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Simulation decomposition

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SimDec or Simulation decomposition is a hybrid uncertainty and sensitivity analysis method, for visually examining the relationships between the output and input variables of a computational model.


A typical SimDec output for a two-variables, three-levels case.

Approach

SimDec maps multivariable scenarios onto the probability distribution of the model output.[1] This visual analytics approach exposes the underlying nature of the model behavior, including its nonlinear and multivariate interaction effects.[2] SimDec is context-agnostic and can be used for business applications,[3] environmental issues,[4] [5] as well as in science, engineering, and social domains.

SimDec open-source packages are available in Python, R , Julia , and Matlab[6]

Method

SimDec operates on Monte Carlo simulation (or measured) data where both output and input values are recorded. At least one thousand observations (or simulated iterations) are generally recommended to preserve the readability of the resulting histograms. An outline of the decomposition algorithm, which is readily available in multiple programming languages,[6] proceeds as follows:

  1. Select the input variables for decomposition. One can use sensitivity indices (see variance-based sensitivity analysis) to define the most influential variables for decomposition or choose them manually according to the decision-problem context (for example, only those input variables that the decision-maker has the power to change). Two to three input variables, ordered by decreasing value of their sensitivity indices, usually provide the most meaningful decomposition results.
  2. Divide the inputs into states. The numeric ranges of the inputs are split into several intervals with an equal number of observations in each. For categorical variables, the categories represent states.
  3. Form scenarios. All combinations of states of the selected input variables produce unique scenarios or subsets of the data. For example, if the range of X2 is divided into low, medium and high, and X3 takes values of 1 or 2, six scenarios are formed:
    (i) X2 low & X3 = 1,
    (ii) X2 low & X3 = 2,
    (iii) X2 medium & X3 = 1,
    (iv) X2 medium & X3 = 2,
    (v) X2 high & X_3 = 1, and
    (vi) X2 high & X3 = 2.
  4. Assign scenarios to each output value. The simulation data is used to define the scenario index for each simulation run. For example, if an X2 value falls into the low state and X3 is equal to 2, the corresponding scenario, defined in Step 3, is (ii).
  5. Color-code the output distribution. When all output values are assigned scenario indices, they are plotted as series in a stacked histogram, visually separated by color-coding. For ease of visual perception, the states of the most influential input variable are assigned distinct colors, and all the remaining partitions take shades of those colors (see Figure).

All of these steps can be run automatically on the given data using the open-source SimDec packages currently available in Python, R, Julia, and Matlab . A SimDec template in Excel runs a Monte Carlo simulation of a spreadsheet model but possesses only a manual option for input selection.

References

  1. ^ Kozlova, M., & Yeomans, J. S. (2022). Monte Carlo Enhancement via Simulation Decomposition: A “Must-Have” Inclusion for Many Disciplines. INFORMS Transactions on Education, 22(3), 147-159.
  2. ^ Kozlova, M., Moss, R. J., Yeomans, J. S., & Caers, J. (forthcoming). Uncovering Heterogeneous Effects in Computational Models for Sustainable Decision-making. Available at http://dx.doi.org/10.2139/ssrn.4550911
  3. ^ Kozlova, M., Collan, M., & Luukka, P. (2017). Simulation decomposition: New approach for better simulation analysis of multi-variable investment projects.
  4. ^ Deviatkin, I., Kozlova, M., & Yeomans, J. S. (2021). Simulation decomposition for environmental sustainability: Enhanced decision-making in carbon footprint analysis. Socio-Economic Planning Sciences, 75, 100837.
  5. ^ Liu, Y. C., Leifsson, L., Pietrenko-Dabrowska, A., & Koziel, S. (2022). Analysis of Agricultural and Engineering Systems Using Simulation Decomposition. In International Conference on Computational Science (pp. 435-444). Springer, Cham.
  6. ^ a b See Simulation Decomposition https://github.com/Simulation-Decomposition


SimDec youtube channel https://www.youtube.com/@simdec SimDec website]

See also

Sensitivity analysis

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