Sensitivity Analysis, what it is and how it is applied

Sensitivity analysis is the set of mathematical techniques used to observe how changes in certain input variables to a model (which can be of any kind and refers to any field: economic, financial, physical, biological, social, ...) modify its output results. Put simply, we observe how asynchronous variations of individual variables influence the final results.
Although it may seem like a mathematical procedure far removed from everyday life, sensitivity analysis is something we experience all the time: when we change the dosage in a recipe to improve the end result, when we try to leave the house at different times to minimize the time it takes to get to work, when we reflect on a business decision by hypothesizing various options.

Key takeaways

• Sensitivity analysis calculates how asynchronous variations of individual variables affect the final results of a model.
• Sensitivity analysis is not limited to specific fields but is used in any situation where we want to investigate how the results of a phenomenon, process or solution change when its internal parameters vary.
• The benefits are manifold and concern understanding which factors most influence an outcome, assessing the robustness of a decision and enabling better risk management.

There is no large company or process with a significant amount of uncertainty that does not use sensitivity analyses to substantiate its choices and analyse its results. This is because the set of techniques (some of which are particularly immediate) has significantly beneficial implications in any field of application. These benefits include:
Understanding which factors most influence the final results of a process, particularly useful when the inputs are multiple and the relationships between them not explicit.
Assessing under what conditions a solution or choice remains beneficial.
Risk management, ergo the planning and management of uncertainty for processes and companies and how this affects their results.

Under the umbrella of sensitivity analysis fall a broad spectrum of analyses and methodologies, united by the purposes outlined above. Through these methods, it is possible not only to identify critical factors in a model, but also to improve understanding and confidence in the results produced. A (non-exhaustive) list follows:
One-at-a-Time Analysis (OAT): You vary one input at a time while holding all others constant and record the effects on the final result.
Analysis of Variance (ANOVA): A more sophisticated analysis that assesses the importance of each input and their interrelationships by decomposing the variance of the final result on the individual inputs.
Global Analysis: Instead of examining one input at a time, this methodology varies all inputs simultaneously within certain limits. The Monte Carlo method belongs to this type.
Sobol method: This is a type of global analysis that determines the significance of each input and their interactions through a decomposition of the variance of the final outputs.
Morris method: This method is a form of On-at-a-Time analysis, but with a systematic approach. Different options are selected across possible combinations of inputs to evaluate the effect of each variable.
Scenario Analysis: Rather than systematically varying inputs, in this methodology specific scenarios or combinations of inputs are studied to understand particular circumstances or outcomes. More commonly recognised as 'best-case - worst-case analysis'.

Evaluating a property for short-term rentals
Let us imagine that we own a property and use it for short-term rentals for tourism purposes (e.g. AirBnB). So we want to perform a series of analyses to understand how profitable such a property will be. The first step will be to calculate the turnover at the end of the year, given a number of assumptions, more or less true

• the number of days we manage to rent it out
• how many days fall in high, medium and low season
• the daily price for each of the above seasons
• ...

Having done this we can continue with a sensitivity analysis (one-at-a-time) to understand how the variation of these assumptions would change the turnover initially calculated. And understand which assumptions, if wrong (positively or negatively), would have the greatest effect on the final result.