Description Usage Arguments Details Value Author(s) References See Also Examples
uncertMC
estimates measurement uncertainty from a function,
expression or formula by Monte Carlo simulation.
1 2 
expr 
An expression, function, or formula with no lefthand side (e.g.

x 
A named list or vector of parameters supplied to 
u 
A named list or named vector of length 
method 
Method of uncertainty evaluation. The only method currently supported
by 
df 
A named list or named vector of degrees of freedom. 
cor, cov 
Optional (square, symmetric) correlation or covariance matrices, respectively.
If neither is specified, 
distrib 
A character vector of length 
distrib.pars 
A named list of lists of parameters describing the distributions
associated with 
B 
Number of Monte Carlo replicates. 
keep.x 
If 
vectorized 
If 
... 
Additional parameters to be passed to a function (for the function method) or used in an expression (for expression or formula method). 
Although most likely to be called by uncert
, uncertMC
may be called directly.
If any of x
, u
, df
, distrib
or distrib.pars
are not lists,
they are coerced to lists. If x
is not named, arbitrary names of the form 'Xn'
are applied. If u
, df
, distrib
or distrib.pars
do not have
names, the names will be set to names(x)
if they are of length exactly
length(x)
; if not, an error is returned.
For Monte Carlo evaluation, distributions and distribution parameters are needed but
defaults are used if some or all are absent. If distrib
is missing, or
if it is a list with some members missing, the distribution is assumed Normal
and any missing member of distrib
is set to "norm".
Distributions are usually identified by the root of the distribution function name; for example
to specify the Normal, distrib$name="norm"
. At present, only the random value
generator (e.g. rnorm
) is used. Names of userspecified distributions functions can also be
used, provided they have a random value generator named r<dist>
where <dist>
is the abbreviated distribution. Parameters are passed to distribution functions using
do.call
, so the function must accept the parameters supplied in distrib.pars
.
If distrib.pars
or members of it are missing, an attempt is made to deduce
appropriate distribution parameters from x
, u
, df
and distrib
.
In doing so, the following assumptions and values apply for the respective distributions:
mean=x$name, sd=u$name
.
min=xsqrt(3)*u, max=x+sqrt(3)*u
.
min=xsqrt(6)*u, max=x+sqrt(6)*u, mode=x
.
df=df, mean=x, sd=u
.
If either cor
or cov
are present, a test is made to see if offdiagonal
elements are significant. If not, uncertMC
treats the values as independent.
The test simply checks whether the sum of offdiagonal elements of cor
(calculated
from cov
if cov
is present) is bigger than
.Machine.double.eps*nrow^2
.
Correlation is supported as long as all correlated variables are normally distributed.
If correlation is present, uncertMC
follows a twostage simulation procedure.
First, variables showing correlation are identified. Following a check that
their associated distrib
values are all "norm"
, mvrnorm
from
the MASS library is called to generate the simulated x
values for those variables.
Second, any remaining (i.e. independent) variables are simulated from their respective
distrib
and distrib.pars
.
Vectorisation makes a difference to execution speed. If vectorize=TRUE
, MC evaluation
uses eval
using the simulated data as the evaluation environment; if not, apply
is used rowwise on the simulated input matrix. This makes an appreciable difference to
execution speed (typically eval
is faster by a factor of 5 or more) so the default
assumes vectorised expressions. However, not all functions and expressions take vector arguments,
especially user functions involving complicated arithmetic or numerical solutions. Use vectorize=FALSE
for functions or expressions that do not take vector arguments.
Note: One common symptom of an expression that does not take vector arguments is
an R warning indicating that only the first element (typically of a parameter in x
) is used.
uncertMC may also return NA for u
on attempting to take the sd of a single simulated point.
An object of class uncertMC
. See uncertMCclass
for details.
S. L. R. Ellison s.ellison@lgc.co.uk
JCGM 100 (2008) Evaluation of measurement data  Guide to the expression of uncertainty in measurement. http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf. (JCGM 100:2008 is a public domain copy of ISO/IEC Guide to the expression of uncertainty in measurement (1995) ).
Kragten, J. (1994) Calculating standard deviations and confidence intervals with a universally applicable spreadsheet technique, Analyst, 119, 21612166.
Ellison, S. L. R. (2005) Including correlation effects in an improved spreadsheet calculation of combined standard uncertainties, Accred. Qual. Assur. 10, 338343.
uncert
, uncertclass
, uncertMCclass
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  expr < expression(a+b*2+c*3+d/2)
x < list(a=1, b=3, c=2, d=11)
u < lapply(x, function(x) x/10)
u.MC<uncertMC(expr, x, u, distrib=rep("norm", 4), method="MC")
print(u.MC, simplify=FALSE)
#An example with correlation
u.cor<diag(1,4)
u.cor[3,4]<u.cor[4,3]<0.5
u.formc.MC<uncertMC(~a+b*2+c*3+d/2, x, u, cor=u.cor, keep.x=TRUE)
u.formc.MC
#A nonlinear example
expr < expression(a/(bc))
x < list(a=1, b=3, c=2)
u < lapply(x, function(x) x/20)
set.seed(403)
u.invexpr<uncertMC(expr, x, u, distrib=rep("norm", 3), B=999, keep.x=TRUE )
u.invexpr
#Look at effect of vectorize
system.time(uncertMC(expr, x, u, distrib=rep("norm", 3), B=9999, keep.x=TRUE ))
system.time(uncertMC(expr, x, u, distrib=rep("norm", 3), B=9999, keep.x=TRUE, vectorize=FALSE))

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