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Uncertainty and Monte Carlo

2 tools in the Statistics area.

Uncertainty Propagation

The uncertainty of a computed result from the uncertainties of its inputs, two ways: the GUM law of propagation of uncertainty (JCGM 100, first-order Taylor expansion with sensitivity coefficients by numerical differentiation, an uncertainty budget, effective degrees of freedom by Welch–Satterthwaite, the coverage factor from the t distribution and the expanded uncertainty) and the Monte Carlo propagation of distributions (JCGM 101, each input drawn from its assigned distribution, the output's mean, standard deviation, probabilistically symmetric and shortest coverage intervals and histogram). The inputs may be normal, normal from a certificate's expanded uncertainty, rectangular, triangular, U-shaped, lognormal, Student t, PERT or constant, and may be correlated. The GUM interval is validated against the Monte Carlo one by the numerical-tolerance test of JCGM 101, which tells whether the first-order treatment is adequate for the model. Type the model in plain formula syntax using the input names; the default is the density of a cylinder from its mass, diameter and height.

3 worked examples reproduced, listed on the tool page.

Sensitivity Analysis

Which inputs of a model drive its result: a formula in plain syntax is swept over a variable table (base, low, high) for the one-at-a-time swings and the tornado diagram of Clemen and Reilly, the spider plot, the elasticity of the output to each input at the base case, a scenario table (base, best, worst, all low, all high and the analyst's own scenarios) and the break-even value of each input at which the output reaches a target. When the variables carry distributions a seeded Monte Carlo gives the global sensitivity: first-order and total Sobol' indices by the Saltelli (2010) estimators with bootstrap intervals, standardized regression coefficients with the R² of the linear fit, and Spearman rank correlations. The default case is the Eagle Airlines aircraft purchase of Clemen and Reilly (Making Hard Decisions, Chapter 5), whose base profit of $9,975, all-low and all-high profits and $4,200 money-market alternative the page reproduces; the Ishigami function and the Sobol' g-function with their analytic indices, a five-driver NPV model and the Goferbroke EMV line can be loaded from the example list.

4 worked examples reproduced, listed on the tool page.

Other Statistics sections

Descriptive and Outliers · Hypothesis Tests · Regression and Modelling · Distributions · Forecasting · Surveys and Sampling · Probability