What to remember
- Define the decision and model before distributions.
- Justify each distribution with available evidence.
- Retain dependencies, units and iteration count.
- Read percentiles as conditional results.
Move from ranges to a probabilistic model
Assign a distribution suited to each uncertain variable, such as normal for justified symmetric variation, triangular for minimum, mode and maximum, or lognormal for positive skewed values.
Model material correlations. Assuming independence between variables that move together may understate risk.
Simulate and retain parameters
Each iteration draws a value for every variable and recalculates the model. Retain the distribution, mean and percentiles such as P5 and P95.
The audited code frame uses 10,000 iterations and displays mean, P5 and P95. This describes a local calculation and does not prove public runtime.
| Element | Retain | Risk if absent |
|---|---|---|
| Variable | Definition and unit | Double counting |
| Distribution | Shape and parameters | False precision |
| Dependency | Correlation or causality | Understated risk |
| Output | Mean and percentiles | Reading as forecast |
Read the distribution for the decision
The mean does not describe dispersion or skew. P5 and P95 bound the central 90% of ordered model draws; they are not a confidence interval for the real world.
Compare threshold risk, reserves, choice robustness and assumptions driving variance.
Keep the simulation reviewable
The editorial connection is to Plot for simulation and Atlas for the file, without promising an automated chain.
Retain model, distributions, sources, dependencies, date, outputs and events that require a new run.
Frequently asked questions
How many iterations are needed?
It depends on the required stability and model cost. Test convergence rather than using a habitual number.
Does Monte Carlo replace scenarios?
No. Scenarios organise coherent futures; Monte Carlo explores a quantified model.
Is P95 a guarantee?
No. It is conditional on selected distributions, dependencies and evidence.
Full sources
- GAO, Monte Carlo risk and uncertainty analysis, PDFComplete source available online · Read the complete source
- EPA, guiding principles for Monte Carlo analysis, PDFComplete source available online · Read the complete source
- Investment analysis under risk using Monte Carlo simulation, PDFComplete source available online · Read the complete source