Editing Sensitivity analysis (section)

==Motivation==

A [[mathematical model]] (for example in biology, climate change,  economics, renewable energy, agronomy...) can be highly complex, and as a result, its relationships between inputs and outputs may be faultily understood. In such cases, the model can be viewed as a [[black box]], i.e. the output is an "opaque" function of its inputs. Quite often, some or all of the model inputs are subject to sources of [[Uncertainty quantification|uncertainty]], including [[Measurement uncertainty|errors of measurement]],  errors in input data, parameter estimation and approximation procedure, absence of information and poor or partial understanding of the driving forces and mechanisms, choice of underlying hypothesis of model, and so on. This uncertainty limits our confidence in the [[Reliability (statistics)|reliability]] of the model's response or output. Further, models may have to cope with the natural intrinsic variability of the system (aleatory), such as the occurrence of [[stochastic]] events.<ref>{{cite journal |last1=Der Kiureghian |first1=A. |last2=Ditlevsen |first2=O. |year=2009 |title=Aleatory or epistemic? Does it matter? |journal=Structural Safety |volume=31 |issue=2 |pages=105–112 |doi=10.1016/j.strusafe.2008.06.020}}</ref>

In models involving many input variables, sensitivity analysis is an essential ingredient of model building and quality assurance and can be useful to determine the impact of a uncertain variable for a range of purposes,<ref name="Examples">{{cite journal |last=Pannell |first=D. J. |year=1997 |title=Sensitivity Analysis of Normative Economic Models: Theoretical Framework and Practical Strategies |journal=Agricultural Economics |volume=16 |issue= 2|pages=139–152 
|doi=10.1111/j.1574-0862.1997.tb00449.x|url= https://doi.org/10.1111/j.1574-0862.1997.tb00449.x }}</ref> including:

* Testing the [[robust decision|robustness]] of the results of a model or system in the presence of uncertainty.
* Increased understanding of the relationships between input and output variables in a system or model.
* Uncertainty reduction, through the identification of model input that cause significant uncertainty in the output and should therefore be the focus of attention in order to increase robustness.
* Searching for errors in the model (by encountering unexpected relationships between inputs and outputs).
* Model simplification – fixing model input that has no effect on the output, or identifying and removing redundant parts of the model structure.
* Enhancing communication from modelers to decision makers (e.g. by making recommendations more credible, understandable, compelling or persuasive).
* Finding regions in the space of input factors for which the model output is either maximum or minimum or meets some optimum criterion (see [[optimization]] and [[Monte Carlo method|Monte Carlo filtering]]).
* For calibration of models with large number of parameters, by focusing on the sensitive parameters.<ref name="Hydrology">{{cite journal |last1=Bahremand |first1=A. |last2=De Smedt |first2=F. |year=2008 |title=Distributed Hydrological Modeling and Sensitivity Analysis in Torysa Watershed, Slovakia |journal=Water Resources Management |volume=22 |issue=3 |pages=293–408 |doi=10.1007/s11269-007-9168-x |bibcode=2008WatRM..22..393B |s2cid=9710579 }}</ref>
* To identify important connections between observations, model inputs, and predictions or forecasts, leading to the development of better models.<ref name="Model Analysis">{{cite journal |last1=Hill |first1=M. |last2=Kavetski |first2=D. |last3=Clark |first3=M. |last4=Ye |first4=M. |last5=Arabi |first5=M. |last6=Lu |first6=D. |last7=Foglia |first7=L. |last8=Mehl |first8=S. |year=2015 |title=Practical use of computationally frugal model analysis methods |journal=Groundwater |volume=54 |issue=2 |pages=159–170 |doi=10.1111/gwat.12330|pmid=25810333 |osti=1286771 |doi-access=free }}</ref><ref name="Methods and Guidelines">{{cite book |last1=Hill |first1=M. |last2=Tiedeman |first2=C. |year=2007 |title=Effective Groundwater Model Calibration, with Analysis of Data, Sensitivities, Predictions, and Uncertainty |publisher=John Wiley & Sons }}</ref>