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Statistica Sinica 12(2002), 311-335



Mary Sara McPeek

The University of Chicago

Abstract: The problem of error detection in general inbred and outbred pedigrees on the basis of genome screen data is considered. We develop a novel characterization of pairwise relationships, which is extended to $k$-wise relationships. Given an arbitrary pedigree specifying the relationship among a set of $k$ individuals, we show how to prune the pedigree so that no information on the genetic relationships is lost and yet no excess meioses remain. We take a likelihood-based approach to inference. Under the assumption of no interference, all the crossover processes in a pedigree can be viewed jointly as a continuous time Markov random walk on the vertices of a hypercube, so a hidden Markov method is a natural approach for likelihood calculation. One strategy to make likelihood calculation feasible is to use aspects of the pedigree structure to find the orbits of the group of symmetries on the hypercube that preserve the information of identity by descent. We describe strategies for accomplishing this for arbitrary pedigrees and give weak sufficient conditions under which the resulting chain has the minimum number of states needed to both contain all the information of the IBD process and to satisfy the Markov property under no interference.

Key words and phrases: Crossover process, HMM, IBD, Markov chain, misspecified relationship, pairwise relationship, pedigree error, pedigree graph, relationship estimation, relationship inference.

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