## Introduction

Sensitivity analysis is a powerful tool used in risk analysis and decision making. This type of analysis allows users to study how small changes to certain variables within a model affect the overall outcome. Through sensitivity analysis, users can identify potential risks, review the effects of certain events, and develop better strategies. In this post, we will discuss what sensitivity analysis is, explain why it is important, and provide some tips for using it in your models.

## Step 1: Identify Variable Ranges

In order to properly use sensitivity analysis in your models, the first step is to identify the variable ranges which you will use in the analysis. This involves collecting data on the various parameters of your model, including the range over which each variable might change. Sensitivity analysis identifies relationships between each variable within the specified range, so it’s important to get an accurate estimate of the range for all variables.

### Collect Data on Variable Ranges

To start, gather data that can be used to identify the range for each variable. This information may be available from past analyses or from experimenting to determine the range of the variable. Alternatively, you may need to generate data from a simulation to build your ranges. Once the data is gathered, you can use it to map out the range of potential variable values.

### Identify Relative Variable Importance

Once you have identified the range of variable values, it’s important to also assess the relative importance of each variable. This can be done by analyzing the impact each variable has on the overall performance of the model. By understanding which variables have the most significant effect, you can determine which ones should be targeted for in-depth analysis during the sensitivity analysis.

With the ranges and relative importance of each variable in hand, you are now ready to begin the sensitivity analysis process. By properly identifying the variable ranges, you can ensure that your analysis is conducted with the most accurate data possible.

## Step 2: Set Data Points

Sensitivity analysis helps to analyze the performance of a model by testing various scenarios and making changes in those scenarios. The next step in using sensitivity analysis in your models is to set data points. This step involves defining a base case and creating additional data points for comparison.

### Establishing the Base Case

The base case is defined by the set of assumptions used in the original model. It is the benchmark that all other scenarios will be compared to. Before setting additional data points, it is important to confirm that the base case data is correct and that there is accurate analysis associated with it.

### Establishing Data Points Outside Base Case

It is important to establish data points outside the base case in order to understand the effects of different scenarios. Begin by identifying the variables that need to be compared. These variables are typically the ones that will likely have the strongest impact on the model's results. It is also important to consider the range of possible values for each variable to ensure an accurate comparison.

Once the variables have been identified and the range of possible values has been determined, the data points can be established. This may involve setting one or multiple additional data points for each variable. The data points should be selected such that they cover multiple ranges of the variable and capture different conditions. If a variable has a large range, the data points can be set in the form of intervals instead of individual data points.

With the data points established, your model will be ready for the next step of sensitivity analysis and be able to comprehend the effects of different variables.

## Step 3: Building the Model

Once you have identified the key variables and relationships that will be used in your model (Steps 1 and 2), you can now begin to build the model. This involves identifying the dependent and independent variables, and defining the relationships between them.

### Identifying the Dependent and Independent Variables

The dependent variable is the one that you are trying to explain or predict; it is the output of the system. The independent variables are the inputs to the system, and are the factors that affect the dependent variable. To identify and define these variables, you will need to identify the cause-effect relationships between them. Once these relationships have been determined, you can then assign each variable to one of the two categories.

### Defining the Relationships Between Variables

The next step is to define the relationships between the variables. This involves understanding the interrelationships between the variables, the direction of causality, and the nature of the relationship (linear, non-linear, etc). You can also use sensitivity analysis to determine how changes in one variable will affect the other variables. This will allow you to accurately predict how changes to one variable will affect the overall output of the model.

By clearly defining the relationships between the variables, you can ensure that your model is an accurate representation of the system you are trying to explain or predict. This will improve the accuracy of your predictions and help you identify the most sensitive variables in the system.

