Editing Sensitivity analysis (section)

== Mathematical formulation and vocabulary ==
[[File:Sensitivity scheme.jpg|thumb|right | upright=2 | Figure 1. Schematic representation of uncertainty analysis and sensitivity analysis. In mathematical modeling, uncertainty arises from a variety of sources - errors in input data, parameter estimation and approximation procedure, underlying hypothesis, choice of model, alternative model structures and so on. They propagate through the model and have an impact on the output. The uncertainty on the output is described via uncertainty analysis (represented [[Probability density function|pdf]] on the output) and their relative importance is quantified via sensitivity analysis (represented by [[pie chart]]s showing the proportion that each source of uncertainty contributes to the total uncertainty of the output).]]
The object of study for sensitivity analysis is a function <math>f</math>, (called "'''mathematical model'''" or "'''programming code'''"), viewed as a [[black box]], with the <math>p</math>-dimensional '''input''' vector <math>X=(X_1,...,X_p)</math> and the '''output''' <math>Y</math>, presented as following:

<math display="block">Y=f(X).</math>

The variability in input parameters <math>X_i,i=1,\ldots,p</math> have an impact on the output <math>Y</math>. While [[uncertainty analysis]] aims to describe the distribution of the output <math>Y</math> (providing its [[statistics]], [[Moment measure|moments]], [[Probability density function|pdf]], [[Cumulative distribution function|cdf]],...), sensitivity analysis aims to measure and quantify the impact of each input <math>X_i</math> or a group of inputs on the variability of the output <math>Y</math> (by calculating the corresponding sensitivity indices). Figure 1 provides a schematic representation of this statement.