# findSeTheta: Scale pooled standard errors after polar transformation In beadarrayMSV: Analysis of Illumina BeadArray SNP data including MSV markers

## 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

 `1` ```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`

## 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.

## Value

Matrix of transformed standard errors

## Author(s)

Lars Gidskehaug

`cart2pol`, `createAlleleSet`
 ```1 2 3 4 5``` ```#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) ```