Sobolindexen

Sobolindices, also known as Sobol sensitivity indices, are quantitative measures used in global sensitivity analysis to evaluate the contribution of input variables to the variance of a model's output. These indices help identify which parameters most significantly influence model behavior, thereby informing model simplification, uncertainty quantification, and decision-making processes.

The Sobol method decomposes a mathematical model into hierarchical terms based on variance contributions from individual inputs and their interactions. The primary types of Sobolindices include the first-order index, which measures the effect of a single input variable independently, and the total-order index, which captures the overall effect of an input, including its interactions with other variables. These indices are derived using variance-based techniques, often employing Monte Carlo simulations or quasi-Monte Carlo methods to estimate the sensitivity measures.

Sobolindices are particularly valuable in complex models where numerous inputs interact non-linearly or non-additively. They provide a comprehensive understanding of input importance and can highlight parameters that can be fixed or simplified without significantly affecting model accuracy. The indices are expressed as normalized values between 0 and 1, where higher values indicate greater influence on output variance.

The computation of Sobolindices assumes a model with probabilistic or uncertain inputs, often modeled as random variables with defined probability distributions. Software tools and frameworks implementing the Sobol method are widely available in sensitivity analysis and uncertainty quantification packages.

Overall, Sobolindices serve as essential tools for model analysis, fostering transparency and robustness in computational modeling across fields such as engineering, environmental science, finance, and systems biology.