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Sensitivity analysis

Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem.

The process of recalculating outcomes under alternative assumptions to determine the impact of a variable under sensitivity analysis can be useful for a range of purposes,[1] including:

Overview[edit]

A mathematical model (for example in biology, climate change, economics, or engineering) can be highly complex, and as a result, its relationships between inputs and outputs may be poorly 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, including errors of measurement, absence of information and poor or partial understanding of the driving forces and mechanisms. This uncertainty imposes a limit on our confidence in the response or output of the model. Further, models may have to cope with the natural intrinsic variability of the system (aleatory), such as the occurrence of stochastic events.[5]


In models involving many input variables, sensitivity analysis is an essential ingredient of model building and quality assurance. National and international agencies involved in impact assessment studies have included sections devoted to sensitivity analysis in their guidelines. Examples are the European Commission (see e.g. the guidelines for impact assessment),[6] the White House Office of Management and Budget, the Intergovernmental Panel on Climate Change and US Environmental Protection Agency's modeling guidelines.[7]

Settings, constraints, and related issues[edit]

Settings and constraints[edit]

The choice of method of sensitivity analysis is typically dictated by a number of problem constraints or settings. Some of the most common are

moving one input variable, keeping others at their baseline (nominal) values, then,

returning the variable to its nominal value, then repeating for each of the other inputs in the same way.

[33] (also known as kriging), where any combination of output points is assumed to be distributed as a multivariate Gaussian distribution. Recently, "treed" Gaussian processes have been used to deal with heteroscedastic and discontinuous responses.[34][35]

Gaussian processes

,[31] in which a large number of decision trees are trained, and the result averaged.

Random forests

,[31] where a succession of simple regressions are used to weight data points to sequentially reduce error.

Gradient boosting

,[36] which use orthogonal polynomials to approximate the response surface.

Polynomial chaos expansions

,[37] normally used in conjunction with HDMR truncations (see below).

Smoothing splines

Discrete ,[38] in conjunction with canonical models such as noisy models. Noisy models exploit information on the conditional independence between variables to significantly reduce dimensionality.

Bayesian networks

Environmental sciences

Business

Social sciences

Chemistry

Engineering

Epidemiology

Meta-analysis

Multi-criteria decision making

Time-critical decision making

Model calibration

Uncertainty Quantification

Chaos theory

population genetics

Examples of sensitivity analyses can be found in various area of application, such as:

Related concepts[edit]

Sensitivity analysis is closely related with uncertainty analysis; while the latter studies the overall uncertainty in the conclusions of the study, sensitivity analysis tries to identify what source of uncertainty weighs more on the study's conclusions.


The problem setting in sensitivity analysis also has strong similarities with the field of design of experiments.[48] In a design of experiments, one studies the effect of some process or intervention (the 'treatment') on some objects (the 'experimental units'). In sensitivity analysis one looks at the effect of varying the inputs of a mathematical model on the output of the model itself. In both disciplines one strives to obtain information from the system with a minimum of physical or numerical experiments.

Cannavó, F. (2012). "Sensitivity analysis for volcanic source modeling quality assessment and model selection". Computers & Geosciences. 44: 52–59. :2012CG.....44...52C. doi:10.1016/j.cageo.2012.03.008.

Bibcode

Fassò A. (2007) "Statistical sensitivity analysis and water quality". In Wymer L. Ed, Statistical Framework for Water Quality Criteria and Monitoring. Wiley, New York.

Fassò A., Perri P.F. (2002) "Sensitivity Analysis". In Abdel H. El-Shaarawi and Walter W. Piegorsch (eds) Encyclopedia of Environmetrics, Volume 4, pp 1968–1982, Wiley.

Fassò A., Esposito E., Porcu E., Reverberi A.P., Vegliò F. (2003) "Statistical Sensitivity Analysis of Packed Column Reactors for Contaminated Wastewater". Environmetrics. Vol. 14, n.8, 743–759.

Haug, Edward J.; Choi, Kyung K.; (1986) Design sensitivity analysis of structural systems. Mathematics in Science and Engineering, 177. Academic Press, Inc., Orlando, FL.

Komkov, Vadim

Pianosi, F.; Beven, K.; Freer, J.; Hall, J.W.; Rougier, J.; Stephenson, D.B.; Wagener, T. (2016). . Environmental Modelling & Software. 79: 214–232. Bibcode:2016EnvMS..79..214P. doi:10.1016/j.envsoft.2016.02.008. hdl:10871/21086.

"Sensitivity analysis of environmental models: A systematic review with practical workflow"

Pilkey, O. H. and L. Pilkey-Jarvis (2007), Useless Arithmetic. Why Environmental Scientists Can't Predict the Future. New York: Columbia University Press.

Santner, T. J.; Williams, B. J.; Notz, W.I. (2003) Design and Analysis of Computer Experiments; Springer-Verlag.

Taleb, N. N., (2007) The Black Swan: The Impact of the Highly Improbable, Random House.

Web site with material from SAMO conference series (1995-2025)

– (Joint Research Centre of the European Commission)

web-page on Sensitivity analysis

the free software for global sensitivity analysis of the Joint Research Centre

SimLab

Archived 2013-04-24 at the Wayback Machine – Extensive resources for uncertainty and sensitivity analysis of computationally-demanding models.

MUCM Project