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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.

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How should I choose input distributions for the model inputs?

Sensitivity analysis is not concerned with the choice of the distributions fo

llowed 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.

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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.

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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 str

engths 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.

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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.

More information: Sensitivity analysis

What is difference between uncertainty and sensitivity analysis?

Although closely related, uncertainty analysis and sensitivity analysis are t

wo 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.

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What are the reasons to conduct sensitivity analysis?

Modellers 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.

More information: Sensitivity analysis

Why do I need sensitivity analysis?

A mathematical model is defined by a series of equations, input factors, para

meters, and variables aimed to characterise 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 modelling practice requires that the modeller provides an evaluation of the confidence in the model, possibly assessing the uncertainties associated with the modelling process and with the outcome of the model itself. Uncertainty and sensitivity analysis offer valid tools for characterising the uncertainty associated with a model.

More information: Sensitivity analysis

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.

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What are the pros and cons of composite indicators?

Synthetically the pros and cons of composite indicators could be summarised a

s follows:


  • Composite indicators can be used to summarise complex or multi-dimensional issues in view of supporting decision-makers.
  • Composite indicators provide the big picture. They can be easier to interpret than trying to find a trend in many separate indicators. They facilitate the task of ranking countries on complex issues.
  • Composite indicators can help attracting public interest by providing a summary figure with which to compare the performance across Countries and their progress over time.
  • Composite indicators could help to reduce the size of a list of indicators or to include more information within the existing size limit


  • Composite indicators may send misleading, non-robust policy messages if they are poorly constructed or misinterpreted. Sensitivity analysis can be used to test composite indicators for robustness.
  • The simple “big picture” results which composite indicators show may invite politicians to draw simplistic policy conclusions. Composite indicators should be used in combination with the sub-indicators to draw sophisticated policy conclusions.
  • The construction of composite indicators involves stages where judgement has to be made: the selection of sub-indicators, choice of model, weighting indicators and treatment of missing values etc. These judgements should be transparent and based on sound statistical principles.
  • There could be more scope for Member States about composite indicators than on individual indicators. The selection of sub-indicators and weights could be the target of political challenge

More info: Composite Indicators Research Group (COIN)