Simulation Decomposition¶
A hybrid uncertainty-and-sensitivity visualization that partitions selected inputs into states, crosses those states into joint scenarios, and decomposes the sampled output distribution into scenario-labeled subdistributions.
Core Idea¶
Simulation Decomposition, usually abbreviated SimDec, is a named method for showing how joint states of selected inputs contribute to the full distribution of a model output. Starting from row-linked input and output values—usually generated by Monte Carlo simulation—the analyst partitions a few inputs into discrete states, forms every joint combination of those states, assigns each observation to exactly one scenario, and preserves those labels when plotting the output distribution. A stacked, scenario-colored histogram then shows not only how uncertain the output is but which regions of input space produced different parts of that uncertainty.
Scope of Application¶
The home scope is uncertainty analysis, global sensitivity analysis, simulation analytics, and decision support for computational models. Original applications addressed multivariable investment projects. Cross-domain work subsequently used the method in geology, business, and environmental science; a carbon-footprint study decomposed uncertainty in a wooden-pallet life-cycle case; independent engineering researchers applied it to a nondestructive-evaluation system and an agricultural food-water-energy model.
System-dynamics work uses SimDec to connect uncertain drivers to urban-planning outcomes, while a quantitative extension tests heterogeneous effects in several computational decision models.
Clarity¶
A record qualifies as Simulation Decomposition when six questions have clear answers:
- What is the row-linked ensemble? Identify the runs or records, selected inputs, output, sampling design, filters, and missing-data treatment. 2. Which inputs were selected, and why? State whether selection reflects sensitivity indices, decision control, scientific interest, or another rule. 3. How was each selected input partitioned? List interval boundaries or category mappings; “low” and “high” are insufficient without definitions.
Manages Complexity¶
A probability distribution communicates output range, central tendency, spread, skewness, and tails, but it hides which input combinations populate those regions. A sensitivity index can rank inputs but compresses the shape of their effects into numbers. Scatter plots expose pairwise relationships but become difficult when several uncertain inputs interact. SimDec keeps the output distribution familiar while overlaying a finite joint-state account.
Abstract Reasoning¶
Conservation inference. If the scenario states are mutually exclusive and exhaustive, each output observation contributes exactly once. Counts and empirical probabilities add across scenarios. A mismatch indicates boundary, filtering, missingness, or implementation error.
No-effect diagnostic. If an input's states have identical population-conditional output distributions under the design, changing that state does not alter the represented output law.
Knowledge Transfer¶
The method transfers literally wherever four data conditions remain intact: paired input-output records, defensible input states, enough coverage of joint scenarios, and an output representation capable of preserving scenario membership. A financial analyst can label simulated net-present-value outcomes by cost and demand states; an environmental analyst can label carbon-footprint outcomes by material and process states; an engineer can label reliability outcomes by load and material-property states. The application vocabulary changes, while row assignment, mixture recomposition, and interpretation remain identical.
Relationships to Other Abstractions¶
Current abstraction Simulation Decomposition Domain-specific
Parents (1) — more general patterns this builds on
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Simulation Decomposition is a kind of Decomposition Prime
Decomposition is the minimal live parent.
Hierarchy path (1) — routes to 1 parentless root
- Simulation Decomposition → Decomposition
Neighborhood in Abstraction Space¶
Simulation Decomposition sits in a sparse region of the domain-specific corpus (89th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (1565 abstractions)
Nearest neighbors
- Nonrecursive (FIR) Filter — 0.81
- Generalized Semi-Infinite Programming — 0.80
- Language of Temporal Ordering Specification — 0.79
- Particle Filter — 0.78
- Probability Bounds Analysis — 0.78
Computed from structural-signature embeddings · 2026-09-08