Global sensitivity analysis (GSA) is essential for understanding which input variables matter most in computational models. Yet many real-world models include interactions, dependencies, missing input combinations, and high dimensionality—conditions under which classic Sobol’ indices become difficult, inefficient, or even unsuitable.

A new 2025 study introduces a unified framework that combines a Simple Binning Algorithm (SBA) for computing global sensitivity indices with SimDec for visualizing multidimensional effects. Together, these methods provide an intuitive and computationally efficient way to analyse complex models, including those with dependent variables.

The paper demonstrates that SBA can dramatically reduce computational cost while SimDec reveals the shapes and nonlinear patterns that indices alone cannot capture.

Why SBA was needed

Traditional Sobol’ estimators require multiple simulation matrices and tens of thousands of model evaluations. The SBA follows the original conceptual idea of variance-based indices—bin the input, compute the average output per bin, and measure variance of these conditional means (Fig. 1 on page 2). It extends this method to:

• automated binning
• dependent inputs
• second-order effects
• categorical variables
• empirical datasets
• intermediate outputs in multi-level simulation models
  

This allows researchers to compute first-order, second-order, and combined indices using only one simulation matrix, greatly reducing computational load.

Demonstrated accuracy and efficiency

Across benchmark tests—including the portfolio model, Ishigami function, and mechanical engineering cases—the SBA matched or exceeded the accuracy of Sobol’ indices while using drastically fewer samples.

• For the portfolio model, SBA reproduced all key first- and second-order indices using 1,000 simulations, compared to 21,000 required by the Saltelli estimator (Table 2, page 5).
• In tests with quasi–Monte Carlo sampling, SBA produced cleaner and more stable estimates than both simple random sampling and full factorial designs (Fig. 4, page 6).
  

A large-scale experiment (Table 6, page 9) shows the minimum number of simulations required to maintain accuracy across models with 2 to 300 variables, providing practical guidelines for modelers.

Handling dependent variables and correlation

Unlike many classic GSA methods, SBA naturally handles dependent inputs without data transformation.
In the engineering model (Tables 4–5, pages 8–9), dependence between geometric variables produced:

• strong negative second-order effects
• corrected first-order contributions
• realistic changes in variance explained
  

Section 4 demonstrates how second-order indices respond to different types and strengths of correlation, showing both overlapping effects and synergistic behaviour (Fig. 9, page 12).

Why visualization matters: The role of SimDec

Sensitivity indices reveal how strong an effect is—but they cannot show what its shape looks like. The paper provides several examples where identical second-order amplitudes hide completely different interaction structures, visible only through visualization.

SimDec overcomes this limitation by:

• partitioning output distributions into regions formed by combinations of influential input states
• applying a colour-coded decomposition
• exposing nonlinearities, flips in effect direction, and heterogeneous interactions
  

The structural reliability 4R model (Fig. 11, page 14) showcases this clearly: residual stress, stress ratio, and steel grade interact in ways that are invisible from sensitivity indices alone but fully revealed in the decomposed output distribution.

A new standard for sensitivity analysis workflows

The SBA + SimDec framework offers a practical, intuitive, and computationally efficient alternative to traditional GSA. It enables:

• rapid identification of influential variables
• detection of correlations and interactions
• visualization of multidimensional effects
• use of empirical datasets
• robustness across business, engineering, and environmental models

The workflow is fully open-source, with implementations in Python, R, Julia, and MATLAB.

Reference

Kozlova, M., Ahola, A., Roy, P., & Yeomans, J. S. (2025). Simple Binning Algorithm and SimDec Visualization for Comprehensive Sensitivity Analysis of Complex Computational Models. Journal of Environmental Informatics Letters, 13(1), 38–56. https://doi.org/10.3808/jeil.202400149

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