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What is Sensitivity Analysis?

Sensitivity Analysis (SA) is the study of how the variation in the output of a model (numerical or otherwise) can be apportioned, qualitatively or quantitatively, to different sources of variation.

Why do I need Sensitivity Analysis?

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 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.



What are the reasons to conduct Sensitivity Analysis?

Modelers may conduct SA 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,
  5. optimal regions within the space of factors for use in a subsequent calibration study,
  6. interactions between factors.


What is difference between Uncertainty and Sensitivity Analysis?

Although closely related, Uncertainty Analysis and Sensitivity Analysis are two different disciplines. Uncertainty Analysis assesses the uncertainty in model outputs that derives from uncertainty in inputs. Sensitivity Analysis assesses the contributions of the inputs to the total uncertainty in analysis outcomes


What are the general steps needed to perform Uncertainty and Sensitivity Analysis?

There are several possible procedures to perform uncertainty and sensitivity analysis. 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. 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 distribution function to the selected factors
  3. generate a matrix of inputs with that distribution(s) through an appropriate design 
  4. evaluate the model and compute the distribution of the target function
  5. select a method for assessing the influence or relative importance of each input factor on the target function.


Which is the best method to perform SA on my model?

The choice of which SA method to adopt is difficult as each technique has strengths and weaknesses. Such a choice depends on the problem the investigator is trying to address, on the characteristics of the model under study, and also on the computational cost that the investigator can afford. 

What can I do if my model has a large number of inputs?

You should start by performing a screening exercise. This is a preliminary analysis that allows you to select the subset of the most potentially explanatory factors. Afterwards, a quantitative method is recommended on the subset of pre-selected inputs.

How should I choose input distributions for the model inputs?

Sensitivity analysis is not concerned with the choice of the distributions followed by the model inputs. These distributions have to be derived from available sources of information, such as expert opinions or literature. Results of the sensitivity analysis exercise are conditional upon the distributions chosen.


How can I treat multiple model output (such as time series)?

The objective function of a sensitivity analysis exercise is assumed to be a scalar function. When the model has several output variables, the analysis has to be repeated several times, one for each output variable.