Sampling distribution for microsatellites amplified by PCR: mean field approximation and its applications to genotyping

Due to microsatellite mutations during PCR, stutter patterns may appear in the final PCR product, which hinder us from accurate genotyping microsatellite markers. The existing methods for microsatellite stutter pattern deconvolution required large amount of data. A mathematical model for microsatellite mutations during PCR and an estimation method based on mean field approximation for branching processes have recently been developed. In this paper, we study the asymptotic behaviors for mean field approximation when experiments are started from a large number of molecules, and we derive an upper bound for the approximation error when experiments are started from a finite number of molecules. Based on the theories of mean field approximation and Bayesian statistics, we develop a novel method for microsatellite stutter pattern deconvolution.