Monte Carlo estimation of identity by descent in populations
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Genetic similarity between organisms arises from segments of shared genome, which are said to be identical by descent (IBD). Modeling IBD in pedigrees forms the basis of classical linkage analysis and has been a fruitful method for inferring trait locations. We examine methods for modeling IBD in more general settings where relationships among subjects are not known completely. A natural approach is to use a hidden Markov model (HMM) based on a transition model for IBD along the chromosome, but the number of possible IBD states for more than a few individuals makes makes standard HMM calculations infeasible. We describe two broad approaches to sampling from this model. First, we decompose the group IBD model into a series of pairwise approximations which can be sampled efficiently. This decomposition permits other modifications to the model so that it can be used with unphased genotypes or incomplete pedigree information. Second, we implement a particle Gibbs sampling algorithm for the HMM, which is computationally intensive but targets the correct model. Both methods are compared against exact HMM sampling. The particle Gibbs method more accurately captures the true model distribution at the expense of increased computation time.
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