Sensitivity Analysis - Problem Formulation

How uncertainty in the output of a model can be apportioned to different sources of uncertainty in the model input - Andrea Saltelli, 2007

Local Sensitivity Analysis. A method based on derivatives, $\partial_x f(x;\theta)$. It is computationally efficient. However, it does not consider input uncertainty and model non-linearity.

Global Sensitivity Analysis. A method based on simulations, $x^{(k)}\sim p(x;\theta)$. This method is more computationally expensive. It is used to hollistically assess uncertainty and model behaviour. It can be used to reduce the dimensionality and/or inform additional experiments.

Relationship to Uncertainty¶

In general, both SA and UQ are absolutely necessary for doing post-model analysis.

1. Propagate Input Uncertainties

Generate viable Monte Carlo simulations.

2. Analyze the Input-Output Dataset

Quantify Uncertainty. How uncertain are model outputs given uncertain inputs?

Quantify Sensitivity. Which inputs mostly contribute to the output uncertainty?

Stress Testing. What designs perform well enough across a large range of inputs? What are threshold values in the inputs that lead to “good enough outputs”?