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What is multivariate and univariate sensitivity analysis?
Univariate - Assesses the impact on the results of changing one variable.
Its Quick, simple, and easy to communicate results. Is sufficient if each of the uncertain variables is independent of the others.
Evaluates the uncertainty related to multiple parameters by varying more than one parameter at once.
Generates more pragmatic results than univariate sensitivity analysis.
2.One of the reason for doin sensitivity analysis is uncertainty in modelling .While models tend to report single summary outcomes, such as ‘the incremental cost per incremental life year’, the interpretation of those results will largely depend on the level of confidence or uncertainty in various factors. These might involve the methodology that has been used in constructing the model (that is, the model structure) or could be related to the actual values that have been used to populate the model. For example, a reviewer of a model might suspect that one particular value (for example, the probability of a treatment being successful) is too high in the model. In this case, the reviewer may wish to know the likely impact of using an alternative value. Such an exercise would involve examining the sensitivity of the model to changes in its inputs
The technique used to determine how independent variable values will impact a particular dependent variable under a given set of assumptions is defined as sensitive analysis. It’s usage will depend on one or more input variables within the specific boundaries, such as the effect that changes in interest rates will have on a bond’s price.

It is also known as the what – if analysis. Sensitivity analysis can be used for any activity or system. All from planning a family vacation with the variables in mind to the decisions at corporate levels can be done through sensitivity analysis.
Methods of Sensitivity Analysis
There are different methods to carry out the sensitivity analysis:

Modeling and simulation techniques
Scenario management tools through Microsoft excel
There are mainly two approaches to analyzing 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.

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.

Local sensitivity analysis is a one-at-a-time (OAT) technique that analyzes the impact of one parameter on the cost function at a time, keeping the other parameters fixed.

Global sensitivity analysis is the second approach to sensitivity analysis, often implemented using Monte Carlo techniques. This approach uses a global set of samples to explore the design space.
The various techniques widely applied include:

Differential sensitivity analysis: It is also referred to the direct method. It involves solving simple partial derivatives to temporal sensitivity analysis. Although this method is computationally efficient, solving equations is intensive task to handle.
One at a time sensitivity measures: It is the most fundamental method with partial differentiation, in which varying parameters values are taken one at a time. It is also called as local analysis as it is an indicator only for the addressed point estimates and not the entire distribution.
Factorial Analysis: It involves the selection of given number of samples for a specific parameter and then running the model for the combinations. The outcome is then used to carry out parameter sensitivity.
Sensitivity analysis attempts to provide a measure of the sensitivity of either parameters, or forcing functions, or submodels to the state variables of greatest interest in the model. Sensitivity analysis is performed using the following formula: S = (dx/x)/(dp/p) , where S = sensitivity, x = state variable, P = parameter, dx and dp are change of values of state variables, parameters, and forcing functions, respectively, at ± 10% level in temporal scale. Those parameters, which are almost impossible to determine from the field are calibrated using a range of values (minimum to maximum) from the literature first and further the appropriate value for that parameter for this estuary is determined according to the best fit of the value during the model run by using standard calibration procedure. :bored: :bored: :bored: :bored:

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