Sobolindices

Sobol indices are a set of quantitative measures used in sensitivity analysis to determine the influence of input variables on the output of a mathematical model. They are based on the ANOVA (Analysis of Variance) decomposition of the model's output variance. Developed by Ivan Sobol, these indices provide a robust way to understand which input factors contribute most significantly to the uncertainty in a model's predictions.

There are two main types of Sobol indices: first-order and total-order. First-order indices measure the individual contribution of each input variable to the total variance of the model output, assuming all other variables are fixed. They represent the main effects of each input. Total-order indices, on the other hand, account for both the individual effect of an input variable and its interactions with all other input variables. These indices provide a more comprehensive understanding of an input's overall influence.

Calculating Sobol indices typically involves using Monte Carlo sampling methods. A large number of model runs are performed with carefully designed input parameter sets. The variance of the output is then partitioned, and the Sobol indices are estimated based on these results. These indices are particularly useful in complex systems where the relationships between inputs and outputs are non-linear and interdependent, allowing researchers and engineers to focus on the most influential parameters and simplify models or allocate resources more effectively.