Counting methods (EM algorithm) in human pedigree analysis: linkage and segregation analysis.

The likelihood of human pedigree data can be written in such a form as to allow the computation of derivatives. This is done for various parameters in linkage and segregation analysis. The equations for the maximum likelihood estimates are represented in a particularly appealing form which allows iterative solutions. This process is an extension to pedigress of Smith's (1957) counting methods. All these procedures belong to a general class of MLE methods for incomplete data called EM algorithms (Dempster et al. 1976).