Simulation Decomposition (SimDec) is a next-generation approach to global sensitivity analysis — a way to understand how and why model results change when inputs vary.

Instead of reporting only numeric sensitivity indices, SimDec transforms them into visual, interpretable decompositions that expose which factors drive outcomes, how they interact, and when those effects reverse or overlap .Traditional sensitivity analysis often ends with a ranking of inputs.

SimDec goes further: by decomposing simulation results into scenarios based on influential input combinations, it reveals the shape of interactions and actionable patterns inside complex models.

The SimDec Algorithm

At its core, SimDec maps multivariable scenarios onto the model’s output distribution. This produces a stacked histogram (or box plot) where each colour corresponds to a specific state of input variables.

The graph itself is the analysis — it shows which factors shift the output most strongly and which only matter in certain conditions

The method has two main components:

• Sensitivity indices calculation

  Uses a variance-based “simple binning” approach (Kozlova et al., 2025) to compute first-order, second-order, and combined effects.
  This binning approach maintains high accuracy even for small data sets, handles dependent variables, and works with a given data

  • First-order → individual influence of an input.
  • Second-order → interaction between inputs.
  • Combined → total effect of each input (Shapley allocation rule: individual effect + halved interaction)

• Decomposition

  • Selects the most influential variables (until cumulative importance exceeds a set threshold, e.g. 70%).
  • Splits each variable’s range into states (typically 2 or 3). For categorical variables each value is a state.
  • Forms all possible state combinations → “scenarios.”
  • Maps every simulation run to its scenario.
  • Cerates a decomposed visual: either a stacked histogram where series are scenarios or a box plot with boxes as scenarios.
  • Primary colours mark the states of the dominant variable; shades show further subdivisions.

The result is a stacked histogram or a box plot that visually explains the sources of variability in Y — clear, self-explanatory, and directly linked to decision questions.

Tests of the 'simple binning' method for variance-based sensitivity indices are conducted in:

• Kozlova, M., Ahola, A., Roy, P. T., & 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.

Details on the entire algorithm & cases in our book:

• Kozlova, M., & Yeomans, J. S. (Eds.). (2024). Sensitivity analysis for business, technology, and policymaking: Made easy with Simulation Decomposition (SimDec) (402 pages). Taylor & Francis. Open Access

Software and Open-Source Ecosystem

SimDec is fully open-source and available across multiple environments. Our GitHub Organization.

• No-code dashboard at simdec.io
  
• Python (pip install simdec), see documentation at simdec.readthedocs.io
  
• R – functions sensitivity_indices() and simdec_visualization() for automatic decomposition
  
• Matlab – two main functions: sensitivity_indices.m and simdec_visualization.m
• Julia – manual decomposition example, no sensitivity indices
• Excel – manual decomposition, no sensitivity indices

Good Practices for Using SimDec

Extensive experimentation suggest these guidelines, which, however, can be ignored in the spirit of exploration.

• Sampling – Use simple or quasi-random sampling. At least 1 000 data points (10 000 preferred for smooth visuals).
  
• Variable selection for decomposition – Let sensitivity indices pick the most influential inputs, unless domain knowledge or decision context dictates otherwise.
  
• State formation – Default equal-frequency states are safest to avoid visual distortion; adjust only for explicit decision thresholds.
  
• Visualization type – Stacked histograms first to see the shape of the distribution; switch to box plots if some scenarios have too little data or the distribution is too skewed.

How to Interpret SimDec

SimDec combines quantitative sensitivity indices with a visual decomposition that shows how inputs shape model outcomes.
The sensitivity indices measure how much of the output’s variability each input explains. An index of 0.6, for example, means that that input alone 60% of output variance is explained. Second-order indices will be positive if input variables interact, and negative if they are dependent.
When the sum of all indices approaches one, the selected inputs capture nearly all variability; deviations hint at higher order effects, or highly skewed distributions, or other model complexities. The method is numerical and smaller deviations can be attributed to simulation noise.

Interpreting SimDec means reading both its numbers and its shapes.Indices show how much each factor matters; the visual decomposition reveals how and why—turning sensitivity analysis into an accessible map of model behaviour.

More on non-linear non-monotonic effects in our publication:

• Kozlova, M., Moss, R. J., Yeomans, J. S., & Caers, J. (2024). Uncovering heterogeneous effects in computational models for sustainable decision-making. Environmental Modelling & Software, 171, 105898. Open Access