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Sensitivity Analysis- Your amazing guide towards Success


Hey guys. Lately, I have been talking about analysis a lot. It’s because analyses are really important before you take any major decisions. In this article, I will talk about another type of analysis that is Sensitivity analysis.

Sensitivity analysis is a method which is used to identify, how various values of an independent variable make an impact on a particular variable which is dependent and is a given set of assumptions.

Let’s now move on to the details. In this article, I will cover the following:

  • What is Sensitivity analysis?
  • Why should I use Sensitivity analysis?
  • Constraints and Settings in Sensitivity analysis.
  • Applications of Sensitivity analysis.
  • Pitfalls in Sensitivity analyses.

Let’s get started.

1) What is Sensitivity analysis?

Image: Source


Sensitivity analysis is a method to find out how the unpredictability in the results of a system or model can be alloted to different sources of unpredictability in its inputs.

This method is used within some boundaries which depends on one or more input variables. It includes the effects that change in interest rates have on the bond prices.

Sensitivity analysis is also seen as similar to simulation analysis. It is a way by which you can predict the outcome of a decision which is given in the form of a particular range of variables. With the creation of a set of variables, the analyst can identify that how changes in a variable put an impact on the outcome.

A mathematical model like an economic model can be very hard to understand, and as a result, it’s relation to inputs and outputs will not be understood properly. In these kinds of cases, the model is viewed as a black box, i.e., the output is an uncertain way of its inputs.

It often happens, that some of the model inputs are a source of uncertainty. It includes the absence of information, errors of measurements and poor or lesser information of the forces that derive the mechanisms. There should be no uncertainty as it effects your confidence and puts a limit in the response of the model.


Image Source: Example Of Sensitivity Analysis

We all need that the efforts we put in should give results. They will give the result if you follow the method correctly. The best way of modeling practice is when the modeler gives an evaluation of the confidence in a model.

For this to happen, firstly you need a valuation of the uncertainty in any of the model results. This is also known as uncertainty analysis. Secondly, you need to evaluate how much each input is giving to the output uncertainty.

Sensitivity analysis is a necessary forerunner. It addresses the 2nd of these issues. It also performs the role of ordering by focusing on strength and relevance of the inputs and also helps in determining the variations in the output.

For models which involve many input variables, sensitivity analysis acts as an important ingredient for quality assurance and model building. Even the national and international companies now involve sensitivity analysis in their guidelines for impact assessment.

Sensitivity analysis example

Just imagine that Alex is a sales manager and he wants to understand the impact of customer traffic on overall sales. He made his mind that sales are a process of price and transaction volume. One gadget is $100, and Alex sold 50 this year, and the total sale cost came out to be $5,000.

Alex was able to determine that there was a particular percentage of rising in customer traffic which led to the raise in the transaction volume as well. This info allowed him to make a financial model and sensitivity analysis. This can now tell him that what will happen if the customer traffic grows by 5%, 10% or up to 100%.

The raise in customer traffic by these percentage will also show the rise in transaction volume or total sale. There will be an increase in transaction volume as well with some amount of numbers concerning the percentage increase in customer traffic. Thus, now you can understand that here, sensitivity analysis showcase that sales are highly sensitive to all variations in the customer traffic.

2) Why should I use Sensitivity Analysis?



Following points will make it very clear, that why you should use sensitivity analysis. Sensitivity analysis-

  1. Increases the understanding of the correlation between input and output variables in a model or system.
  2. Tests the strength of the output of a system or model in the presence of uncertainty.
  3. Search for the errors in the system or model by finding out the unexpected relation of the outputs with the inputs.
  4. Reduces uncertainty by identifying model inputs which cause uncertainty in the output. It should, therefore, be the center of attention to grow the strength. It can only happen by a deep research.
  5. Improves communication between modelers and decision makers. It happens by making recommendations which are more understandable, credible, persuasive or compelling.
  6. Helps in model simplification by fixing the model inputs which have zero effect on the outputs. It may also happen by verifying and removing unnecessary parts of the model structure.
  7. Finds region in the space of input factors and for this, the model output is either minimum or maximum or it meets some other optimum criteria.
  8. Seeks to identify crucial connections between different observations, predictions or forecasts and model inputs, which leads to the development of better models.
  9. Eases the calibration stage by emphasizing the sensitive parameters. Sensitivity parameters should be known as without that the result can be, a total wastage of time being spent on the non-sensitive sections.

