summary.propagate: Summary function for 'propagate' objects

In propagate: Propagation of Uncertainty

Description

Provides a printed summary of the results obtained by propagate, such as statistics of the first/second-order uncertainty propagation, Monte Carlo simulation, the covariance matrix, symbolic as well as evaluated versions of the Gradient ("sensitivity") and Hessian matrices, relative contributions, the coverage factor and the Welch-Satterthwaite degrees of freedom. If do.sim = TRUE was set in propagate, skewness/kurtosis and Shapiro-Wilks/Kolmogorov-Smirnov tests for normality are calculated on the Monte-Carlo evaluations.

Usage

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

Arguments

object	an object returned from propagate.
...	other parameters for future methods.

Details

Calculates the "sensitivity"" S_i of each variable x_i to the propagated uncertainty, as defined in the Expression of the Uncertainty of Measurement in Calibration, Eqn 4.2, page 9 (see 'References'):

S_i = \mathrm{eval}≤ft(\frac{\partial f}{\partial x_i}\right)

The "contribution" matrix is then \mathbf{C} = \mathbf{SS}^T\mathbf{Σ}, where \mathbf{Σ} is the covariance matrix. In the implementation here, the "relative contribution" matrix \mathbf{C}_{\mathrm{rel}} is rescaled to sum up to 1.

Value

A printed output with the items listed in 'Description'.

Author(s)

Andrej-Nikolai Spiess

References

Expression of the Uncertainty of Measurement in Calibration.
European Cooperation for Accreditation (EA-4/02), 1999.

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", 
                  do.sim = TRUE, verbose = TRUE, nsim = 100000)
summary(RES1)

Example output

Loading required package: MASS
Loading required package: tmvtnorm
Loading required package: mvtnorm
Loading required package: Matrix
Loading required package: stats4
Loading required package: gmm
Loading required package: sandwich
Loading required package: Rcpp
Loading required package: ff
Loading required package: bit

Attaching package: ‘bit’

The following object is masked from ‘package:base’:

    xor

Attaching package ff
- getOption("fftempdir")=="/work/tmp/tmp/Rtmp63cdaR/ff"

- getOption("ffextension")=="ff"

- getOption("ffdrop")==TRUE

- getOption("fffinonexit")==TRUE

- getOption("ffpagesize")==65536

- getOption("ffcaching")=="mmnoflush"  -- consider "ffeachflush" if your system stalls on large writes

- getOption("ffbatchbytes")==16777216 -- consider a different value for tuning your system

- getOption("ffmaxbytes")==536870912 -- consider a different value for tuning your system


Attaching package: ‘ff’

The following objects are masked from ‘package:utils’:

    write.csv, write.csv2

The following objects are masked from ‘package:base’:

    is.factor, is.ordered

Loading required package: minpack.lm
Results from error propagation:
    Mean.1     Mean.2       sd.1       sd.2       2.5%      97.5% 
21.0367746 21.0358069  0.1591419  0.1591498 20.7238788 21.3477351 
Results from Monte Carlo simulation:
      Mean         sd     Median        MAD       2.5%      97.5% 
21.0348702  0.1588202 21.0356245  0.1584078 20.7213530 21.3437740 
Welch-Satterthwaite degrees of freedom:
[1] 1674903
Coverage factor (k):
[1] 1.959965
Expanded uncertainty:
[1] 0.3119281
Symbolic gradient matrix:
[1] "2 * x * sin(y)" "x^2 * cos(y)"  
Evaluated gradient matrix (sensitivity):
[1]  8.41471 13.50756
Symbolic hessian matrix:
[1] "2 * sin(y)"     "2 * x * cos(y)"
[1] "2 * x * cos(y)"  "-(x^2 * sin(y))"
Evaluated hessian matrix:
[1] 1.682942 5.403023
[1]   5.403023 -21.036775
Covariance matrix:
      x     y
x 1e-04 0e+00
y 0e+00 1e-04
Relative contribution:
         x        y
x 0.279582 0.000000
y 0.000000 0.720418
Skewness / Excess Kurtosis of MC evaluations:
-0.02459043 / -0.0097384 
Shapiro-Wilk test for normality: 
0.4819199 => normal
Kolmogorov-Smirnov test for normality: 
0.2681195 => normal

propagate documentation built on May 2, 2019, 5:39 a.m.