Monte Carlo evaluation of uncertainty (GUM Supplement 1)
Instead of propagating standard uncertainties analytically, sample every input from its distribution, compute the result many times, and read the interval off the output histogram.
JCGM 101 describes the propagation of distributions by Monte Carlo. Each input quantity is assigned a probability distribution; a large number of trials (10⁵–10⁶) draws a value from each distribution, evaluates the model, and stores the result. The distribution of results yields the best estimate, its standard uncertainty and a coverage interval at the desired probability.
When it is worth it
- A dominant rectangular component, where the output is not normal.
- Non-linear models such as humidity from dew point, or MKT from a temperature series.
- Asymmetric inputs, e.g. a truncating display or one-sided limits.
- Validating an analytical budget: if the GUM result and the Monte Carlo interval agree, the linear approximation holds.
The method demands the same care in defining inputs; garbage distributions produce a precise-looking garbage interval.
Frequently asked questions
- Can Monte Carlo be done in a spreadsheet?
- Yes for simple models, with a random-number function and a few thousand rows. Dedicated tools are more convenient for large trial counts and reproducibility.
References
- [1]JCGM 101:2008 — Supplement 1 to the GUM: Propagation of distributions using a Monte Carlo method
General technical guidance written against the cited sources. It is not regulatory or legal advice and does not replace the applicable standard, guideline or a qualified reviewer's judgement.
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Combine Type A and Type B components per the GUM: divisors by distribution, sensitivity coefficients, u_c, effective degrees of freedom and U at k = 2.
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