summary.propagate: Summary function for 'propagate' objects

In propagate: Propagation of Uncertainty

Summary function for 'propagate' objects

Description

Provides a printed summary of the results obtained by propagate, with many GUM (2008) and GUM Supplement 1 (2008) relevant statistics, as outlined in 'Details'.

Usage

## S3 method for class 'propagate'
summary(object, normality = FALSE, ...)

Arguments

object	an object returned from propagate.
normality	logical. If TRUE, the three repeated subsampling normality tests are performed. See 'Details'.
...	other parameters for future methods.

Details

summary.propagate provides an extensive output and overview on the results of propagate:

For classical JCGM 100:2008 output:

1. Results of the first- (mean.1, u.1) and second-order (mean.2, u.2) uncertainty propagation, as well as from MC simulation (mean.MC, u.MC, median.MC, mad.MC), including confidence intervals

2. The Welch-Satterthwaite degrees of freedom \mathrm{ws.df}, as obtained from WelchSatter

3. The coverage factor k = t_{\mathrm{ws.df}}(1-\alpha/2)

4. The expanded uncertainty U = k \cdot u, where u can be either first-order u.1 or second-order u.2, see propagate

5. The symbolic gradient matrix \nabla, also often termed \mathbf{G}, \mathbf{J} or \mathbf{C_x} (JCGM 102:2011)

6. The evaluated gradient matrix, also known as "sensitivities", c_i = \mathrm{eval}(\partial f / \partial x_i)

7. The relative contribution (summing up to 1)

   \mathrm{RC}_{ii} = \mathrm{diag}\left(\frac{|c_i \cdot c_j \cdot \Sigma_{ij}|}{\sum_{k,\ell} |c_k \cdot c_\ell \cdot \Sigma_{k\ell}|}\right)

8. The symbolic Hessian matrix \mathbf{H}, also often termed \nabla^2

9. The evaluated Hessian matrix h_{ij} = \mathrm{eval}\left(\frac{\partial^2 f}{\partial x_i \partial x_j}\right)

10. The input covariance matrix \mathbf{\Sigma}, as provided from (i) the uncertainies in the 2nd row of the input data, (ii) estimation from the raw data, or (iii) an externally supplied one. Also often termed \mathbf{V} or \mathbf{U_x} (JCGM 102:2011)
    
    For JCGM 101:2008, but extended with checks of input parameters for the Copula vs. the output attributes of the MC-generated random matrix \mathbf{X}^\text{MC}:

11. The covariance estimated from the MC simulations of the Copula distribution, \hat{\mathbf{\Sigma}}^\text{MC} = \mathrm{cov}(\mathbf{X}^\text{MC})

12. The Frobenius norm of the estimated vs. input covariance matrix, \|\hat{\mathbf{\Sigma}}^\text{MC} - \mathbf{\Sigma} \|_F

13. The correlation matrix \mathbf{R} derived from \mathbf{\Sigma} (by cov2cor) to construct the Gaussian Copula with t-margins, \mathcal{C}^{\text{Gauss, t}}

14. The correlation matrix estimated from the MC simulations of the Copula distribution, \hat{\mathbf{R}}^\text{MC} = \mathrm{cor}(\mathbf{X}^\text{MC})

15. The Frobenius norm of the estimated vs. input correlation matrix, \|\hat{\mathbf{R}}_\text{MC} - \mathbf{R} \|_F

16. A comparison of Copula-input and MC-derived moments/DOFs, to check for similarity and success of the Copula construction/MC sampling
    
    Further repeated subsampling tests for normality on the evaluated MC samples, Y = \mathbf{X}^\text{MC}:

17. Skewness and Excess Kurtosis

18. Shapiro-Wilk test (2000 repeats, 5000 samples)

19. Anderson-Darling test (1000 repeats, 10000 samples)

20. Lilliefors test (1000 repeats, 10000 samples) For the three tests, the median of the log p-values is calculated, as the resulting p-distribution is more or less log-normal, \mathrm{med}(P) = \mathrm{exp}(\mathrm{med}(\mathrm{log}(P))).

Value

A printed output with the items listed under 'Details'.

Author(s)

Andrej-Nikolai Spiess

References

See propagate

Examples

EXPR1 <- expression(x^2 * sin(y))
x <- c(5, 0.01)
y <- c(1, 0.01)
DF1 <- cbind(x, y)
RES1 <- propagate(expr = EXPR1, data = DF1, type = "stat", 
                  nsim = 10000, check = TRUE)
summary(RES1)

propagate documentation built on Feb. 25, 2026, 5:08 p.m.