A Graphical Modelling Approach to Complex Applications in Genetics

Analyses of genetic data on groups of related individuals, or pedigrees, frequently require the calculation of probabilities and likelihoods. Exact computational methods such as peeling (Cannings et al. 1978) are intractable either when the pedigree or the genetic model under consideration is too complex. The fact that a pedigree can be represented as a graph naturally leads to an exploitation of graphical models (Lauritzen 1996) for these applications in genetics. The idea behind these models is to reduce a complex problem into small manageable components, thereby facilitating understanding of the computational issues involved and informing the devel-opment of more efficient algorithms. In particular, under the usual assumptions of the genetic model, a pedigree problem can be represented as a directed acyclic graph for which the local Markov property (Lauritzen et al. 1990) is satisfied. Such structures are some-times called Bayesian Networks (Jensen 1996). Algorithms for performing calculations on general Bayesian networks which fully exploit all the conditional independence struc-tures of the problem (e. g. Lauritzen & Spiegelhalter, 1988) can then be applied. These algorithms are essentially the same as the peeling method but are a little more efficien