Sensitivity Analysis

Definitions:
1. A procedure to determine the sensitivity of the outcomes of an alternative to changes in its parameters (as opposed to changes in the environment; see contingency analysis, a fortiori analysis). If a small change in a parameter results in relatively large changes in the outcomes, the outcomes are said to be sensitive to that parameter. This may mean that the parameter has to be determined very accurately or that the alternative has to be redesigned for low sensitivity. (IIASA)
2. Sensitivity analysis (SA) is the study of how the variation (uncertainty) in the output of a mathematical model can be apportioned,
qualitatively or quantitatively, to different sources of variation in the input
of a model.
3. A technique used to determine how different values of an independent variable will impact a particular dependent variable under a given set of assumptions. This technique is used within specific boundaries that will depend on one or more input variables, such as the effect that changes in interest rates will have on a bond's price. Sensitivity analysis is a way to predict the outcome of a decision if a situation turns out to be different compared to the key prediction(s).
4. Sensitivity
analysis is very useful when attempting to determine the impact the actual outcome of a particular variable will have if it differs from what was previously assumed. By creating a given set of scenarios, the analyst can determine how changes in one variable(s) will impact the target variable.
5. Investigation into how projected performance varies along with changes in the key assumptions on which the projections are based.
6. An analysis used to determine how sensitive the results of a study or systematic review are to changes in how it was done. Sensitivity analyses are used to assess how robust the results are to uncertain decisions or assumptions about the data and the methods that were used.
Criteria on which sensitivity analysis may be based include (but is not
limited to:
1. Random versus nonrandom studies
2. Blind versus open studies
3. By dose of intervention
4. By duration of intervention
5. By duration of observations
6. By severity of condition at start of a trial
7. By magnitude of outcome
8. By size of trial
9. By geographical location of study
10.By quality of study
11. By validity of study

Diagram:
https://i.servimg.com/u/f40/11/10/02/04/sa-110.jpg

For example, an analyst might create a financial model that will value a
company's equity (the dependent variable) given the amount of earnings per share (an independent variable) the company reports at the end of the year and the company's price-to-earnings multiple (another independent variable) at that time. The analyst can create a table of predicted price-to-earnings multiples and a corresponding value of the company's equity based on different values for each of the independent variables.
In more general terms uncertainty and sensitivity analyses investigate the
robustness of a study when the study includes some form of mathematical modelling. While uncertainty analysis studies the overall uncertainty in the conclusions of the study, sensitivity analysis tries to identify what source of uncertainty weights more on the study's conclusions. For example, several guidelines for modelling or for impact assessment prescribe sensitivity analysis as a tool to ensure the quality of the modelling /assessment. The problem setting in sensitivity analysis has strong similarities with Design of experiments. In 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.
Overview
Most mathematical problems met in social, economic or natural sciences
entail the use of mathematical models, which are generally too complex for an easy appreciation of the relationship between input factors (what goes into the model) and output (the model’s dependent variables). Such an appreciation, i.e. the understanding of how the model behaves in response to changes in its inputs, is of fundamental importance to ensure a correct use of the models.
A mathematical model is defined by a series of equations,
input factors, parameters, and variables aimed to characterize the process being investigated.Input is subject to many 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, such as the occurrence of stochastic events. Good modeling practice requires that the modeler provides an evaluation of the confidence in the model, possibly assessing the uncertainties associated with the modeling process and with the outcome of the model itself. Uncertainty
and Sensitivity Analysis offer valid tools for characterizing the uncertainty
associated with a model. Uncertainty analysis (UA) quantifies the
uncertainty in the outcome of a model. Sensitivity Analysis has the
complementary role of ordering by importance the strength and relevance of the inputs in determining the variation in the output. 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 section devoted to sensitivity analysis in their guidelines. Examples are the European Commission, the White House Office for Budget and Management, the Intergovernmental Panel on Climate Change and the US Environmental Protection Agency.
Methodology
There are several possible procedures to perform uncertainty (UA) and
sensitivity analysis (SA). The most common sensitivity analysis is sampling-based. A sampling-based sensitivity is one in which the model is executed repeatedly for combinations of values sampled from the distribution (assumed known) of the input factors. Sampling based methods can also be used to decompose the variance of the model output. In general, UA and SA are performed jointly by executing the model repeatedly for combination of factor values sampled with some probability distribution. The following steps can be listed:

1. Specify the target function and select the input of interest
   
2. Assign a probability density function to the selected factors
   
3. Generate a matrix of inputs with that distribution(s) through an appropriate design Evaluate the model and compute the distribution of the target function
   
4. Select a method for assessing the influence or relative importance of each input factor on the target function.
   

Applications
Sensitivity Analysis can be used to determine:

1. The model resemblance with the process under study
   
2. The quality of model definition
   
3. Factors that mostly contribute to the output variability
   
4. The region in the space of input factors for which the model variation is maximum Optimal - or instability - regions within the space of factors for use in a subsequent calibration study
   
5. Interactions between factors
   

For more detail please visit following website:

http://sysdyn.clexchange.org/sdep/Roadmaps/RM8/D-4526-2.pdf