## Step 4: Analyzing Outputs

After performing a sensitivity analysis, you should examine and interpret the results to draw meaningful insights. Here are the steps that you should follow when analyzing the outputs of your model:

### Interpreting the results

The results of a sensitivity analysis will generally come in the form of a table or a chart. Each of these visualizations will provide a different set of information. Tables, in particular, are useful for understanding the impact of a given variable on model performance. Generally, tables will show the interactions among the different variables and their effects on model results.

Charts, on the other hand, are more useful for understanding trends and uncovering patterns in the data. Charts provide a graphical representation of the results, which can be used to understand the relationships among the different variables and how they influence the model. By analyzing the outputs from the sensitivity analysis, you can identify which variables are most important in determining model performance, as well as how those variables interact with each other.

### Examining the sensitivity of changes in the model

When interpreting the results of a sensitivity analysis, you should also look for insight into the sensitivity of changes in the model. If a variable has a high sensitivity, then even small changes in that variable can have significant impacts on the model results. Conversely, if a variable has a low sensitivity, then even large changes in that variable may have a minimal effect on model performance.

By examining the sensitivity of changes in the model, you can identify which variables have the greatest potential to cause instability or inaccuracy. This allows you to focus on those variables and make changes to the model accordingly.

## Step 5: Troubleshooting

Sensitivity analysis provides a useful tool to evaluate a model, seeking out potential points of failure, and potential areas for improvement. The final step of the process is to troubleshoot and make any necessary changes to the model based on the results of the analysis.

### Problem Solving

Interpreting the results of the sensitivity analysis is the first stage in problem solving. This involves looking at the areas that have been identified by the analysis as a source of unreliability and making an initial assessment of those findings.

This assessment should involve determining the degree of uncertainty in the area in question and assessing the impact that any potential error might have on the outcomes of the model. It is important to ensure that any weak points in the model have been successfully identified, as well as addressing any issues that have been identified in the process of sensitivity analysis.

### Making Adjustments to the Model

Once the issues have been isolated, the next step is to decide upon the appropriate adjustments to make to the model. This can involve making changes to the model itself, or making changes to any assumptions used in the model. It is important to consider the potential impact of any changes on the results of the sensitivity analysis, and to ensure that the model continues to accurately reflect the behaviour of the system being modelled.

In addition to making adjustments to the model, it is also important to test any changes before accepting them as valid. This involves running the sensitivity analysis multiple times, with the new assumptions in place, to ensure that the model continues to perform as expected. This can involve comparing the results of the sensitivity analysis with the original results in order to ensure that the model remains reliable.

## Conclusion

Sensitivity analysis is a valuable tool for any model user to understand the overall impact and potential outcomes of their changes or decisions. In this blog post, we outlined the seven main steps for using sensitivity analysis in your models.

### Summary of the Steps of Sensitivity Analysis

- 1. Identify the variables: Start by determining which variables you would like to analyze.
- 2. Determine the data ranges: Establish what data ranges you would like to analyze.
- 3. Estimate the parameters: Estimate the parameters (if necessary).
- 4. Create a baseline modeling scenario: Set a baseline modeling scenario with the current values of the variables.
- 5. Create the alternative scenarios: Make changes to the baseline model, keeping the rest of the inputs constant.
- 6. Model the results: Calculate the results for each of the alternative scenarios.
- 7. Visualize the data: Display the results in a visual format for easy comparison of the different scenarios.

### Benefits of Using Sensitivity Analysis in Your Models

The primary benefit of using sensitivity analysis in your models is to inform decisions or changes that are best suited for the desired outcomes with minimal risk. As outlined above, it also helps to clarify and visualize data and aid in understanding the complex relationships between input variables. Additionally, it can be used to discover and test unexplored ideas. For example, by running sensitivity analysis, you can find unexpected results or explore unknown interactions among parameters, which can help identify beneficial relationships that weren't previously considered.

Overall, sensitivity analysis is an invaluable tool for any model user and greatly enhances the overall value of the model. By following the steps outlined above, it is a great way to gain insights and make informed decisions which can ultimately improve productivity and efficiency.

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