propagate (version 1.0-4)

mixCov: Mixing covariances matrices, raw data, summary data or error values into a single covariance matrix

Description

This function 'mixes' (aggregates) data from covariances matrices, raw and summary (mu, error) data or single error values into one final covariance matrix suitable for use in propagate.

Usage

mixCov(..., use = "everything", method = "pearson")

Arguments

...

either covariance matrices, raw data, summary data or error values to be aggregated into a single covariance matrix.

use

see cov.

method

see cov.

Value

The 'mixed' (aggregated) covariance matrix.

Details

'Mixes' (aggregates) data of the following types into a final covariance matrix: 1) matrix/dataframe \(\mathbf{A}\) of raw data with \(A_1, A_2, \ldots, A_m\) variables and at least two observations per variable. This will be transformed into a covariance matrix. 2) vectors of summary data of type c(mu, sigma). 3) covariance matrices \(\mathbf{V}\) that are already available. 4) single error values \(\sigma\).

This is accomplished by filling a \(m_1 + m_2 + \ldots + m_n\) sized square matrix \(\mathbf{C}\) succesively with elements \(1 \ldots m_1, m_1 + 1 \ldots m1 + m2, \ldots, m_n + 1 \ldots m_n + m_{n + 1}\) with either covariance matrices at \(C_{m_n + 1 \ldots m_n + m_{n + 1}, m_n + 1 \ldots m_n + m_{n + 1}}\) or single variance values on the diagonals at \(C_{m_n, m_n}\).

References

Evaluation of measurement data - Guide to the expression of uncertainty in measurement. JCGM 100:2008 (GUM 1995 with minor corrections). http://www.bipm.org/utils/common/documents/jcgm/JCGM_100_2008_E.pdf.

Evaluation of measurement data - Supplement 1 to the Guide to the expression of uncertainty in measurement - Propagation of distributions using a Monte Carlo Method. JCGM 101:2008. http://www.bipm.org/utils/common/documents/jcgm/JCGM_101_2008_E.pdf.

Examples

# NOT RUN {
#######################################################
## Example in Annex H.4 from the GUM 2008 manual
## (see 'References'), measurement of activity.
## This will give exactly the same values as Table H.8.
data(H.4)
attach(H.4)
T0 <- 60
lambda <- 1.25894E-4
Rx <- ((Cx - Cb)/60) * exp(lambda * tx)
Rs <- ((Cs - Cb)/60) * exp(lambda * ts)

mRx <- mean(Rx)
sRx <- sd(Rx)/sqrt(6)
mRx
sRx

mRs <- mean(Rs)
sRs <- sd(Rs)/sqrt(6)
mRs
sRs

R <- Rx/Rs
mR <- mean(R)
sR <- sd(R)/sqrt(6)
mR
sR

cor(Rx, Rs)

## Definition as in H.4.3.
As <- c(0.1368, 0.0018)
ms <- c(5.0192, 0.005)
mx <- c(5.0571, 0.001)

## We have to scale Rs/Rx by sqrt(6) to get the 
## corresponding covariances.
Rs <- Rs/sqrt(6)
Rx <- Rx/sqrt(6)

## Here we mix the raw data in matrix format 
## and the summary data of the variables.
COV <- mixCov(cbind(Rs, Rx), As, ms, mx)
COV

## Prepare the data for 'propagate'.
MEANS <- c(mRs, mRx, As[1], ms[1], mx[1])
SDS <- c(sRs, sRx, As[2], ms[2], mx[2])
DAT <- rbind(MEANS, SDS)
colnames(DAT) <- c("Rs", "Rx", "As", "ms", "mx")

## This will give exactly the same values as 
## in H.4.3/H.4.3.1.
EXPR <- expression(As * (ms/mx) * (Rx/Rs))
RES <- propagate(EXPR, data = DAT, type = "stat", 
                 use.cov = COV, do.sim = TRUE)

RES$prop
RES$sim
# }