CCS

Epidemic Modeling Group at Tulane CCS

• Individual Biographies
• Research Program

Research

Exploring how to quantify both a mathematical model and the uncertainty, both its and yours.

You have interest in a phenomenon that exhibits order and chaos

• Physics -- Fluids, Genetics
• Human -- Economics, Social Networks
• Both -- Ecology, Epidemiology

You'd like to

• simulate "What If" scenarios
  • explore behavior change, possible mitigations
• at times, short-term prediction -- http://lega.uazmath.org/?p=389
  • approximation; fit a surface to it
• analyze parameter sensitivity (UQ)
  • derivatives; necessarily a wide range?
• helps build our intuition about the whole system -- http://math.lanl.gov/~mac/papers/bio/HL03.pdf

So you model it -- describe the order and chaos

• Input Parameters, x
• Outputs, F(x)
  • Deterministic
  • Stochastic
• Known Unknowns (Aleatoric / Accuracy)
  • Measurer not accurate
  • Generally normal distributions?
• Unknown Unknowns (Epistemic / Precision)
  • Missing terms in model
  • Maybe you don't know enough about your phenomenon

If you reasonably measure it, you might

• cross-validate your model
  • 10-fold, n-fold, all subsets?
• want parameters such that the model matches measurements
  • minimize residuals, bootstrap

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