# Global Sensitivity Analysis

Sensitivity analysis (SA) is the study of how uncertainty in the output of a model can be apportioned to different sources of uncertainty in the model input. A sensitivity analysis is considered to be global when all the input factors are varied simultaneously and the sensitivity is evaluated over the entire range of each input factor. It provides an overall view on the influence of inputs on outputs as opposed to a local view of partial derivatives as in local sensitivity analysis.

DiffEqSensitivity.jl currently provides the following global sensitivity analysis methods:

1. Morris OAT Method
2. Sobol Method
3. eFAST Method
4. Regression based sensitivity
5. Derivative Based Global Sensitivity Measures

Global Sensitivity Analysis (GSA) is performed using the gsa function. This function's signature is:

DiffEqSensitivity.gsa(m::PumasModel, population::Population, params::NamedTuple, method::DiffEqSensitivity.GSAMethod,
vars = [:dv], p_range_low=NamedTuple{keys(params)}([par.*0.05 for par in values(params)]),
p_range_high=NamedTuple{keys(params)}([par.*1.95 for par in values(params)]),
args...; kwargs...)

The arguments are:

• m: a PumasModel, either defined by the @model DSL or the function-based interface.
• population: a Population.
• params: a named tuple of parameters. Used as the initial condition for the optimizer.
• method: one of the GSAMethods from DiffEqSensitivity.jl, Sobol(), Morris(), eFAST(), RegressionGSA().
• vars: a list of the derived variables to run GSA on.
• p_range_low & p_range_high: the lower and upper bounds for the parameters.

For method specific arguments that are passed with the method constructor you can refer to the DiffEqSensitivity.jl documentation.

The gsa provided in Pumas assumes that you want to run GSA on all of the parameters of the model and also constraints you to run GSA only on variable in the @derived block. For more control on the input and output you can create a custom function and use the gsa function from DiffEqSensitivity.jl which is callable on any julia function directly.