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## Description

1. Discuss about sensitivity analysis in statistical modelling. 5marks

ANS.A sensitivity analysis is a technique used to determine how different values of an
independent variable impact a particular dependent variable under a given set of
assumptions. This technique is used within specific boundaries that depend on one or more
input variables.

• It helps in analysing how sensitive the output is, by the changes in one input while
keeping the other inputs constant.

PRINCIPLE: Sensitivity analysis works on simple principle. That is change the model and
observe the behaviour.

The parameters that one needs to note while doing the above are:
A)Experimental design: It includes combination of parameters that are to be varied. This
includes a check on which and how many parameters need to vary at a given point in time,
assigning values (maximum and minimum levels) before the experiment, study the
correlations: positive or negative and accordingly assign values for the combination.

B) What to vary:The different parameters that can be chosen to vary in the model could be:
a) the number of activities
b) the objective in relation to the risk assumed and the profits expected
c) technical parameters
d) number of constraints and its limits

C) What to observe:
a) the value of the objective as per the strategy
b) value of the decision variables
c) value of the objective function between two strategies adopted

Methods of Sensitivity Analysis

There are different methods to carry out the sensitivity analysis:

• Modelling and simulation techniques
• Scenario management tools through Microsoft excel

There are mainly two approaches to analysing sensitivity:

• Local Sensitivity Analysis
• Global Sensitivity Analysis

Local sensitivity analysis is derivative based (numerical or analytical). The term local
indicates that the derivatives are taken at a single point. This method is apt for simple cost
functions, but not feasible for complex models, like models with discontinuities do not
always have derivatives.

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Mathematically, the sensitivity of the cost function with respect to certain parameters is
equal to the partial derivative of the cost function with respect to those parameters.

Uses of Sensitivity Analysis

• The key application of sensitivity analysis is to indicate the sensitivity of simulation to
uncertainties in the input values of the model.

• They help in decision making
• Sensitivity analysis is a method for predicting the outcome of a decision if a situation

turns out to be different compared to the key predictions.
• It helps in assessing the riskiness of a strategy.
• Helps in identifying how dependent the output is on a particular input value.

Analyses if the dependency in turn helps in assessing the risk associated.
• Helps in taking informed and appropriate decisions
• Aids searching for errors in the model.

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