3) Constraints and Settings in Sensitivity analysis



The method by which the sensitivity analysis will be done depends on some settings or problem constraints. I will be discussing the most common ones with you. Following are the constraints or settings:

  1. Computational expense: Sensitivity analysis is performed by running a possibly large model and some times. It is a sampling-based initialization. But, this can become an issue when-
    • a single workout process of a model, takes a particular amount of time like few minutes, an hour or may longer than that. This happens with much difficult models.
    • the a model has various number of uncertain inputs. Sensitivity analysis grows as the number of inputs grow.

    Some of the methods to reduce computational expense includes the use of screening methods to reduce the dimensionality of the issue and the use of emulators for larger models. Another method which can be used is to do an event based sensitivity analysis for variable selection while time-constrained applications.

  2. Correlated inputs: this is one of the most commonly used sensitivity analysis methods. It assumes independence inputs of models, but sometimes these inputs can be strongly interrelated.
  3. Nonlinearity: Sometimes, results based on linear regression can wrongly calculate sensitivity. It happens when the model’s depiction is nonlinear concerning the inputs.
  4. Model interactions: Interactions happen when the disruption of two or more inputs one after another, causes a difference in the results greater than that of changing each of the inputs all alone. The effect of this constraint can be calculated by the total-order sensitivity index.
  5. Multiple Outputs: Many models result or output a bigger number of possibly time-dependent data. However, for those models in which the outputs are interrelated, it becomes harder to interpret the sensitivity measures.
  6. Given data: In many cases, the person practicing, has access to the model. But, in some cases, a sensitivity analysis must be done with “given data.”It is where the values of the model inputs can’t be chosen by the analyst.
    This happens when the data is used for an uncertainty analysis or optimization or when the data is derived from a discrete source.

Applications of Sensitivity Analysis

Following is the list of few examples of sensitivity analysis, performed in different disciplines:

i. Environmental

Environmental computer models are vastly used in various varieties of studies and other applications. It includes Global Climate models which are used for both long-term climate change and short-term weather forecasts.

Computer models are now highly being used for environmental decision making on a local scale like for examining the impact of a waste water treatment plant on a flowing river, etc. The analysis may help to understand these phenomena.

ii. Business

Sensitivity analysis can help in various circumstances related to business. It helps to:

  • Identify serious assumptions or helps to compare different model structures.
  • Guide in for future data collections.
  • Improve resources allotment.
  • Improve the tolerance of manufactured parts in regard with the variations in the parameters.

Multi-criteria decision making

MCDM, i.e., Multi-criteria decision making studies the issue of how to select the best one among some other alternative which competes. The criteria behind it are connected with weights of importance.

There are some other discipline examples too like Social Sciences, Chemistry, Engineering, In the meta-analysis, Time-critical decision making and Model calibration and improvement. You will do something.

Pitfalls in Sensitivity analysis

Some of the common difficulties with sensitivity analysis are as follows:

  • There are way too many model inputs which have to be analyzed. Screening is used to lessen up the dimensionality.
  • The model takes a longer period to run. But, Emulators are used to lessening the number of model runs which are needed.
  • This analysis provides lesser information to make probability distributions for the inputs.
  • If there is an unclear purpose of the analysis, then many variants of measures and statistical tests are applied to the problem, and therefore different factors rankings are gained.
  • Too many model outputs are taken. This may be accepted for quality assurance of sub-models. This should be ignored when presenting the outputs of the overall analysis.
  • It is also known as piecewise sensitivity. It is when someone performs analysis on one sub-model at an individual time. This method is nonconservative as it might oversee interactions within factors in different sub-models.


So, guys, this was all about Sensitivity analysis. I hope you guys liked this information. I have tried to cover all the points. If you liked this article, then do let me know your views in the comment section below and also do subscribe to my Blog for more such informative articles.

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