beadarrayMSV (version 1.0.2)

findSeTheta: Scale pooled standard errors after polar transformation

Description

After polar transformation of Cartesian intensity values, the estimated standard errors are no longer useful. This function normalizes the standard errors depending on the polar intensity value

Usage

findSeTheta(pooledSE.raw, R, dist = "manhattan", pNorm = NULL)

Arguments

pooledSE.raw

Matrix of pooled standard errors of the Cartesian intensities A and B (see createAlleleSet)

R

Matrix of polar coordinates intensities

dist

Distance measure. See cart2pol

pNorm

Minkowski norm. See cart2pol

Value

• Matrix of transformed standard errors

Details

Usually called from within createAlleleSet. The standard errors of the Cartesian intensities A and B are not meaningful when the polar coordinates theta and intensity are plotted on Cartesian axes. In a plot of homoscedastic B vs. A (see transformChannels), the standard error of each bead-type is independent of the signal intensities. In a Cartesian plot of intensity vs. theta, however, bead-types with low intensity will have a large uncertainty, and the precision of the points will increase with increasing intensity. This is beacause the arc-length of the first quadrant semi-circle, which increases with the distance from origin, gets a constant value of unity as the polar coordinates are plotted on Cartesian axes. The pooled standard errors are therefore scaled with the intensity dependent arc-length of the semi-circle between 0 and 90 degrees. The arc-lengths by which the standard errors are scaled also depend on dist and pNorm. The circumference of a circle in Manhattan geometry, using a Euclidean metric, is 4*sqrt(2)*R, and the circumference of a Euclidean circle is 2*pi*R. It follows that the arc-lengths in the first quadrant only are sqrt(2)*R and pi*R/2, respectively. The more general arc-length of a Minkowski geometry circle is estimated by numerical integration along the the curve of the super-ellipse between 0 to 90 degrees.

References

L. Gidskehaug, M. Kent, B. Hayes, and S. Lien. Genotype calling and mapping of multisite variants using an Atlantic salmon iSelect SNP-array. Submitted

See Also

cart2pol, createAlleleSet

Examples

#A single standard error value for points of increasing intensity
R <- .1:10
pooledSE.raw <- 1
pooledSE.theta <- findSeTheta(pooledSE.raw=pooledSE.raw,R=R)
print(pooledSE.theta)