Generalized Beta Convolution Model of the True Intensity for the Illumina Bead Arrays

Abstract

Microarray data, which come from many steps of production, have been known to contain noise. The pre-processing is implemented to reduce the noise, where the background is corrected. Prior to further analysis, many IlluminaBeadArrays users had applied the convolution model, a model which had been adapted from when it was first developed on the Affymetrix platform, to adjust the intensity value:  corrected background intensity value.

Several models based on the different underlying distributions and or the parameters estimation methods have been proposed and applied. For instance: the exponential-gamma, the normal-gamma, and the exponential-normal convolutions with maximum likelihood estimation, non-parametric, Bayesian and moment methods of the parameters estimation, including two recent exponential-lognormal and gamma-lognormal convolutions.

In this paper, we propose models and derive the corrected background intensity based on the generalized betas and the generalized beta-normal convolutions as a generalization of the existing models.