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errors: Uncertainty Propagation for R Vectors

Source: R/errors.R
errors-package.Rd

Support for measurement errors in R vectors, matrices and arrays: automatic uncertainty propagation and reporting.

Details

Every measurement has an unknown error associated. Uncertainty is the acknowledgement of that error: we are aware that our representation of reality may differ from reality itself. This package provides support for measurement errors in R vectors, matrices and arrays. Uncertainty metadata is associated to quantity values (see errors), and this uncertainty is automatically propagated when you operate with errors objects (see groupGeneric.errors), or with errors and numeric objects (then numeric values are automatically coerced to errors objects with no uncertainty).

Correlations between measurements are also supported. In particular, any operation (e.g., z <- x + y) results in a correlation between output and input variables (i.e., z is correlated to x and y, even if there was no correlation between x and y). And in general, the user can establish correlations between any pair of variables (see correl).

This package treats uncertainty as coming from Gaussian and linear sources (note that, even for non-Gaussian non-linear sources, this is a reasonable assumption for averages of many measurements), and propagates them using the first-order Taylor series method for propagation of uncertainty. Although the above assumptions are valid in a wide range of applications in science and engineering, the practitioner should evaluate whether they apply for each particular case.

References

Iñaki Ucar, Edzer Pebesma and Arturo Azcorra (2018). Measurement Errors in R. The R Journal, 10(2), 549-557. doi:10.32614/RJ-2018-075

See also

datasets for a description of the datasets used in the examples below.

Author

Iñaki Ucar

Examples

## Simultaneous resistance and reactance measurements

# Obtain mean values and uncertainty from measured values
V   <- mean(set_errors(GUM.H.2$V))
I   <- mean(set_errors(GUM.H.2$I))
phi <- mean(set_errors(GUM.H.2$phi))

# Set correlations between variables
correl(V, I)   <- with(GUM.H.2, cor(V, I))
correl(V, phi) <- with(GUM.H.2, cor(V, phi))
correl(I, phi) <- with(GUM.H.2, cor(I, phi))

# Computation of resistance, reactance and impedance values
(R <- (V / I) * cos(phi))
#> 127.73(7)
(X <- (V / I) * sin(phi))
#> 219.8(3)
(Z <- (V / I))
#> 254.3(2)

# Correlations between derived quantities
correl(R, X)
#> [1] -0.5884298
correl(R, Z)
#> [1] -0.4852592
correl(X, Z)
#> [1] 0.9925116

## Calibration of a thermometer

# Least-squares fit for a reference temperature of 20 degC
fit <- lm(bk ~ I(tk - 20), data = GUM.H.3)

# Extract coefficients and set correlation using the covariance matrix
y1 <- set_errors(coef(fit)[1], sqrt(vcov(fit)[1, 1]))
y2 <- set_errors(coef(fit)[2], sqrt(vcov(fit)[2, 2]))
covar(y1, y2) <- vcov(fit)[1, 2]

# Predicted correction for 30 degC
(b.30 <- y1 + y2 * set_errors(30 - 20))
#> -0.149(4)